Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,5,Mod(113,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.113");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.e (of order \(2\), degree \(1\), not 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: | \(31.4244687775\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 996 x^{18} + 408854 x^{16} + 89661524 x^{14} + 11414409521 x^{12} + 861580608848 x^{10} + \cdots + 34\!\cdots\!64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{50} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.11 | ||
Root | \(1.48358i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.113 |
Dual form | 304.5.e.f.113.10 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.48358i | 0.164843i | 0.996598 | + | 0.0824214i | \(0.0262653\pi\) | ||||
−0.996598 | + | 0.0824214i | \(0.973735\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −22.0416 | −0.881665 | −0.440832 | − | 0.897589i | \(-0.645317\pi\) | ||||
−0.440832 | + | 0.897589i | \(0.645317\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −25.0930 | −0.512102 | −0.256051 | − | 0.966663i | \(-0.582421\pi\) | ||||
−0.256051 | + | 0.966663i | \(0.582421\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 78.7990 | 0.972827 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 90.5788 | 0.748585 | 0.374292 | − | 0.927311i | \(-0.377886\pi\) | ||||
0.374292 | + | 0.927311i | \(0.377886\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 89.9607i | − | 0.532312i | −0.963930 | − | 0.266156i | \(-0.914246\pi\) | ||
0.963930 | − | 0.266156i | \(-0.0857536\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 32.7006i | − | 0.145336i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −493.355 | −1.70711 | −0.853556 | − | 0.521002i | \(-0.825559\pi\) | ||||
−0.853556 | + | 0.521002i | \(0.825559\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 74.3224 | − | 353.266i | 0.205879 | − | 0.978577i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 37.2276i | − | 0.0844162i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 781.178 | 1.47671 | 0.738354 | − | 0.674414i | \(-0.235603\pi\) | ||||
0.738354 | + | 0.674414i | \(0.235603\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −139.167 | −0.222667 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 237.075i | 0.325206i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1270.23i | 1.51038i | 0.655504 | + | 0.755192i | \(0.272456\pi\) | ||||
−0.655504 | + | 0.755192i | \(0.727544\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1620.99i | 1.68678i | 0.537303 | + | 0.843389i | \(0.319443\pi\) | ||||
−0.537303 | + | 0.843389i | \(0.680557\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 134.381i | 0.123399i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 553.090 | 0.451502 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2410.90i | 1.76107i | 0.473983 | + | 0.880534i | \(0.342816\pi\) | ||||
−0.473983 | + | 0.880534i | \(0.657184\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 133.464 | 0.0877477 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1675.60i | − | 0.996788i | −0.866951 | − | 0.498394i | \(-0.833923\pi\) | ||
0.866951 | − | 0.498394i | \(-0.166077\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 633.074 | 0.342387 | 0.171194 | − | 0.985237i | \(-0.445238\pi\) | ||||
0.171194 | + | 0.985237i | \(0.445238\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1736.86 | −0.857707 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3088.77 | 1.39827 | 0.699134 | − | 0.714991i | \(-0.253569\pi\) | ||||
0.699134 | + | 0.714991i | \(0.253569\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1771.34 | −0.737752 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 731.934i | − | 0.281405i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2109.89i | 0.751117i | 0.926799 | + | 0.375558i | \(0.122549\pi\) | ||||
−0.926799 | + | 0.375558i | \(0.877451\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1996.50 | −0.660001 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 524.101 | + | 110.264i | 0.161311 | + | 0.0339377i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5338.68i | 1.53366i | 0.641848 | + | 0.766832i | \(0.278168\pi\) | ||||
−0.641848 | + | 0.766832i | \(0.721832\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2965.04 | 0.796840 | 0.398420 | − | 0.917203i | \(-0.369559\pi\) | ||||
0.398420 | + | 0.917203i | \(0.369559\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1977.30 | −0.498186 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1982.88i | 0.469321i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1715.97i | 0.382261i | 0.981565 | + | 0.191131i | \(0.0612154\pi\) | ||||
−0.981565 | + | 0.191131i | \(0.938785\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1158.94i | 0.243425i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3689.95i | − | 0.731988i | −0.930617 | − | 0.365994i | \(-0.880729\pi\) | ||
0.930617 | − | 0.365994i | \(-0.119271\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2412.51 | 0.452714 | 0.226357 | − | 0.974044i | \(-0.427318\pi\) | ||||
0.226357 | + | 0.974044i | \(0.427318\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 206.466i | − | 0.0367051i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2272.89 | −0.383351 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10187.8i | 1.63240i | 0.577767 | + | 0.816202i | \(0.303924\pi\) | ||||
−0.577767 | + | 0.816202i | \(0.696076\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6031.00 | 0.919219 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8009.63 | −1.16267 | −0.581335 | − | 0.813664i | \(-0.697469\pi\) | ||||
−0.581335 | + | 0.813664i | \(0.697469\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10874.3 | 1.50510 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1884.50 | −0.248976 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11847.4i | 1.49570i | 0.663870 | + | 0.747848i | \(0.268913\pi\) | ||||
−0.663870 | + | 0.747848i | \(0.731087\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2257.38i | 0.272598i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2404.88 | −0.278053 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1638.19 | + | 7786.56i | −0.181517 | + | 0.862777i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4008.24i | − | 0.426001i | −0.977052 | − | 0.213000i | \(-0.931676\pi\) | ||
0.977052 | − | 0.213000i | \(-0.0683235\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7137.51 | 0.728243 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 719.191 | 0.0705021 | 0.0352510 | − | 0.999378i | \(-0.488777\pi\) | ||||
0.0352510 | + | 0.999378i | \(0.488777\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10439.2i | − | 0.983995i | −0.870597 | − | 0.491998i | \(-0.836267\pi\) | ||
