Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [124,6,Mod(33,124)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(124, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("124.33");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 124 = 2^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 124.f (of order \(5\), degree \(4\), 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: | \(19.8875936568\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Character | \(\chi\) | \(=\) | 124.109 |
Dual form | 124.6.f.a.33.2 |
$q$-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 \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).
\(n\) | \(63\) | \(65\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −21.3000 | − | 15.4753i | −1.36639 | − | 0.992743i | −0.998009 | − | 0.0630696i | \(-0.979911\pi\) |
−0.368385 | − | 0.929674i | \(-0.620089\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 92.0001 | 1.64575 | 0.822874 | − | 0.568224i | \(-0.192369\pi\) | ||||
0.822874 | + | 0.568224i | \(0.192369\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 26.8893 | − | 82.7567i | 0.207412 | − | 0.638349i | −0.792194 | − | 0.610270i | \(-0.791061\pi\) |
0.999606 | − | 0.0280791i | \(-0.00893904\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 139.112 | + | 428.142i | 0.572476 | + | 1.76190i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −196.836 | + | 605.799i | −0.490482 | + | 1.50955i | 0.333400 | + | 0.942785i | \(0.391804\pi\) |
−0.823882 | + | 0.566762i | \(0.808196\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 225.634 | + | 163.933i | 0.370293 | + | 0.269034i | 0.757333 | − | 0.653029i | \(-0.226502\pi\) |
−0.387039 | + | 0.922063i | \(0.626502\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1959.60 | − | 1423.73i | −2.24874 | − | 1.63380i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 382.219 | + | 1176.35i | 0.320767 | + | 0.987219i | 0.973315 | + | 0.229472i | \(0.0737000\pi\) |
−0.652548 | + | 0.757747i | \(0.726300\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1587.34 | − | 1153.27i | 1.00876 | − | 0.732904i | 0.0448077 | − | 0.998996i | \(-0.485732\pi\) |
0.963948 | + | 0.266092i | \(0.0857325\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1853.43 | + | 1346.60i | −0.917123 | + | 0.666329i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 726.521 | + | 2236.00i | 0.286371 | + | 0.881358i | 0.985984 | + | 0.166837i | \(0.0533554\pi\) |
−0.699614 | + | 0.714521i | \(0.746645\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5339.02 | 1.70849 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1685.54 | − | 5187.57i | 0.444970 | − | 1.36948i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3261.85 | − | 2369.87i | 0.720227 | − | 0.523275i | −0.166230 | − | 0.986087i | \(-0.553159\pi\) |
0.886457 | + | 0.462812i | \(0.153159\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 851.215 | − | 5282.48i | 0.159087 | − | 0.987265i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13567.5 | − | 9857.39i | 2.16878 | − | 1.57571i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2473.82 | − | 7613.63i | 0.341348 | − | 1.05056i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3614.50 | 0.434054 | 0.217027 | − | 0.976166i | \(-0.430364\pi\) | ||||
0.217027 | + | 0.976166i | \(0.430364\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2269.08 | − | 6983.52i | −0.238885 | − | 0.735213i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6762.45 | + | 4913.21i | −0.628267 | + | 0.456463i | −0.855800 | − | 0.517308i | \(-0.826934\pi\) |
0.227532 | + | 0.973771i | \(0.426934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6386.36 | − | 4639.96i | 0.526723 | − | 0.382686i | −0.292408 | − | 0.956294i | \(-0.594456\pi\) |
0.819130 | + | 0.573607i | \(0.194456\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12798.3 | + | 39389.1i | 0.942151 | + | 2.89964i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12861.0 | − | 9344.07i | −0.849240 | − | 0.617009i | 0.0756961 | − | 0.997131i | \(-0.475882\pi\) |
−0.924936 | + | 0.380122i | \(0.875882\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7471.51 | + | 5428.37i | 0.444547 | + | 0.322982i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10063.1 | − | 30971.1i | 0.541761 | − | 1.66737i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5266.64 | + | 16209.1i | 0.257540 | + | 0.792625i | 0.993319 | + | 0.115404i | \(0.0368162\pi\) |
−0.735779 | + | 0.677222i | \(0.763184\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18108.9 | + | 55733.5i | −0.807209 | + | 2.48433i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −51657.5 | −2.10594 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −19214.1 | − | 13959.9i | −0.718606 | − | 0.522098i | 0.167333 | − | 0.985900i | \(-0.446485\pi\) |
−0.885938 | + | 0.463803i | \(0.846485\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −746.505 | −0.0256867 | −0.0128433 | − | 0.999918i | \(-0.504088\pi\) | ||||
−0.0128433 | + | 0.999918i | \(0.504088\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 39172.2 | 1.24345 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 20758.3 | + | 15081.8i | 0.609410 | + | 0.442762i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 52388.5 | 1.42577 | 0.712884 | − | 0.701282i | \(-0.247389\pi\) | ||||
0.712884 | + | 0.701282i | \(0.247389\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19128.0 | − | 58869.9i | 0.483667 | − | 1.48858i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2993.42 | − | 9212.79i | −0.0704727 | − | 0.216893i | 0.909617 | − | 0.415448i | \(-0.136375\pi\) |
−0.980090 | + | 0.198555i | \(0.936375\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 22224.9 | − | 68401.1i | 0.488126 | − | 1.50230i | −0.339276 | − | 0.940687i | \(-0.610182\pi\) |
0.827402 | − | 0.561610i | \(-0.189818\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −113721. | − | 82623.1i | −2.33446 | − | 1.69609i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 44841.1 | + | 32579.0i | 0.861886 | + | 0.626197i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 23898.1 | + | 73550.7i | 0.430819 | + | 1.32592i | 0.897311 | + | 0.441399i | \(0.145518\pi\) |
−0.466492 | + | 0.884526i | \(0.654482\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −27681.1 | + | 20111.5i | −0.468783 | + | 0.340591i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −87903.8 | + | 63865.8i | −1.40059 | + | 1.01759i | −0.405987 | + | 0.913879i | \(0.633072\pi\) |
−0.994607 | + | 0.103713i | \(0.966928\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 35164.2 | + | 108224.i | 0.527902 | + | 1.62471i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −106152. | −1.50359 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 42405.2 | − | 130510.i | 0.567471 | − | 1.74650i | −0.0930219 | − | 0.995664i | \(-0.529653\pi\) |
0.660493 | − | 0.750832i | \(-0.270347\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19633.7 | − | 14264.7i | 0.248541 | − | 0.180576i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −99879.0 | + | 99343.8i | −1.19748 | + | 1.19106i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 146035. | − | 106101.i | 1.66016 | − | 1.20617i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −25537.7 | + | 78596.9i | −0.275583 | + | 0.848157i | 0.713482 | + | 0.700674i | \(0.247117\pi\) |
−0.989065 | + | 0.147483i | \(0.952883\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −286750. | −2.94046 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −39449.7 | − | 121414.i | −0.384805 | − | 1.18431i | −0.936622 | − | 0.350342i | \(-0.886065\pi\) |
0.551817 | − | 0.833965i | \(-0.313935\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 151684. | − | 110205.i | 1.40879 | − | 1.02354i | 0.415290 | − | 0.909689i | \(-0.363680\pi\) |
0.993497 | − | 0.113855i | \(-0.0363199\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −170516. | + | 123887.i | −1.50935 | + | 1.09661i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 59717.1 | + | 183790.i | 0.504242 | + | 1.55190i | 0.802041 | + | 0.597269i | \(0.203747\pi\) |
−0.297799 | + | 0.954628i | \(0.596253\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −35378.8 | − | 25704.2i | −0.285218 | − | 0.207223i | 0.435972 | − | 0.899960i | \(-0.356405\pi\) |
−0.721190 | + | 0.692737i | \(0.756405\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −76988.7 | − | 55935.5i | −0.593088 | − | 0.430904i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −60304.0 | + | 185597.i | −0.444273 | + | 1.36733i | 0.439006 | + | 0.898484i | \(0.355331\pi\) |
−0.883279 | + | 0.468847i | \(0.844669\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 66840.0 | + | 205712.i | 0.471294 | + | 1.45049i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −38798.1 | + | 119408.i | −0.262027 | + | 0.806435i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 107628. | 0.696722 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −197955. | − | 143823.i | −1.22914 | − | 0.893025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 220074. | 1.31161 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 203690. | 1.16599 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 133806. | + | 97215.9i | 0.736151 | + | 0.534845i | 0.891503 | − | 0.453014i | \(-0.149651\pi\) |
−0.155352 | + | 0.987859i | \(0.549651\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −207834. | −1.09962 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −928.745 | + | 2858.38i | −0.00472845 | + | 0.0145527i | −0.953393 | − | 0.301732i | \(-0.902435\pi\) |
0.948664 | + | 0.316284i | \(0.102435\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −52758.4 | − | 162374.i | −0.258620 | − | 0.795951i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 155070. | − | 477257.i | 0.732309 | − | 2.25381i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 247431. | + | 179769.i | 1.12630 | + | 0.818301i | 0.985151 | − | 0.171688i | \(-0.0549220\pi\) |
0.141144 | + | 0.989989i | \(0.454922\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −260998. | − | 189626.i | −1.14578 | − | 0.832455i | −0.157862 | − | 0.987461i | \(-0.550460\pi\) |
−0.987913 | + | 0.155006i | \(0.950460\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 129337. | + | 398057.i | 0.547865 | + | 1.68616i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −143723. | + | 104421.i | −0.587741 | + | 0.427019i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 300091. | − | 218029.i | 1.18531 | − | 0.861179i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −75137.1 | − | 231248.i | −0.286788 | − | 0.882642i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 81148.0 | 0.299442 | 0.149721 | − | 0.988728i | \(-0.452163\pi\) | ||||
0.149721 | + | 0.988728i | \(0.452163\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 84746.8 | − | 260824.i | 0.302469 | − | 0.930904i | −0.678140 | − | 0.734932i | \(-0.737214\pi\) |
0.980610 | − | 0.195972i | \(-0.0627861\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −450472. | + | 327287.i | −1.55575 | + | 1.13032i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 78311.8 | − | 485989.i | 0.261817 | − | 1.62479i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −285793. | + | 207641.i | −0.925342 | + | 0.672300i | −0.944848 | − | 0.327510i | \(-0.893791\pi\) |
0.0195060 | + | 0.999810i | \(0.493791\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 138661. | − | 426755.i | 0.434973 | − | 1.33871i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 204580. | 0.622011 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5140.88 | − | 15822.0i | −0.0151554 | − | 0.0466436i | 0.943193 | − | 0.332246i | \(-0.107806\pi\) |
−0.958348 | + | 0.285602i | \(0.907806\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.24821e6 | − | 906881.i | 3.56927 | − | 2.59323i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −335277. | + | 243593.i | −0.930279 | + | 0.675887i | −0.946061 | − | 0.323988i | \(-0.894976\pi\) |
0.0157823 | + | 0.999875i | \(0.494976\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −90699.1 | − | 279143.i | −0.244279 | − | 0.751814i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 714580. | + | 519173.i | 1.86879 | + | 1.35776i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 316373. | + | 229858.i | 0.803681 | + | 0.583908i | 0.911992 | − | 0.410209i | \(-0.134544\pi\) |
−0.108311 | + | 0.994117i | \(0.534544\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 143562. | − | 441840.i | 0.354361 | − | 1.09061i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 193226. | + | 594690.i | 0.463589 | + | 1.42678i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −211623. | + | 651310.i | −0.493664 | + | 1.51934i | 0.325366 | + | 0.945588i | \(0.394513\pi\) |
−0.819029 | + | 0.573752i | \(0.805487\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 160308. | 0.363712 | 0.181856 | − | 0.983325i | \(-0.441789\pi\) | ||||
0.181856 | + | 0.983325i | \(0.441789\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15900.5 | + | 11552.4i | 0.0350981 | + | 0.0255003i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 332534. | 0.714343 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −787865. | −1.64758 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −383984. | − | 278980.i | −0.781912 | − | 0.568093i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 425784. | 0.844512 | 0.422256 | − | 0.906477i | \(-0.361238\pi\) | ||||
0.422256 | + | 0.906477i | \(0.361238\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23069.6 | + | 71001.0i | −0.0445807 | + | 0.137205i | −0.970869 | − | 0.239609i | \(-0.922981\pi\) |
0.926289 | + | 0.376815i | \(0.122981\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −208756. | − | 642485.i | −0.393144 | − | 1.20997i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −58729.3 | + | 180750.i | −0.107818 | + | 0.331828i | −0.990381 | − | 0.138364i | \(-0.955816\pi\) |
0.882564 | + | 0.470193i | \(0.155816\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 493567. | + | 358597.i | 0.883513 | + | 0.641910i | 0.934179 | − | 0.356806i | \(-0.116134\pi\) |
−0.0506653 | + | 0.998716i | \(0.516134\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.11587e6 | − | 810729.i | −1.94816 | − | 1.41542i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −108414. | − | 333664.i | −0.184649 | − | 0.568290i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −622146. | + | 452016.i | −1.03397 | + | 0.751223i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −856258. | + | 622108.i | −1.38892 | + | 1.00911i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 386204. | + | 1.18861e6i | 0.611577 | + | 1.88224i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 433626. | 0.670515 | 0.335258 | − | 0.942126i | \(-0.391177\pi\) | ||||
0.335258 | + | 0.942126i | \(0.391177\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −78811.3 | + | 242556.i | −0.119025 | + | 0.366322i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 587545. | − | 426877.i | 0.866852 | − | 0.629805i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −414272. | − | 212486.i | −0.597223 | − | 0.306324i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.53192e6 | + | 1.11300e6i | −2.15837 | + | 1.56815i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −106600. | + | 328082.i | −0.146818 | + | 0.451858i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 403593. | 0.543478 | 0.271739 | − | 0.962371i | \(-0.412401\pi\) | ||||
0.271739 | + | 0.962371i | \(0.412401\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 742719. | + | 2.28585e6i | 0.978067 | + | 3.01018i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 475055. | − | 345147.i | 0.611898 | − | 0.444570i | −0.238184 | − | 0.971220i | \(-0.576552\pi\) |
0.850082 | + | 0.526650i | \(0.176552\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −930234. | + | 675854.i | −1.17220 | + | 0.851657i | −0.991271 | − | 0.131839i | \(-0.957912\pi\) |
−0.180933 | + | 0.983495i | \(0.557912\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −450944. | − | 1.38786e6i | −0.556023 | − | 1.71126i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −703630. | − | 511217.i | −0.849092 | − | 0.616901i | 0.0758036 | − | 0.997123i | \(-0.475848\pi\) |