0.870597 | − | 0.491998i | \(-0.163733\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 820.556i | 0.0744268i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5911.14i | 0.516302i | 0.966105 | + | 0.258151i | \(0.0831132\pi\) | ||||
−0.966105 | + | 0.258151i | \(0.916887\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14685.2i | 1.23602i | 0.786169 | + | 0.618012i | \(0.212062\pi\) | ||||
−0.786169 | + | 0.618012i | \(0.787938\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3576.78 | −0.290299 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 19906.4i | − | 1.55896i | −0.626428 | − | 0.779480i | \(-0.715484\pi\) | ||
0.626428 | − | 0.779480i | \(-0.284516\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17218.4 | −1.30196 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 7088.81i | − | 0.517847i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12379.8 | 0.874215 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6436.49 | −0.439621 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2485.89 | 0.164313 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 16843.5 | 1.07798 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2693.51i | − | 0.166998i | −0.996508 | − | 0.0834990i | \(-0.973390\pi\) | ||
0.996508 | − | 0.0834990i | \(-0.0266095\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 939.219i | 0.0564401i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −514.799 | −0.0299982 | −0.0149991 | − | 0.999888i | \(-0.504775\pi\) | ||||
−0.0149991 | + | 0.999888i | \(0.504775\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1864.97 | + | 8864.51i | −0.105431 | + | 0.501131i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 5225.52i | − | 0.286723i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12605.6 | 0.671619 | 0.335810 | − | 0.941930i | \(-0.390990\pi\) | ||||
0.335810 | + | 0.941930i | \(0.390990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7368.93 | 0.381395 | 0.190698 | − | 0.981649i | \(-0.438925\pi\) | ||||
0.190698 | + | 0.981649i | \(0.438925\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4582.46i | 0.230494i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 8148.53i | − | 0.398481i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 27998.0i | − | 1.33165i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 2627.94i | − | 0.121613i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −41469.6 | −1.86791 | −0.933957 | − | 0.357385i | \(-0.883669\pi\) | ||||
−0.933957 | + | 0.357385i | \(0.883669\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21320.9i | 0.935087i | 0.883970 | + | 0.467543i | \(0.154861\pi\) | ||||
−0.883970 | + | 0.467543i | \(0.845139\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −38875.9 | −1.66072 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 35729.3i | − | 1.48717i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2105.40 | −0.0854152 | −0.0427076 | − | 0.999088i | \(-0.513598\pi\) | ||||
−0.0427076 | + | 0.999088i | \(0.513598\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3130.20 | −0.123816 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19602.1 | −0.756224 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 47528.0 | 1.78885 | 0.894425 | − | 0.447218i | \(-0.147585\pi\) | ||||
0.894425 | + | 0.447218i | \(0.147585\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 2961.98i | − | 0.108796i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 44354.6i | − | 1.59040i | −0.606349 | − | 0.795199i | \(-0.707366\pi\) | ||
0.606349 | − | 0.795199i | \(-0.292634\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20468.1 | 0.716644 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5856.53 | − | 27837.0i | 0.200285 | − | 0.951986i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 23078.2i | − | 0.771100i | −0.922687 | − | 0.385550i | \(-0.874012\pi\) | ||
0.922687 | − | 0.385550i | \(-0.125988\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3492.11 | 0.114028 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7920.39 | −0.252813 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12699.6i | 0.396355i | 0.980166 | + | 0.198177i | \(0.0635022\pi\) | ||||
−0.980166 | + | 0.198177i | \(0.936498\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12065.9i | 0.368302i | 0.982898 | + | 0.184151i | \(0.0589535\pi\) | ||||
−0.982898 | + | 0.184151i | \(0.941046\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4398.89i | 0.131353i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 53140.2i | − | 1.55267i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −44687.5 | −1.27792 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 5948.93i | − | 0.166539i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18113.1 | 0.496507 | 0.248254 | − | 0.968695i | \(-0.420143\pi\) | ||||
0.248254 | + | 0.968695i | \(0.420143\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22968.4i | 0.616618i | 0.951286 | + | 0.308309i | \(0.0997631\pi\) | ||||
−0.951286 | + | 0.308309i | \(0.900237\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2941.77 | −0.0773641 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17113.6 | −0.440970 | −0.220485 | − | 0.975390i | \(-0.570764\pi\) | ||||
−0.220485 | + | 0.975390i | \(0.570764\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −35012.4 | −0.884129 | −0.442064 | − | 0.896983i | \(-0.645754\pi\) | ||||
−0.442064 | + | 0.896983i | \(0.645754\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2545.79 | −0.0630130 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 31873.9i | − | 0.773470i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 36932.9i | 0.878833i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 61556.1 | 1.43658 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6732.04 | − | 31998.4i | 0.154118 | − | 0.732548i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 43106.1i | 0.968220i | 0.875007 | + | 0.484110i | \(0.160857\pi\) | ||||
−0.875007 | + | 0.484110i | \(0.839143\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5474.35 | 0.120663 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13954.0 | −0.301871 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 40675.6i | − | 0.863802i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3579.17i | 0.0746266i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 44382.6i | 0.908716i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 20353.6i | − | 0.409291i | −0.978836 | − | 0.204645i | \(-0.934396\pi\) | ||
0.978836 | − | 0.204645i | \(-0.0656041\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10966.2 | −0.216617 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1145.39i | − | 0.0222280i | −0.999938 | − | 0.0111140i | \(-0.996462\pi\) | ||
0.999938 | − | 0.0111140i | \(-0.00353778\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 75560.6 | 1.44087 | 0.720435 | − | 0.693523i | \(-0.243942\pi\) | ||||