−0.924896 | + | 0.380221i | \(0.875848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.18321e6 | − | 859656.i | −1.39764 | − | 1.01544i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 629193. | − | 1.93646e6i | 0.727634 | − | 2.23943i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 235545. | + | 724932.i | 0.266734 | + | 0.820923i | 0.991289 | + | 0.131706i | \(0.0420454\pi\) |
−0.724555 | + | 0.689217i | \(0.757955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 502696. | − | 1.54714e6i | 0.557523 | − | 1.71588i | −0.131662 | − | 0.991295i | \(-0.542031\pi\) |
0.689185 | − | 0.724585i | \(-0.257969\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −424612. | −0.461293 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 687379. | + | 499410.i | 0.731613 | + | 0.531548i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 547216. | 0.570711 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.86069e6 | 2.92397 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.11268e6 | − | 808410.i | −1.11477 | − | 0.809930i | −0.131364 | − | 0.991334i | \(-0.541936\pi\) |
−0.983409 | + | 0.181404i | \(0.941936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.49757e6 | −1.47091 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 925809. | − | 2.84935e6i | 0.891602 | − | 2.74407i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −172755. | − | 531684.i | −0.163154 | − | 0.502135i | 0.835742 | − | 0.549122i | \(-0.185038\pi\) |
−0.998895 | + | 0.0469874i | \(0.985038\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 97191.3 | − | 299124.i | 0.0900280 | − | 0.277078i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.46840e6 | + | 1.06686e6i | 1.33427 | + | 0.969405i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −485571. | − | 352788.i | −0.432876 | − | 0.314503i | 0.349922 | − | 0.936779i | \(-0.386208\pi\) |
−0.782798 | + | 0.622276i | \(0.786208\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 484531. | + | 1.49123e6i | 0.423845 | + | 1.30446i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.92291e6 | + | 2.12362e6i | −2.50921 | + | 1.82305i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.29546e6 | + | 941209.i | −1.09155 | + | 0.793059i | −0.979661 | − | 0.200661i | \(-0.935691\pi\) |
−0.111892 | + | 0.993720i | \(0.535691\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 340093. | + | 1.04670e6i | 0.281303 | + | 0.865762i | 0.987482 | + | 0.157729i | \(0.0504172\pi\) |
−0.706179 | + | 0.708033i | \(0.749583\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −638947. | −0.518870 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.05091e6 | + | 3.23437e6i | −0.837981 | + | 2.57904i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −370053. | + | 268859.i | −0.289778 | + | 0.210536i | −0.723171 | − | 0.690669i | \(-0.757316\pi\) |
0.433393 | + | 0.901205i | \(0.357316\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.38006e6 | − | 370414.i | 1.83053 | − | 0.284890i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.21900e6 | − | 885652.i | 0.920951 | − | 0.669110i | −0.0228099 | − | 0.999740i | \(-0.507261\pi\) |
0.943760 | + | 0.330630i | \(0.107261\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 379910. | − | 1.16924e6i | 0.281977 | − | 0.867837i | −0.705311 | − | 0.708898i | \(-0.749193\pi\) |
0.987288 | − | 0.158939i | \(-0.0508073\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.75250e6 | −3.46585 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 224764. | + | 691751.i | 0.161072 | + | 0.495730i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −89015.7 | + | 64673.7i | −0.0626934 | + | 0.0455494i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.76027e6 | − | 1.27891e6i | 1.21856 | − | 0.885333i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −256614. | − | 789777.i | −0.174627 | − | 0.537447i | 0.824989 | − | 0.565148i | \(-0.191181\pi\) |
−0.999616 | + | 0.0277019i | \(0.991181\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.76770e6 | − | 1.28431e6i | −1.18264 | − | 0.859241i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.81085e6 | + | 2.04220e6i | 1.84904 | + | 1.34341i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −202626. | + | 623618.i | −0.131074 | + | 0.403405i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −212263. | − | 653279.i | −0.135039 | − | 0.415607i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.03864e6 | + | 3.19661e6i | −0.649918 | + | 2.00024i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −68678.5 | −0.0422738 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 402908. | + | 292730.i | 0.243983 | + | 0.177264i | 0.703056 | − | 0.711135i | \(-0.251818\pi\) |
−0.459073 | + | 0.888399i | \(0.651818\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.93631e6 | −2.94107 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.84521e6 | −1.08180 | −0.540899 | − | 0.841088i | \(-0.681916\pi\) | ||||
−0.540899 | + | 0.841088i | \(0.681916\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.19380e6 | − | 867344.i | −0.688763 | − | 0.500415i | 0.187491 | − | 0.982266i | \(-0.439965\pi\) |
−0.876253 | + | 0.481851i | \(0.839965\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.60385e6 | 2.04640 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 749684. | − | 2.30729e6i | 0.419016 | − | 1.28960i | −0.489594 | − | 0.871951i | \(-0.662855\pi\) |
0.908609 | − | 0.417647i | \(-0.137145\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 793617. | + | 2.44250e6i | 0.436651 | + | 1.34387i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.57224e6 | − | 4.83887e6i | 0.851642 | − | 2.62108i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.96336e6 | + | 1.42646e6i | 1.04711 | + | 0.760771i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.20466e6 | + | 875239.i | 0.632641 | + | 0.459641i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 355786. | + | 1.09500e6i | 0.184001 | + | 0.566297i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.11911e6 | + | 813080.i | −0.570010 | + | 0.414137i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −298376. | + | 216783.i | −0.149691 | + | 0.108757i | −0.660110 | − | 0.751169i | \(-0.729490\pi\) |
0.510419 | + | 0.859926i | \(0.329490\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 502818. | + | 1.54752e6i | 0.248485 | + | 0.764759i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.81975e6 | 2.34645 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 124044. | − | 381769.i | 0.0594979 | − | 0.183116i | −0.916890 | − | 0.399140i | \(-0.869309\pi\) |
0.976388 | + | 0.216024i | \(0.0693089\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.15664e6 | − | 3.01998e6i | 1.96446 | − | 1.42726i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.03257e6 | + | 1.55545e6i | 1.41229 | + | 0.724384i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.83330e6 | − | 1.33197e6i | 0.841392 | − | 0.611307i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.75978e6 | − | 5.41604e6i | 0.795994 | − | 2.44982i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.31110e6 | −1.92205 | −0.961025 | − | 0.276463i | \(-0.910838\pi\) | ||||
−0.961025 | + | 0.276463i | \(0.910838\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −181554. | − | 558765.i | −0.0797888 | − | 0.245565i | 0.903203 | − | 0.429213i | \(-0.141209\pi\) |
−0.982992 | + | 0.183649i | \(0.941209\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.23073e6 | − | 894177.i | 0.533205 | − | 0.387396i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.47323e6 | − | 1.07036e6i | 0.629263 | − | 0.457187i | −0.226882 | − | 0.973922i | \(-0.572853\pi\) |
0.856145 | + | 0.516736i | \(0.172853\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −275394. | − | 847577.i | −0.115980 | − | 0.356951i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.29248e6 | − | 1.66558e6i | −0.951996 | − | 0.691665i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 227973. | + | 165632.i | 0.0933570 | + | 0.0678278i | 0.633485 | − | 0.773755i | \(-0.281624\pi\) |