0.720435 | + | 0.693523i | \(0.243942\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 3372.03i | − | 0.0631927i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15230.4 | −0.280542 | −0.140271 | − | 0.990113i | \(-0.544797\pi\) | ||||
−0.140271 | + | 0.990113i | \(0.544797\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −68081.6 | −1.23280 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15114.5 | −0.269090 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −63021.4 | −1.10330 | −0.551648 | − | 0.834077i | \(-0.686001\pi\) | ||||
−0.551648 | + | 0.834077i | \(0.686001\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 69567.0i | − | 1.19776i | −0.800839 | − | 0.598879i | \(-0.795613\pi\) | ||
0.800839 | − | 0.598879i | \(-0.204387\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 28150.6i | 0.476733i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 39043.3 | 0.650450 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −31780.1 | − | 6686.10i | −0.520908 | − | 0.109592i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 11883.0i | − | 0.191658i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 108698. | 1.72534 | 0.862671 | − | 0.505766i | \(-0.168790\pi\) | ||||
0.862671 | + | 0.505766i | \(0.168790\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 70758.2 | 1.10544 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16133.0i | 0.248105i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 29231.5i | − | 0.442573i | −0.975209 | − | 0.221287i | \(-0.928974\pi\) | ||
0.975209 | − | 0.221287i | \(-0.0710257\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 60496.7i | − | 0.901845i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 100093.i | 1.46934i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6152.13 | 0.0889435 | 0.0444718 | − | 0.999011i | \(-0.485840\pi\) | ||||
0.0444718 | + | 0.999011i | \(0.485840\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 46505.3i | − | 0.662233i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17576.6 | −0.246555 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 89153.5i | 1.23207i | 0.787721 | + | 0.616033i | \(0.211261\pi\) | ||||
−0.787721 | + | 0.616033i | \(0.788739\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −65642.1 | −0.893808 | −0.446904 | − | 0.894582i | \(-0.647473\pi\) | ||||
−0.446904 | + | 0.894582i | \(0.647473\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3349.02 | −0.0449358 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12605.6 | −0.166685 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24522.7 | −0.319601 | −0.159800 | − | 0.987149i | \(-0.551085\pi\) | ||||
−0.159800 | + | 0.987149i | \(0.551085\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 127733.i | 1.64094i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 83782.6i | − | 1.06106i | −0.847665 | − | 0.530532i | \(-0.821992\pi\) | ||
0.847665 | − | 0.530532i | \(-0.178008\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −74948.5 | −0.935816 | −0.467908 | − | 0.883777i | \(-0.654992\pi\) | ||||
−0.467908 | + | 0.883777i | \(0.654992\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11552.0 | − | 2430.39i | −0.142223 | − | 0.0299217i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 42045.8i | 0.510457i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 159878. | 1.91423 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5946.56 | 0.0702231 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24472.6i | 0.285066i | 0.989790 | + | 0.142533i | \(0.0455247\pi\) | ||||
−0.989790 | + | 0.142533i | \(0.954475\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 117673.i | − | 1.35218i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21474.0i | 0.243444i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 70275.4i | − | 0.786069i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15885.7 | −0.175337 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1066.98i | 0.0116218i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −65354.3 | −0.702546 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 67113.8i | 0.712091i | 0.934469 | + | 0.356045i | \(0.115875\pi\) | ||||
−0.934469 | + | 0.356045i | \(0.884125\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15487.4 | 0.162204 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 75928.7 | 0.785028 | 0.392514 | − | 0.919746i | \(-0.371605\pi\) | ||||
0.392514 | + | 0.919746i | \(0.371605\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29188.4 | 0.297935 | 0.148968 | − | 0.988842i | \(-0.452405\pi\) | ||||
0.148968 | + | 0.988842i | \(0.452405\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 43582.9 | 0.439233 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 66441.5i | 0.661182i | 0.943774 | + | 0.330591i | \(0.107248\pi\) | ||||
−0.943774 | + | 0.330591i | \(0.892752\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 115056.i | 1.13065i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8769.68 | −0.0851086 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −36667.4 | + | 174286.i | −0.351459 | + | 1.67054i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12519.6i | 0.118528i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21786.7 | −0.203750 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −77506.5 | −0.716055 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 136481.i | 1.24571i | 0.782338 | + | 0.622854i | \(0.214027\pi\) | ||||
−0.782338 | + | 0.622854i | \(0.785973\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 189977.i | 1.71321i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 37822.8i | − | 0.337026i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 140060.i | 1.23326i | 0.787255 | + | 0.616628i | \(0.211502\pi\) | ||||
−0.787255 | + | 0.616628i | \(0.788498\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29532.8 | 0.256983 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 146828.i | 1.26270i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 104696. | 0.889906 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 25545.0i | − | 0.214619i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 128168. | 1.06444 | 0.532218 | − | 0.846607i | \(-0.321359\pi\) | ||||
0.532218 | + | 0.846607i | \(0.321359\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 49366.2 | 0.405302 | 0.202651 | − | 0.979251i | \(-0.435044\pi\) | ||||
0.202651 | + | 0.979251i | \(0.435044\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21327.5 | 0.173111 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −193639. | −1.55397 | −0.776985 | − | 0.629519i | \(-0.783252\pi\) | ||||