−0.540128 | + | 0.841583i | \(0.681624\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 424459. | − | 1.30635e6i | 0.171423 | − | 0.527584i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.99073e6 | + | 6.12683e6i | 0.792949 | + | 2.44045i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.04469e6 | − | 6.29291e6i | 0.803332 | − | 2.47240i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.30343e6 | −0.505152 | −0.252576 | − | 0.967577i | \(-0.581278\pi\) | ||||
−0.252576 | + | 0.967577i | \(0.581278\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.04428e6 | − | 2.21180e6i | −1.16391 | − | 0.845630i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.48302e6 | 0.559388 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.89977e6 | −0.707015 | −0.353507 | − | 0.935432i | \(-0.615011\pi\) | ||||
−0.353507 | + | 0.935432i | \(0.615011\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.33859e6 | − | 3.15217e6i | −1.59320 | − | 1.15753i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.12448e6 | 0.407474 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 534798. | − | 1.64594e6i | 0.191246 | − | 0.588594i | −0.808754 | − | 0.588147i | \(-0.799858\pi\) |
1.00000 | 0.000447235i | \(-0.000142359\pi\) | ||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.34562e6 | − | 4.14139e6i | −0.474908 | − | 1.46162i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.10330e6 | + | 3.39562e6i | −0.384324 | + | 1.18283i | 0.552645 | + | 0.833417i | \(0.313619\pi\) |
−0.936969 | + | 0.349412i | \(0.886381\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.12539e6 | + | 2.99727e6i | 1.41845 | + | 1.03056i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.87498e6 | + | 2.08879e6i | 0.975791 | + | 0.708954i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 190079. | + | 585003.i | 0.0636883 | + | 0.196013i | 0.977837 | − | 0.209366i | \(-0.0671399\pi\) |
−0.914149 | + | 0.405378i | \(0.867140\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.35263e6 | + | 1.70928e6i | −0.778236 | + | 0.565421i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 64016.7 | − | 46510.9i | 0.0209080 | − | 0.0151905i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.19862e6 | + | 6.76667e6i | 0.709020 | + | 2.18214i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.74680e6 | −0.556245 | −0.278123 | − | 0.960546i | \(-0.589712\pi\) | ||||
−0.278123 | + | 0.960546i | \(0.589712\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.38903e6 | + | 4.27501e6i | −0.436798 | + | 1.34433i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.90297e6 | − | 1.38259e6i | 0.590978 | − | 0.429371i | −0.251687 | − | 0.967809i | \(-0.580985\pi\) |
0.842665 | + | 0.538438i | \(0.180985\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.05803e6 | − | 1.05236e6i | 0.324517 | − | 0.322778i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.54667e6 | + | 1.85026e6i | −0.771498 | + | 0.560526i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −711463. | + | 2.18966e6i | −0.212895 | + | 0.655224i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 243721. | 0.0720419 | 0.0360210 | − | 0.999351i | \(-0.488532\pi\) | ||||
0.0360210 | + | 0.999351i | \(0.488532\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.48828e6 | − | 7.65815e6i | −0.726600 | − | 2.23624i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.67193e6 | + | 1.21473e6i | −0.482328 | + | 0.350432i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.08716e6 | + | 5.87566e6i | −2.30502 | + | 1.67470i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.62472e6 | + | 8.07805e6i | 0.739167 | + | 2.27492i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.04588e6 | + | 759873.i | 0.291035 | + | 0.211449i | 0.723716 | − | 0.690098i | \(-0.242432\pi\) |
−0.432681 | + | 0.901547i | \(0.642432\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.67580e6 | − | 2.67063e6i | −1.01076 | − | 0.734358i | −0.0463897 | − | 0.998923i | \(-0.514772\pi\) |
−0.964368 | + | 0.264565i | \(0.914772\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.21147e6 | − | 6.80620e6i | 0.600939 | − | 1.84950i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.04067e6 | + | 6.28054e6i | 0.548026 | + | 1.68665i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20073.0 | + | 61778.3i | −0.00532773 | + | 0.0163971i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.67724e6 | 1.22701 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.08870e6 | + | 3.69715e6i | 1.31951 | + | 0.958682i | 0.999938 | + | 0.0111204i | \(0.00353981\pi\) |
0.319574 | + | 0.947561i | \(0.396460\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.24187e6 | −1.08727 | −0.543636 | − | 0.839321i | \(-0.682953\pi\) | ||||
−0.543636 | + | 0.839321i | \(0.682953\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.76599e6 | −2.47453 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.73195e6 | + | 2.71142e6i | 0.934829 | + | 0.679193i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.51917e6 | −1.36682 | −0.683412 | − | 0.730033i | \(-0.739505\pi\) | ||||
−0.683412 | + | 0.730033i | \(0.739505\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.28474e6 | + | 3.95401e6i | −0.314570 | + | 0.968147i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.54539e6 | − | 4.75621e6i | −0.374134 | − | 1.15147i | −0.944061 | − | 0.329772i | \(-0.893028\pi\) |
0.569926 | − | 0.821696i | \(-0.306972\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.90128e6 | − | 1.20069e7i | 0.933914 | − | 2.87429i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.72845e6 | − | 1.25579e6i | −0.409155 | − | 0.297269i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.90141e6 | − | 1.38146e6i | −0.445103 | − | 0.323387i | 0.342556 | − | 0.939497i | \(-0.388707\pi\) |
−0.787659 | + | 0.616111i | \(0.788707\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.64532e6 | − | 5.06378e6i | −0.380899 | − | 1.17229i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.84144e6 | + | 4.24406e6i | −1.33744 | + | 0.971707i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.80630e6 | − | 1.31235e6i | 0.409036 | − | 0.297182i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 435833. | + | 1.34135e6i | 0.0976179 | + | 0.300437i | 0.987927 | − | 0.154920i | \(-0.0495118\pi\) |
−0.890309 | + | 0.455356i | \(0.849512\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.74664e6 | 1.49471 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 681148. | − | 2.09636e6i | 0.149276 | − | 0.459423i | −0.848260 | − | 0.529579i | \(-0.822350\pi\) |
0.997536 | + | 0.0701562i | \(0.0223498\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.30779e6 | − | 2.40325e6i | 0.717109 | − | 0.521010i | −0.168350 | − | 0.985727i | \(-0.553844\pi\) |
0.885459 | + | 0.464717i | \(0.153844\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.18887e6 | + | 9.13964e6i | −1.97074 | + | 1.96018i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.62498e6 | + | 3.36025e6i | −0.981336 | + | 0.712983i | −0.958007 | − | 0.286745i | \(-0.907427\pi\) |
−0.0233296 | + | 0.999728i | \(0.507427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.40869e6 | − | 4.33550e6i | 0.295722 | − | 0.910138i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.30069e6 | 1.93180 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.55382e6 | + | 4.78216e6i | 0.319335 | + | 0.982813i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.47483e6 | − | 6.15733e6i | 1.72344 | − | 1.25216i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.20712e6 | + | 4.50973e6i | −1.24909 | + | 0.907518i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 845373. | + | 2.60179e6i | 0.168349 | + | 0.518124i | 0.999267 | − | 0.0382699i | \(-0.0121847\pi\) |
−0.830919 | + | 0.556394i | \(0.812185\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 815553. | + | 592534.i | 0.160727 | + | 0.116775i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.35754e6 | − | 3.16594e6i | −0.849912 | − | 0.617497i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.34947e6 | + | 7.23092e6i | −0.453540 | + | 1.39585i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 474428. | + | 1.46014e6i | 0.0906458 | + | 0.278979i | 0.986094 | − | 0.166186i | \(-0.0531451\pi\) |