−0.776985 | + | 0.629519i | \(0.783252\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 81332.5i | 0.645368i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18366.4i | 0.144108i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 151082. | 1.17226 | 0.586129 | − | 0.810218i | \(-0.300651\pi\) | ||||
0.586129 | + | 0.810218i | \(0.300651\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −119273. | − | 52511.3i | −0.915227 | − | 0.402938i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 9549.07i | − | 0.0724683i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −53175.7 | −0.399142 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 41282.3 | 0.306501 | 0.153251 | − | 0.988187i | \(-0.451026\pi\) | ||||
0.153251 | + | 0.988187i | \(0.451026\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 132036.i | − | 0.969702i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 52943.3i | − | 0.384648i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 14176.2i | − | 0.101892i | −0.998701 | − | 0.0509461i | \(-0.983776\pi\) | ||
0.998701 | − | 0.0509461i | \(-0.0162237\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24988.7i | 0.177698i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 114271. | 0.803995 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 22732.7i | − | 0.158261i | −0.996864 | − | 0.0791304i | \(-0.974786\pi\) | ||
0.996864 | − | 0.0791304i | \(-0.0252144\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3996.05 | 0.0275284 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 183863.i | − | 1.25342i | −0.779253 | − | 0.626709i | \(-0.784401\pi\) | ||
0.779253 | − | 0.626709i | \(-0.215599\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 50098.2 | 0.337988 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 49885.6 | 0.333084 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −92679.5 | −0.612470 | −0.306235 | − | 0.951956i | \(-0.599069\pi\) | ||||
−0.306235 | + | 0.951956i | \(0.599069\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −385398. | −2.52090 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 763.747i | − | 0.00494498i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 224556.i | − | 1.43923i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 60594.9 | 0.384464 | 0.192232 | − | 0.981350i | \(-0.438427\pi\) | ||||
0.192232 | + | 0.981350i | \(0.438427\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13151.2 | − | 2766.84i | −0.0826078 | − | 0.0173796i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 217565.i | − | 1.35301i | −0.736440 | − | 0.676503i | \(-0.763494\pi\) | ||
0.736440 | − | 0.676503i | \(-0.236506\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 145826. | 0.897892 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −132933. | −0.810443 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 218376.i | 1.31831i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 222271.i | 1.32873i | 0.747408 | + | 0.664365i | \(0.231298\pi\) | ||||
−0.747408 | + | 0.664365i | \(0.768702\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18701.5i | 0.110712i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 133963.i | − | 0.785391i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 176545. | 1.02509 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10932.4i | 0.0628702i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −169872. | −0.967593 | −0.483796 | − | 0.875181i | \(-0.660742\pi\) | ||||
−0.483796 | + | 0.875181i | \(0.660742\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 172925.i | 0.975650i | 0.872941 | + | 0.487825i | \(0.162210\pi\) | ||||
−0.872941 | + | 0.487825i | \(0.837790\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 243392. | 1.36027 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 68658.8 | 0.380118 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −74401.7 | −0.408063 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12089.0 | 0.0656866 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 140649.i | − | 0.757152i | −0.925570 | − | 0.378576i | \(-0.876414\pi\) | ||
0.925570 | − | 0.378576i | \(-0.123586\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 245244.i | 1.30805i | 0.756475 | + | 0.654023i | \(0.226920\pi\) | ||||
−0.756475 | + | 0.654023i | \(0.773080\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 41537.4 | 0.219513 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 58059.1 | − | 275964.i | 0.304024 | − | 1.44507i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 202225.i | 1.04931i | 0.851314 | + | 0.524657i | \(0.175806\pi\) | ||||
−0.851314 | + | 0.524657i | \(0.824194\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −139580. | −0.717705 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −168391. | −0.858048 | −0.429024 | − | 0.903293i | \(-0.641142\pi\) | ||||
−0.429024 | + | 0.903293i | \(0.641142\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 261136.i | − | 1.31870i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 61523.6i | − | 0.307912i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 36906.9i | − | 0.183069i | −0.995802 | − | 0.0915346i | \(-0.970823\pi\) | ||
0.995802 | − | 0.0915346i | \(-0.0291772\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 151774.i | − | 0.746180i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −31631.4 | −0.154142 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 49756.4i | − | 0.240340i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27462.6 | −0.131495 | −0.0657475 | − | 0.997836i | \(-0.520943\pi\) | ||||
−0.0657475 | + | 0.997836i | \(0.520943\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 116962.i | − | 0.555163i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 144326. | 0.679116 | 0.339558 | − | 0.940585i | \(-0.389723\pi\) | ||||
0.339558 | + | 0.940585i | \(0.389723\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 73496.6 | 0.342851 | 0.171425 | − | 0.985197i | \(-0.445163\pi\) | ||||
0.171425 | + | 0.985197i | \(0.445163\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 53007.5 | 0.245150 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 205290. | 0.941311 | 0.470656 | − | 0.882317i | \(-0.344017\pi\) | ||||
0.470656 | + | 0.882317i | \(0.344017\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 43058.8i | − | 0.195757i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 3123.54i | − | 0.0140801i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 57343.1 | 0.256306 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10343.2 | + | 49163.0i | −0.0458426 | + | 0.217897i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 166257.i | 0.730707i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −360535. | −1.57136 | −0.785681 | − | 0.618632i | \(-0.787687\pi\) | ||||