−0.895449 | + | 0.445165i | \(0.853145\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −135350. | + | 416565.i | −0.0255968 | + | 0.0787790i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.38069e6 | −0.445655 | −0.222827 | − | 0.974858i | \(-0.571529\pi\) | ||||
−0.222827 | + | 0.974858i | \(0.571529\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.03454e6 | + | 2.93126e6i | 0.747612 | + | 0.543172i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.63810e7 | −4.83925 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −842911. | −0.153070 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.08363e6 | + | 2.24039e6i | 0.554384 | + | 0.402784i | 0.829399 | − | 0.558656i | \(-0.188683\pi\) |
−0.275015 | + | 0.961440i | \(0.588683\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.09111e7 | 1.94211 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −216949. | + | 667701.i | −0.0382329 | + | 0.117669i | −0.968351 | − | 0.249591i | \(-0.919704\pi\) |
0.930118 | + | 0.367260i | \(0.119704\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.62938e6 | − | 1.11701e7i | −0.633292 | − | 1.94907i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.38794e6 | + | 7.34934e6i | −0.412576 | + | 1.26978i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 596994. | + | 433742.i | 0.102135 | + | 0.0742056i | 0.637681 | − | 0.770301i | \(-0.279894\pi\) |
−0.535545 | + | 0.844506i | \(0.679894\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.06304e6 | − | 3.67851e6i | −0.857747 | − | 0.623190i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.30714e6 | − | 1.01783e7i | −0.554829 | − | 1.70759i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.39549e7 | − | 1.01388e7i | 2.31851 | − | 1.68450i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.19214e6 | − | 5.95194e6i | 1.34794 | − | 0.979337i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.18160e6 | − | 9.79195e6i | −0.518474 | − | 1.59570i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 758303. | 0.122391 | 0.0611954 | − | 0.998126i | \(-0.480509\pi\) | ||||
0.0611954 | + | 0.998126i | \(0.480509\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.40674e6 | + | 7.40719e6i | −0.384747 | + | 1.18413i | 0.551917 | + | 0.833899i | \(0.313897\pi\) |
−0.936664 | + | 0.350230i | \(0.886103\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.89549e6 | + | 7.18949e6i | −1.56689 | + | 1.13841i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.53939e6 | − | 1.01774e6i | 1.02568 | − | 0.159628i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 735240. | − | 534183.i | 0.114233 | − | 0.0829948i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.30390e6 | − | 1.01683e7i | 0.508499 | − | 1.56500i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.33127e6 | −0.355447 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.49397e6 | + | 1.69087e7i | 0.829855 | + | 2.55403i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.45868e7 | − | 1.05979e7i | 2.18285 | − | 1.58594i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.75916e6 | + | 3.45773e6i | −0.705599 | + | 0.512648i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.41122e6 | + | 7.42096e6i | 0.354196 | + | 1.09010i | 0.956474 | + | 0.291816i | \(0.0942596\pi\) |
−0.602279 | + | 0.798286i | \(0.705740\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.41455e6 | − | 2.48082e6i | −0.496974 | − | 0.361073i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.25485e6 | − | 2.36479e6i | −0.469397 | − | 0.341037i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.82431e6 | + | 8.69234e6i | −0.403594 | + | 1.24213i | 0.518470 | + | 0.855096i | \(0.326502\pi\) |
−0.922064 | + | 0.387038i | \(0.873498\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −103847. | − | 319610.i | −0.0147050 | − | 0.0452573i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.44456e6 | − | 7.52359e6i | 0.343022 | − | 1.05571i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.72942e6 | 0.935760 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.08296e6 | − | 5.14607e6i | −0.976074 | − | 0.709159i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 812063. | 0.110905 | 0.0554526 | − | 0.998461i | \(-0.482340\pi\) | ||||
0.0554526 | + | 0.998461i | \(0.482340\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.20162e6 | 0.297998 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.67815e7 | + | 1.21925e7i | 2.25125 | + | 1.63563i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.50634e6 | 0.466211 | 0.233105 | − | 0.972451i | \(-0.425111\pi\) | ||||
0.233105 | + | 0.972451i | \(0.425111\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.54797e6 | + | 1.70749e7i | −0.731161 | + | 2.25028i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 920038. | + | 2.83159e6i | 0.120184 | + | 0.369890i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.32677e6 | − | 7.16107e6i | 0.301282 | − | 0.927251i | −0.679756 | − | 0.733438i | \(-0.737914\pi\) |
0.981038 | − | 0.193813i | \(-0.0620855\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.60569e6 | + | 1.89314e6i | 0.334450 | + | 0.242992i | 0.742317 | − | 0.670049i | \(-0.233727\pi\) |
−0.407866 | + | 0.913042i | \(0.633727\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.06919e6 | − | 6.58915e6i | −1.15394 | − | 0.838384i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.87891e6 | + | 1.19381e7i | 0.489260 | + | 1.50579i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.84653e6 | − | 2.06813e6i | 0.355940 | − | 0.258605i | −0.395417 | − | 0.918502i | \(-0.629400\pi\) |
0.751357 | + | 0.659896i | \(0.229400\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.59015e6 | − | 1.15531e6i | 0.197125 | − | 0.143219i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.92166e6 | + | 8.99194e6i | 0.359078 | + | 1.10513i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.08561e7 | −1.32282 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.56943e6 | + | 1.09856e7i | −0.431230 | + | 1.32719i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.66206e6 | − | 7.01990e6i | 1.15738 | − | 0.840883i | 0.167933 | − | 0.985798i | \(-0.446291\pi\) |
0.989444 | + | 0.144915i | \(0.0462909\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.74096e6 | − | 9.36677e6i | −0.563090 | − | 1.11250i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.04810e6 | − | 2.94112e6i | 0.476741 | − | 0.346373i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.27919e6 | − | 3.93693e6i | 0.149382 | − | 0.459749i | −0.848167 | − | 0.529729i | \(-0.822294\pi\) |
0.997548 | + | 0.0699799i | \(0.0222935\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.90182e6 | 1.14663 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.96354e6 | − | 1.52762e7i | −0.569975 | − | 1.75420i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.51390e6 | + | 1.82645e6i | −0.286273 | + | 0.207990i | −0.721649 | − | 0.692259i | \(-0.756616\pi\) |
0.435376 | + | 0.900249i | \(0.356616\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.92636e6 | − | 1.39959e6i | 0.217547 | − | 0.158057i | −0.473675 | − | 0.880700i | \(-0.657073\pi\) |
0.691222 | + | 0.722643i | \(0.257073\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.28785e6 | + | 2.24297e7i | 0.816218 | + | 2.51206i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.82118e7 | − | 1.32317e7i | −2.02286 | − | 1.46969i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.05726e7 | − | 7.68141e6i | −1.16468 | − | 0.846193i | −0.174322 | − | 0.984689i | \(-0.555773\pi\) |
−0.990363 | + | 0.138496i | \(0.955773\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.85435e6 | + | 8.78479e6i | −0.311863 | + | 0.959816i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.37008e6 | − | 4.21668e6i | −0.148472 | − | 0.456949i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −50272.2 | + | 154722.i | −0.00540352 | + | 0.0166303i | −0.953722 | − | 0.300690i | \(-0.902783\pi\) |