−0.785681 | + | 0.618632i | \(0.787687\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 216886. | 0.937437 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 29081.4i | − | 0.124658i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 88348.1i | 0.375590i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 217780.i | 0.918249i | 0.888372 | + | 0.459125i | \(0.151837\pi\) | ||||
−0.888372 | + | 0.459125i | \(0.848163\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 70511.7i | 0.294879i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −68766.9 | −0.285244 | −0.142622 | − | 0.989777i | \(-0.545553\pi\) | ||||
−0.142622 | + | 0.989777i | \(0.545553\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 626676.i | − | 2.57839i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −157322. | −0.642067 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 92591.8i | 0.374852i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −439361. | −1.76450 | −0.882248 | − | 0.470784i | \(-0.843971\pi\) | ||||
−0.882248 | + | 0.470784i | \(0.843971\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 65803.8 | 0.262166 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −165528. | −0.654239 | −0.327120 | − | 0.944983i | \(-0.606078\pi\) | ||||
−0.327120 | + | 0.944983i | \(0.606078\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15852.1 | −0.0621592 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 30366.1i | 0.118134i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 65330.2i | − | 0.252161i | −0.992020 | − | 0.126081i | \(-0.959760\pi\) | ||
0.992020 | − | 0.126081i | \(-0.0402398\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −60537.2 | −0.231836 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 83750.7 | + | 17620.0i | 0.318239 | + | 0.0669532i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 230097.i | 0.867554i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 279777. | 1.04672 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 34238.5 | 0.127110 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 237321.i | − | 0.874301i | −0.899388 | − | 0.437151i | \(-0.855988\pi\) | ||
0.899388 | − | 0.437151i | \(-0.144012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 321195.i | − | 1.17426i | −0.809491 | − | 0.587132i | \(-0.800257\pi\) | ||
0.809491 | − | 0.587132i | \(-0.199743\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5180.85i | 0.0187967i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 799726.i | − | 2.87952i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 330399. | 1.18067 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 420683.i | 1.49199i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −150738. | −0.530602 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 130291.i | − | 0.455205i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18840.9 | −0.0653362 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −160446. | −0.552270 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −478895. | −1.63624 | −0.818118 | − | 0.575051i | \(-0.804982\pi\) | ||||
−0.818118 | + | 0.575051i | \(0.804982\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17900.8 | −0.0607119 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 323686.i | − | 1.08976i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 276283.i | − | 0.923376i | −0.887042 | − | 0.461688i | \(-0.847244\pi\) | ||
0.887042 | − | 0.461688i | \(-0.152756\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 233642. | 0.775187 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 448730. | + | 94406.8i | 1.47803 | + | 0.310957i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 255643.i | − | 0.835956i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 78837.9 | 0.255947 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −322734. | −1.04024 | −0.520121 | − | 0.854092i | \(-0.674113\pi\) | ||||
−0.520121 | + | 0.854092i | \(0.674113\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 56951.8i | − | 0.182257i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 66297.7i | − | 0.210655i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 224027.i | − | 0.706780i | −0.935476 | − | 0.353390i | \(-0.885029\pi\) | ||
0.935476 | − | 0.353390i | \(-0.114971\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 438768.i | 1.37448i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −151336. | −0.470734 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 305755.i | − | 0.944385i | −0.881495 | − | 0.472193i | \(-0.843463\pi\) | ||
0.881495 | − | 0.472193i | \(-0.156537\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 118145. | 0.362362 | 0.181181 | − | 0.983450i | \(-0.442008\pi\) | ||||
0.181181 | + | 0.983450i | \(0.442008\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26872.3i | 0.0818456i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −108714. | −0.328814 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −443650. | −1.33257 | −0.666283 | − | 0.745699i | \(-0.732116\pi\) | ||||
−0.666283 | + | 0.745699i | \(0.732116\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −34075.6 | −0.101645 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 200986. | 0.595405 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 191111.i | 0.562275i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 156249.i | 0.456568i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 228853. | 0.664172 | 0.332086 | − | 0.943249i | \(-0.392248\pi\) | ||||
0.332086 | + | 0.943249i | \(0.392248\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 572643. | + | 120476.i | 1.65064 | + | 0.347273i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 25389.5i | − | 0.0726907i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −390241. | −1.10975 | −0.554873 | − | 0.831935i | \(-0.687233\pi\) | ||||
−0.554873 | + | 0.831935i | \(0.687233\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −272870. | −0.770764 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 51943.8i | − | 0.145742i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 241501.i | − | 0.673078i | −0.941670 | − | 0.336539i | \(-0.890744\pi\) | ||
0.941670 | − | 0.336539i | \(-0.109256\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 153315.i | 0.424459i | 0.977220 | + | 0.212230i | \(0.0680725\pi\) | ||||
−0.977220 | + | 0.212230i | \(0.931927\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 135217.i | 0.371874i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 141871. | 0.387598 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 570939.i | 1.54958i | 0.632222 | + | 0.774788i | \(0.282143\pi\) | ||||
−0.632222 | + | 0.774788i | \(0.717857\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 47287.7 | 0.127501 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 277868.i | − | 0.744314i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −734286. | −1.95409 | −0.977045 | − | 0.213034i | \(-0.931666\pi\) | ||||