0.948318 | + | 0.317320i | \(0.102783\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.02468e7 | 2.15858 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.33384e6 | − | 3.14872e6i | −0.458310 | − | 0.332982i | 0.334558 | − | 0.942375i | \(-0.391413\pi\) |
−0.792868 | + | 0.609393i | \(0.791413\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.41681e6 | −0.148623 | −0.0743115 | − | 0.997235i | \(-0.523676\pi\) | ||||
−0.0743115 | + | 0.997235i | \(0.523676\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.28240e7 | 1.33443 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.66031e6 | − | 7.01863e6i | −0.997174 | − | 0.724489i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.05505e6 | 0.210437 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.01681e7 | − | 3.12941e7i | 1.03293 | − | 3.17902i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.38153e6 | + | 4.25191e6i | 0.139230 | + | 0.428506i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.85188e6 | + | 5.69950e6i | −0.185157 | + | 0.569853i | −0.999951 | − | 0.00989658i | \(-0.996850\pi\) |
0.814794 | + | 0.579750i | \(0.196850\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.23621e6 | − | 6.71050e6i | −0.916188 | − | 0.665650i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.23102e7 | + | 8.94387e6i | 1.21152 | + | 0.880220i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 795939. | + | 2.44965e6i | 0.0777197 | + | 0.239197i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.52796e6 | − | 2.56321e6i | 0.341799 | − | 0.248332i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.20751e6 | + | 1.60385e6i | −0.212206 | + | 0.154176i | −0.688811 | − | 0.724941i | \(-0.741867\pi\) |
0.476606 | + | 0.879117i | \(0.341867\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 299728. | + | 922467.i | 0.0285890 | + | 0.0879880i | 0.964333 | − | 0.264692i | \(-0.0852704\pi\) |
−0.935744 | + | 0.352680i | \(0.885270\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.91208e7 | −1.80970 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −139635. | + | 429753.i | −0.0131140 | + | 0.0403606i | −0.957399 | − | 0.288767i | \(-0.906755\pi\) |
0.944285 | + | 0.329128i | \(0.106755\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.22389e7 | − | 8.89209e6i | 1.14059 | − | 0.828690i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.53569e6 | + | 1.09369e7i | 0.511941 | + | 1.01145i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.77836e6 | − | 3.47168e6i | 0.438527 | − | 0.318608i | −0.346523 | − | 0.938042i | \(-0.612638\pi\) |
0.785049 | + | 0.619433i | \(0.212638\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −85444.6 | + | 262972.i | −0.00778183 | + | 0.0239500i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.23771e7 | 2.92634 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.15107e6 | − | 1.58534e7i | −0.462045 | − | 1.42203i | −0.862661 | − | 0.505782i | \(-0.831204\pi\) |
0.400617 | − | 0.916246i | \(-0.368796\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.21323e7 | + | 8.81464e6i | −1.08004 | + | 0.784695i | −0.977690 | − | 0.210054i | \(-0.932636\pi\) |
−0.102350 | + | 0.994748i | \(0.532636\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.34777e6 | − | 5.33846e6i | 0.649190 | − | 0.471664i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.85378e6 | − | 1.49384e7i | −0.425624 | − | 1.30993i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.66885e6 | + | 5.57174e6i | 0.667445 | + | 0.484927i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.59653e6 | − | 6.24574e6i | −0.742605 | − | 0.539534i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 146939. | − | 452232.i | 0.0125988 | − | 0.0387752i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.13440e6 | + | 9.64669e6i | 0.266758 | + | 0.820995i | 0.991283 | + | 0.131748i | \(0.0420588\pi\) |
−0.724526 | + | 0.689248i | \(0.757941\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.99915e6 | − | 2.76965e7i | 0.760225 | − | 2.33973i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.00296e7 | −0.841031 | −0.420515 | − | 0.907285i | \(-0.638151\pi\) | ||||
−0.420515 | + | 0.907285i | \(0.638151\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.81773e6 | + | 4.22683e6i | 0.484261 | + | 0.351836i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.54599e7 | −1.27744 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.72101e7 | −1.41167 | −0.705833 | − | 0.708378i | \(-0.749427\pi\) | ||||
−0.705833 | + | 0.708378i | \(0.749427\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.27637e7 | + | 1.65388e7i | 1.85360 | + | 1.34672i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.02730e7 | 2.44717 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.46886e6 | + | 4.52069e6i | −0.117878 | + | 0.362791i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −659314. | − | 2.02916e6i | −0.0525288 | − | 0.161667i | 0.921351 | − | 0.388732i | \(-0.127087\pi\) |
−0.973880 | + | 0.227065i | \(0.927087\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.71050e6 | + | 2.37305e7i | −0.609887 | + | 1.87704i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.40118e7 | − | 1.74456e7i | −1.88566 | − | 1.37001i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.36438e6 | − | 6.07708e6i | −0.652156 | − | 0.473819i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.07604e6 | + | 2.17778e7i | 0.547769 | + | 1.68586i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.93968e7 | + | 1.40926e7i | −1.49086 | + | 1.08317i | −0.517005 | + | 0.855982i | \(0.672953\pi\) |
−0.973851 | + | 0.227188i | \(0.927047\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.73743e6 | − | 4.16849e6i | 0.437854 | − | 0.318120i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.18990e7 | + | 3.66213e7i | 0.901648 | + | 2.77499i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.11086e7 | −0.835815 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.13045e6 | − | 9.63453e6i | 0.233879 | − | 0.719805i | −0.763389 | − | 0.645939i | \(-0.776466\pi\) |
0.997268 | − | 0.0738663i | \(-0.0235338\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.81656e7 | + | 2.04635e7i | −2.08951 | + | 1.51812i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.24301e7 | − | 1.93451e6i | 0.915692 | − | 0.142511i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.32225e7 | + | 9.60673e6i | −0.967274 | + | 0.702766i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.20147e6 | − | 1.90862e7i | 0.450502 | − | 1.38650i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.18439e7 | −1.57583 | −0.787913 | − | 0.615787i | \(-0.788838\pi\) | ||||
−0.787913 | + | 0.615787i | \(0.788838\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.04151e6 | − | 1.55162e7i | −0.361179 | − | 1.11159i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.46499e7 | + | 2.51746e7i | −2.46522 | + | 1.79109i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.74151e7 | − | 1.26528e7i | 1.23050 | − | 0.894008i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.69539e6 | − | 1.75286e7i | −0.399657 | − | 1.23002i | −0.925275 | − | 0.379297i | \(-0.876166\pi\) |
0.525618 | − | 0.850721i | \(-0.323834\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.57708e7 | + | 1.14581e7i | 1.09909 | + | 0.798536i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.89919e6 | + | 5.73910e6i | 0.546751 | + | 0.397238i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.70308e6 | + | 2.06300e7i | −0.460802 | + | 1.41820i | 0.403384 | + | 0.915031i | \(0.367834\pi\) |
−0.864186 | + | 0.503173i | \(0.832166\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.91262e6 | − | 2.12748e7i | −0.471981 | − | 1.45261i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.03119e7 | + | 3.17369e7i | −0.699313 | + | 2.15226i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.08603e7 | −1.40511 | −0.702555 | − | 0.711630i | \(-0.747957\pi\) | ||||
−0.702555 | + | 0.711630i | \(0.747957\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.16557e7 | − | 8.46835e6i | −0.779817 | − | 0.566570i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.24362e7 | −0.826447 | −0.413223 | − | 0.910630i | \(-0.635597\pi\) | ||||
−0.413223 | + | 0.910630i | \(0.635597\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.46562e6 | 0.492805 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.95721e7 | − | 2.87508e7i | −2.59470 | − | 1.88516i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.68156e7 | 1.09524 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.98666e6 | + | 6.11430e6i | −0.128536 | + | 0.395592i | −0.994529 | − | 0.104464i | \(-0.966687\pi\) |
0.865993 | + | 0.500056i | \(0.166687\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.11897e7 | + | 3.44382e7i | 0.719166 | + | 2.21337i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.79671e6 | − | 2.39958e7i | 0.497788 | − | 1.53203i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.18273e6 | − | 859304.i | −0.0750147 | − | 0.0545014i | 0.549646 | − | 0.835398i | \(-0.314763\pi\) |
−0.624661 | + | 0.780896i | \(0.714763\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.18982e7 | + | 2.31754e7i | 2.00984 | + | 1.46024i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 690805. | + | 2.12608e6i | 0.0432408 | + | 0.133081i | 0.970346 | − | 0.241719i | \(-0.0777112\pi\) |
−0.927105 | + | 0.374800i | \(0.877711\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.07851e6 | + | 2.23667e6i | −0.191438 | + | 0.139088i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.14435e7 | + | 3.01105e7i | −2.56037 | + | 1.86022i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.04688e6 | − | 6.29964e6i | −0.125633 | − | 0.386659i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.30960e6 | 0.140838 | 0.0704191 | − | 0.997517i | \(-0.477566\pi\) | ||||
0.0704191 | + | 0.997517i | \(0.477566\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.54832e6 | + | 1.39983e7i | −0.275559 | + | 0.848084i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.24266e6 | + | 3.80901e6i | −0.315575 | + | 0.229279i | −0.734285 | − | 0.678841i | \(-0.762482\pi\) |
0.418710 | + | 0.908120i | \(0.362482\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.54465e6 | − | 2.82032e7i | 0.271798 | − | 1.68673i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.69921e6 | + | 4.86726e6i | −0.398081 | + | 0.289223i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.06805e6 | + | 1.55979e7i | −0.299225 | + | 0.920919i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.17031e6 | 0.361975 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.79590e6 | − | 2.09156e7i | −0.396134 | − | 1.21918i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.62930e7 | + | 1.91030e7i | −1.52288 | + | 1.10644i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.31585e7 | + | 9.56018e6i | −0.757301 | + | 0.550211i | −0.898081 | − | 0.439830i | \(-0.855039\pi\) |
0.140781 | + | 0.990041i | \(0.455039\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.88314e6 | + | 1.50288e7i | 0.279259 | + | 0.859470i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.37378e7 | + | 9.98112e6i | 0.780687 | + | 0.567202i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −168437. | − | 122376.i | −0.00951161 | − | 0.00691059i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.27568e7 | − | 3.92615e7i | 0.715856 | − | 2.20318i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.73726e6 | − | 2.68905e7i | −0.487225 | − | 1.49952i | −0.828733 | − | 0.559644i | \(-0.810938\pi\) |
0.341508 | − | 0.939879i | \(-0.389062\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.07617e6 | − | 1.87005e7i | 0.336715 | − | 1.03630i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.17757e7 | 3.40201 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.70626e7 | + | 2.69276e7i | 2.02837 | + | 1.47370i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.88214e7 | 1.02367 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.21589e7 | 2.27879 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.17431e7 | − | 8.53183e6i | −0.630826 | − | 0.458322i | 0.225860 | − | 0.974160i | \(-0.427481\pi\) |
−0.856686 | + | 0.515838i | \(0.827481\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.18842e7 | −0.634482 | −0.317241 | − | 0.948345i | \(-0.602756\pi\) | ||||
−0.317241 | + | 0.948345i | \(0.602756\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.95404e6 | − | 2.75577e7i | 0.475108 | − | 1.46223i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −472961. | − | 1.45562e6i | −0.0249420 | − | 0.0767636i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.78619e6 | − | 1.47304e7i | 0.250862 | − | 0.772074i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.83858e6 | + | 6.42160e6i | 0.460440 | + | 0.334529i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.93998e7 | − | 2.13602e7i | −1.52225 | − | 1.10598i | −0.960359 | − | 0.278768i | \(-0.910074\pi\) |
−0.561891 | − | 0.827211i | \(-0.689926\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.30367e6 | − | 1.32453e7i | −0.221483 | − | 0.681654i | −0.998630 | − | 0.0523344i | \(-0.983334\pi\) |
0.777147 | − | 0.629319i | \(-0.216666\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.24373e7 | − | 5.26288e7i | 3.70533 | − | 2.69208i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.51525e7 | − | 1.10089e7i | 0.770408 | − | 0.559734i | −0.131677 | − | 0.991293i | \(-0.542036\pi\) |
0.902085 | + | 0.431558i | \(0.142036\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.06015e7 | − | 3.26279e7i | −0.535771 | − | 1.64893i | −0.741977 | − | 0.670426i | \(-0.766112\pi\) |
0.206205 | − | 0.978509i | \(-0.433888\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.20428e7 | 0.604958 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.52990e6 | + | 1.08639e7i | −0.176258 | + | 0.542468i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.08456e7 | + | 2.24106e7i | −1.53100 | + | 1.11234i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.59685e7 | − | 1.33196e7i | −1.28125 | − | 0.657169i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.21668e7 | − | 8.83969e6i | 0.596721 | − | 0.433543i | −0.247993 | − | 0.968762i | \(-0.579771\pi\) |
0.844713 | + | 0.535219i | \(0.179771\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.31492e6 | + | 4.04691e6i | −0.0641076 | + | 0.197303i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.96703e7 | −1.92264 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.34432e6 | − | 2.56812e7i | −0.402022 | − | 1.23730i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.72251e7 | + | 1.25148e7i | −0.825001 | + | 0.599398i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.61865e7 | + | 1.90256e7i | −1.24683 | + | 0.905876i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.62601e6 | + | 8.08202e6i | 0.124300 | + | 0.382557i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.58440e6 | + | 4.05730e6i | 0.262787 | + | 0.190926i | 0.711375 | − | 0.702813i | \(-0.248073\pi\) |
−0.448588 | + | 0.893739i | \(0.648073\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.57414e7 | + | 4.77639e7i | 3.07556 | + | 2.23452i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.78372e6 | − | 8.56742e6i | 0.129472 | − | 0.398472i | −0.865218 | − | 0.501396i | \(-0.832820\pi\) |
0.994689 | + | 0.102924i | \(0.0328198\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.04893e6 | − | 1.55390e7i | −0.233462 | − | 0.718523i | −0.997322 | − | 0.0731403i | \(-0.976698\pi\) |
0.763859 | − | 0.645383i | \(-0.223302\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.91762e6 | − | 1.82126e7i | 0.272044 | − | 0.837266i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.77704e6 | −0.126927 | −0.0634636 | − | 0.997984i | \(-0.520215\pi\) | ||||
−0.0634636 | + | 0.997984i | \(0.520215\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.91063e7 | + | 2.11470e7i | 1.32266 | + | 0.960966i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.89688e6 | 0.130883 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.92609e7 | −2.21285 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.18206e7 | + | 8.58818e6i | 0.527952 | + | 0.383580i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.72032e7 | −1.65213 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.47707e6 | − | 1.68567e7i | 0.241840 | − | 0.744307i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.14838e7 | + | 3.53436e7i | 0.504182 | + | 1.55171i | 0.802141 | + | 0.597135i | \(0.203694\pi\) |