−0.977045 | + | 0.213034i | \(0.931666\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −54793.1 | −0.144869 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 126400. | 0.332030 | 0.166015 | − | 0.986123i | \(-0.446910\pi\) | ||||
0.166015 | + | 0.986123i | \(0.446910\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 223622. | 0.583625 | 0.291812 | − | 0.956476i | \(-0.405742\pi\) | ||||
0.291812 | + | 0.956476i | \(0.405742\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 185198.i | 0.480234i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 297287.i | − | 0.765949i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −284278. | −0.727752 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 47472.4 | + | 9987.54i | 0.120755 | + | 0.0254053i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.18943e6i | − | 3.00634i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 446767. | 1.12208 | 0.561038 | − | 0.827790i | \(-0.310402\pi\) | ||||
0.561038 | + | 0.827790i | \(0.310402\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −63951.6 | −0.159604 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 59369.3i | 0.147236i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 159351.i | 0.392714i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 290764.i | − | 0.712097i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 715029.i | 1.74023i | 0.492846 | + | 0.870116i | \(0.335957\pi\) | ||||
−0.492846 | + | 0.870116i | \(0.664043\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 772328. | 1.86801 | 0.934007 | − | 0.357255i | \(-0.116287\pi\) | ||||
0.934007 | + | 0.357255i | \(0.116287\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 20701.9i | − | 0.0497612i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −453919. | −1.08435 | −0.542175 | − | 0.840266i | \(-0.682399\pi\) | ||||
−0.542175 | + | 0.840266i | \(0.682399\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 483571.i | 1.14808i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 60345.6 | 0.142391 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 41499.5 | 0.0973233 | 0.0486616 | − | 0.998815i | \(-0.484504\pi\) | ||||
0.0486616 | + | 0.998815i | \(0.484504\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11347.0 | 0.0264483 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 190104. | 0.440413 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 234021.i | 0.538871i | 0.963018 | + | 0.269435i | \(0.0868371\pi\) | ||||
−0.963018 | + | 0.269435i | \(0.913163\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 278550.i | 0.637529i | 0.947834 | + | 0.318765i | \(0.103268\pi\) | ||||
−0.947834 | + | 0.318765i | \(0.896732\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −65845.3 | −0.149795 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 41107.0 | − | 195388.i | 0.0929549 | − | 0.441830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 992278.i | 2.23039i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 30196.3 | 0.0674686 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 268570. | 0.596502 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 230099.i | 0.508024i | 0.967201 | + | 0.254012i | \(0.0817504\pi\) | ||||
−0.967201 | + | 0.254012i | \(0.918250\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 32993.1i | − | 0.0724128i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 385800.i | − | 0.841753i | −0.907118 | − | 0.420876i | \(-0.861723\pi\) | ||
0.907118 | − | 0.420876i | \(-0.138277\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 100579.i | 0.218156i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1699.28 | 0.00366413 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 482596.i | − | 1.03453i | −0.855826 | − | 0.517264i | \(-0.826951\pi\) | ||
0.855826 | − | 0.517264i | \(-0.173049\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −277848. | −0.592143 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 112101.i | 0.237517i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 189807. | 0.399828 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 264485. | 0.553917 | 0.276959 | − | 0.960882i | \(-0.410673\pi\) | ||||
0.276959 | + | 0.960882i | \(0.410673\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −179101. | −0.372935 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −162423. | −0.336263 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 826666.i | 1.70163i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 22595.5i | − | 0.0462453i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −221716. | −0.451192 | −0.225596 | − | 0.974221i | \(-0.572433\pi\) | ||||
−0.225596 | + | 0.974221i | \(0.572433\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 851691. | + | 179184.i | 1.72334 | + | 0.362567i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 101005.i | − | 0.203219i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18046.7 | −0.0361042 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −386790. | −0.769454 | −0.384727 | − | 0.923030i | \(-0.625704\pi\) | ||||
−0.384727 | + | 0.923030i | \(0.625704\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 802791.i | 1.58805i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.26629e6i | 2.49088i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 179607.i | 0.351326i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 93497.6i | − | 0.181870i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 178094. | 0.344501 | 0.172250 | − | 0.985053i | \(-0.444896\pi\) | ||||
0.172250 | + | 0.985053i | \(0.444896\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 261951.i | 0.503906i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 103209. | 0.197442 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 176774.i | − | 0.336313i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −84944.4 | −0.160719 | −0.0803593 | − | 0.996766i | \(-0.525607\pi\) | ||||
−0.0803593 | + | 0.996766i | \(0.525607\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 446747. | 0.840633 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −312330. | −0.584493 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −442203. | −0.823026 | −0.411513 | − | 0.911404i | \(-0.635000\pi\) | ||||
−0.411513 | + | 0.911404i | \(0.635000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 57924.0i | 0.107222i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 155431.i | 0.286155i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −135010. | −0.247217 | −0.123609 | − | 0.992331i | \(-0.539447\pi\) | ||||
−0.123609 | + | 0.992331i | \(0.539447\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9919.39 | − | 47148.5i | 0.0180654 | − | 0.0858680i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 768452.i | 1.39200i | 0.718042 | + | 0.695999i | \(0.245038\pi\) | ||||