−0.297958 | + | 0.954579i | \(0.596306\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.75619e6 | + | 2.07934e7i | −0.294937 | + | 0.907723i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.41929e6 | + | 6.84351e6i | 0.408863 | + | 0.297057i | 0.773141 | − | 0.634234i | \(-0.218684\pi\) |
−0.364278 | + | 0.931290i | \(0.618684\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.35344e7 | − | 9.83334e6i | −0.584168 | − | 0.424423i | 0.256056 | − | 0.966662i | \(-0.417577\pi\) |
−0.840224 | + | 0.542239i | \(0.817577\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.77769e7 | + | 5.47115e7i | 0.762951 | + | 2.34812i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.93918e7 | − | 1.40890e7i | 0.827580 | − | 0.601272i | −0.0912935 | − | 0.995824i | \(-0.529100\pi\) |
0.918874 | + | 0.394552i | \(0.129100\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.16432e7 | − | 8.45930e6i | 0.494105 | − | 0.358988i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.73490e6 | − | 2.07279e7i | −0.284208 | − | 0.874703i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.11910e7 | −1.30888 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.94694e7 | + | 5.99206e7i | −0.812446 | + | 2.50045i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.39666e7 | − | 1.01473e7i | 0.579576 | − | 0.421087i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.74227e6 | − | 1.92479e7i | −0.402032 | − | 0.794301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.70545e7 | + | 1.23908e7i | −0.699885 | + | 0.508496i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.58851e6 | + | 1.71997e7i | −0.228075 | + | 0.701941i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.47483e7 | 0.598579 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.64526e6 | + | 2.04520e7i | 0.268221 | + | 0.825501i | 0.990934 | + | 0.134352i | \(0.0428952\pi\) |
−0.722712 | + | 0.691149i | \(0.757105\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.64944e7 | − | 3.37801e7i | 1.86634 | − | 1.35597i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.94967e7 | − | 2.14306e7i | 1.17755 | − | 0.855537i | 0.185653 | − | 0.982615i | \(-0.440560\pi\) |
0.991893 | + | 0.127078i | \(0.0405599\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.13872e7 | − | 6.58231e7i | −0.849136 | − | 2.61337i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.46285e6 | + | 1.06282e6i | 0.0577626 | + | 0.0419670i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 211577. | + | 153720.i | 0.00830894 | + | 0.00603680i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.35041e6 | − | 4.15613e6i | 0.0527444 | − | 0.162330i | −0.921215 | − | 0.389055i | \(-0.872802\pi\) |
0.973959 | + | 0.226724i | \(0.0728017\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.05183e6 | − | 1.24703e7i | −0.157399 | − | 0.484425i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 834860. | − | 2.56944e6i | 0.0322559 | − | 0.0992735i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.92979e7 | 0.741574 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.82841e7 | + | 4.96113e7i | 2.60988 | + | 1.89619i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.31305e7 | 0.499163 | 0.249582 | − | 0.968354i | \(-0.419707\pi\) | ||||
0.249582 | + | 0.968354i | \(0.419707\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.81202e7 | 0.685154 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.93030e7 | + | 2.85553e7i | 1.47816 | + | 1.07395i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.24836e7 | −2.71151 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.70490e6 | + | 2.37132e7i | −0.286694 | + | 0.882352i | 0.699192 | + | 0.714934i | \(0.253543\pi\) |
−0.985886 | + | 0.167419i | \(0.946457\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.20054e7 | + | 3.69488e7i | 0.444337 | + | 1.36753i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.90480e6 | − | 1.20177e7i | 0.143756 | − | 0.442434i | −0.853093 | − | 0.521759i | \(-0.825276\pi\) |
0.996849 | + | 0.0793241i | \(0.0252762\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.58990e7 | − | 1.15513e7i | −0.582225 | − | 0.423011i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.53265e7 | − | 2.56662e7i | −1.28683 | − | 0.934937i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.01647e7 | − | 3.12836e7i | −0.368314 | − | 1.13355i | −0.947880 | − | 0.318628i | \(-0.896778\pi\) |
0.579566 | − | 0.814926i | \(-0.303222\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.62279e7 | − | 1.17902e7i | 0.584919 | − | 0.424968i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.16743e7 | + | 3.75436e7i | −1.85278 | + | 1.34612i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.05996e6 | + | 3.26222e6i | 0.0378057 | + | 0.116354i | 0.968178 | − | 0.250261i | \(-0.0805165\pi\) |
−0.930373 | + | 0.366615i | \(0.880517\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.91722e7 | 1.38985 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.08945e7 | − | 6.43067e7i | 0.737484 | − | 2.26974i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.15303e7 | − | 1.56427e7i | 0.755969 | − | 0.549244i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.71800e7 | − | 8.99305e6i | −0.949383 | − | 0.314122i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.03809e7 | + | 5.11347e7i | −2.44562 | + | 1.77685i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.12241e6 | + | 6.53210e6i | −0.0733686 | + | 0.225805i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.68178e6 | 0.0922266 | 0.0461133 | − | 0.998936i | \(-0.485316\pi\) | ||||
0.0461133 | + | 0.998936i | \(0.485316\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.97445e7 | − | 6.07672e7i | −0.675517 | − | 2.07903i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.76124e6 | − | 2.00616e6i | 0.0939845 | − | 0.0682837i | −0.539801 | − | 0.841793i | \(-0.681500\pi\) |
0.633785 | + | 0.773509i | \(0.281500\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.27109e7 | + | 1.65004e7i | −0.769045 | + | 0.558744i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.21147e7 | − | 3.72851e7i | −0.408132 | − | 1.25610i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.00465e7 | + | 2.90955e7i | 1.34224 | + | 0.975191i | 0.999359 | + | 0.0358106i | \(0.0114013\pi\) |
0.342877 | + | 0.939380i | \(0.388599\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.07157e7 | + | 5.13780e7i | 2.35808 | + | 1.71325i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.08344e6 | − | 1.87229e7i | 0.201826 | − | 0.621156i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.25715e6 | − | 2.23352e7i | −0.239542 | − | 0.737235i | −0.996486 | − | 0.0837555i | \(-0.973309\pi\) |
0.756944 | − | 0.653480i | \(-0.226691\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.40310e6 | + | 1.66290e7i | −0.177440 | + | 0.546106i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.64197e7 | 1.18999 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.50148e7 | + | 1.09089e7i | 0.488122 | + | 0.354641i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.34729e7 | 1.40616 | 0.703079 | − | 0.711111i | \(-0.251808\pi\) | ||||
0.703079 | + | 0.711111i | \(0.251808\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.71020e6 | 0.312503 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.54082e7 | + | 3.29910e7i | 1.45404 | + | 1.05642i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.17903e7 | 1.96871 | 0.984357 | − | 0.176188i | \(-0.0563766\pi\) | ||||
0.984357 | + | 0.176188i | \(0.0563766\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.09240e6 | − | 1.87505e7i | 0.193141 | − | 0.594427i |
(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 | 124.6.f.a.109.2 | yes | 56 | |
31.2 | even | 5 | inner | 124.6.f.a.33.2 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.6.f.a.33.2 | ✓ | 56 | 31.2 | even | 5 | inner | |
124.6.f.a.109.2 | yes | 56 | 1.1 | even | 1 | trivial |