−0.718042 | + | 0.695999i | \(0.754962\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 914057. | 1.64687 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −631151. | −1.13108 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 148328.i | − | 0.264399i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 496024.i | − | 0.879474i | −0.898127 | − | 0.439737i | \(-0.855072\pi\) | ||
0.898127 | − | 0.439737i | \(-0.144928\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 161263.i | 0.284410i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 469947.i | − | 0.824433i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 446372. | 0.778942 | 0.389471 | − | 0.921039i | \(-0.372658\pi\) | ||||
0.389471 | + | 0.921039i | \(0.372658\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 104976.i | 0.182224i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −980410. | −1.69293 | −0.846464 | − | 0.532446i | \(-0.821273\pi\) | ||||
−0.846464 | + | 0.532446i | \(0.821273\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 368495.i | − | 0.632970i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 856888. | 1.46420 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 480271. | 0.816387 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5545.25 | 0.00937710 | 0.00468855 | − | 0.999989i | \(-0.498508\pi\) | ||||
0.00468855 | + | 0.999989i | \(0.498508\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 43367.4 | 0.0729550 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.07628e6i | − | 1.80122i | −0.434627 | − | 0.900611i | \(-0.643120\pi\) | ||
0.434627 | − | 0.900611i | \(-0.356880\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 225589.i | − | 0.375590i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 89752.0 | 0.148663 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −591933. | − | 124535.i | −0.975434 | − | 0.205218i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 334231.i | − | 0.547955i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −301141. | −0.491186 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46406.4 | 0.0753075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 717648.i | 1.15868i | 0.815087 | + | 0.579338i | \(0.196689\pi\) | ||||
−0.815087 | + | 0.579338i | \(0.803311\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9127.21i | 0.0146617i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 499510.i | 0.798346i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 266737.i | − | 0.424167i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 68994.6 | 0.109164 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 42888.1i | − | 0.0675181i | −0.999430 | − | 0.0337590i | \(-0.989252\pi\) | ||
0.999430 | − | 0.0337590i | \(-0.0107479\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.52386e6 | −2.38700 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 933564.i | 1.45505i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 218523. | 0.338895 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 432062. | 0.666736 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −132267. | −0.203097 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 754628. | 1.15302 | 0.576509 | − | 0.817091i | \(-0.304415\pi\) | ||||
0.576509 | + | 0.817091i | \(0.304415\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 566538.i | − | 0.861366i | −0.902503 | − | 0.430683i | \(-0.858273\pi\) | ||
0.902503 | − | 0.430683i | \(-0.141727\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 97385.6i | − | 0.147338i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.04759e6 | −1.57717 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 47051.6 | − | 223644.i | 0.0704905 | − | 0.335053i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 177879.i | 0.265190i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 574408. | 0.852186 | 0.426093 | − | 0.904679i | \(-0.359890\pi\) | ||||
0.426093 | + | 0.904679i | \(0.359890\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 716685. | 1.05810 | 0.529052 | − | 0.848589i | \(-0.322547\pi\) | ||||
0.529052 | + | 0.848589i | \(0.322547\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 18701.4i | − | 0.0274769i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1.16092e6i | − | 1.69743i | −0.528851 | − | 0.848715i | \(-0.677377\pi\) | ||
0.528851 | − | 0.848715i | \(-0.322623\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 261267.i | 0.380167i | 0.981768 | + | 0.190084i | \(0.0608759\pi\) | ||||
−0.981768 | + | 0.190084i | \(0.939124\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 36381.4i | − | 0.0526839i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 873901. | 1.25942 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 977647.i | 1.40220i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −384298. | −0.548551 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 205092.i | 0.291356i | 0.989332 | + | 0.145678i | \(0.0465364\pi\) | ||||
−0.989332 | + | 0.145678i | \(0.953464\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −906209. | −1.28126 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 124299. | 0.174909 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −451149. | −0.631840 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 161511. | 0.225130 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 111193.i | − | 0.154262i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.88334e6i | 2.60058i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −393930. | −0.541403 | −0.270701 | − | 0.962663i | \(-0.587256\pi\) | ||||
−0.270701 | + | 0.962663i | \(0.587256\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −129087. | + | 613573.i | −0.176584 | + | 0.839333i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 667640.i | 0.909035i | 0.890738 | + | 0.454518i | \(0.150188\pi\) | ||||
−0.890738 | + | 0.454518i | \(0.849812\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.31768e6 | 1.78576 | 0.892879 | − | 0.450297i | \(-0.148682\pi\) | ||||
0.892879 | + | 0.450297i | \(0.148682\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −62378.5 | −0.0841451 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 756574.i | − | 1.01585i | −0.861401 | − | 0.507925i | \(-0.830413\pi\) | ||
0.861401 | − | 0.507925i | \(-0.169587\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 508682.i | 0.679851i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 237193.i | 0.315547i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 922801.i | 1.22199i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 154370. | 0.203482 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 315845.i | − | 0.414425i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −422653. | −0.552037 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 193421.i | 0.251481i | 0.992063 | + | 0.125741i | \(0.0401307\pi\) | ||||
−0.992063 | + | 0.125741i | \(0.959869\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −36307.2 | −0.0469911 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 973793. | 1.25463 | 0.627314 | − | 0.778766i | \(-0.284154\pi\) | ||||
0.627314 | + | 0.778766i | \(0.284154\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −327032. | −0.419439 | −0.209720 | − | 0.977762i | \(-0.567255\pi\) | ||||
−0.209720 | + | 0.977762i | \(0.567255\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 174578. | 0.222897 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 171406.i | − | 0.217861i | −0.994049 | − | 0.108931i | \(-0.965257\pi\) | ||
0.994049 | − | 0.108931i | \(-0.0347426\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 67588.2i | 0.0855199i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 546280. | 0.688113 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 229565. | − | 1.09116e6i | 0.287874 | − | 1.36831i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 279920.i | − | 0.349452i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 104259. | 0.129578 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.05904e6 | −2.54768 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.04092e6i | − | 1.28224i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 23567.8i | − | 0.0289030i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 265953.i | − | 0.324719i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.09015e6i | − | 1.32517i | −0.748986 | − | 0.662586i | \(-0.769459\pi\) | ||
0.748986 | − | 0.662586i | \(-0.230541\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 56671.5 | 0.0685863 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 269302.i | − | 0.324491i | −0.986750 | − | 0.162246i | \(-0.948126\pi\) | ||
0.986750 | − | 0.162246i | \(-0.0518737\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −725503. | −0.870357 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 96958.6i | − | 0.115810i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12917.8 | 0.0153621 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32738.8 | 0.0387643 | 0.0193821 | − | 0.999812i | \(-0.493830\pi\) | ||||
0.0193821 | + | 0.999812i | \(0.493830\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −99569.0 | −0.117383 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −331950. | −0.389646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 335518.i | − | 0.392132i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 822599.i | − | 0.957257i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 606224. | 0.702427 | 0.351214 | − | 0.936295i | \(-0.385769\pi\) | ||||
0.351214 | + | 0.936295i | \(0.385769\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −131651. | + | 625756.i | −0.151888 | + | 0.721947i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 112647.i | 0.129406i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 984985. | 1.12670 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −599917. | −0.683301 | −0.341650 | − | 0.939827i | \(-0.610986\pi\) | ||||
−0.341650 | + | 0.939827i | \(0.610986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 43303.5i | 0.0491125i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9550.71i | 0.0107859i | 0.999985 | + | 0.00539295i | \(0.00171664\pi\) | ||||
−0.999985 | + | 0.00539295i | \(0.998283\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.30894e6i | − | 1.47196i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 131124.i | 0.146831i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.60087e6 | 1.78508 | 0.892538 | − | 0.450973i | \(-0.148923\pi\) | ||||
0.892538 | + | 0.450973i | \(0.148923\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 217031.i | − | 0.240985i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −98571.6 | −0.108991 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 451633.i | − | 0.497279i | −0.968596 | − | 0.248639i | \(-0.920017\pi\) | ||
0.968596 | − | 0.248639i | \(-0.0799834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −399242. | −0.437753 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −170695. | −0.186379 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −316313. | −0.343937 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.70410e6 | −1.84522 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 465792.i | 0.502272i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 506261.i | − | 0.543650i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.30999e6 | 1.40093 | 0.700463 | − | 0.713689i | \(-0.252977\pi\) | ||||
0.700463 | + | 0.713689i | \(0.252977\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −258568. | − | 54399.1i | −0.275377 | − | 0.0579355i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.68075e6i | − | 1.78265i | −0.453368 | − | 0.891323i | \(-0.649778\pi\) | ||
0.453368 | − | 0.891323i | \(-0.350222\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −184908. | −0.195313 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −18573.8 | −0.0195385 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 977079.i | − | 1.02362i | −0.859097 | − | 0.511812i | \(-0.828974\pi\) | ||
0.859097 | − | 0.511812i | \(-0.171026\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.07312e6i | 1.11966i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.15718e6i | 1.20244i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 800046.i | 0.827957i | 0.910287 | + | 0.413978i | \(0.135861\pi\) | ||||
−0.910287 | + | 0.413978i | \(0.864139\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 377212. | 0.388788 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 114987.i | − | 0.118036i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 494544. | 0.505606 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.43409e6i | − | 1.46026i | −0.683308 | − | 0.730131i | \(-0.739459\pi\) | ||
0.683308 | − | 0.730131i | \(-0.260541\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −202481. | −0.205346 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 771730. | 0.779505 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29754.6 | −0.0299340 | −0.0149670 | − | 0.999888i | \(-0.504764\pi\) | ||||
−0.0149670 | + | 0.999888i | \(0.504764\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −571565. | −0.572710 |
(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 | 304.5.e.f.113.11 | 20 | ||
4.3 | odd | 2 | 152.5.e.a.113.10 | ✓ | 20 | ||
12.11 | even | 2 | 1368.5.o.a.721.15 | 20 | |||
19.18 | odd | 2 | inner | 304.5.e.f.113.10 | 20 | ||
76.75 | even | 2 | 152.5.e.a.113.11 | yes | 20 | ||
228.227 | odd | 2 | 1368.5.o.a.721.16 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.5.e.a.113.10 | ✓ | 20 | 4.3 | odd | 2 | ||
152.5.e.a.113.11 | yes | 20 | 76.75 | even | 2 | ||
304.5.e.f.113.10 | 20 | 19.18 | odd | 2 | inner | ||
304.5.e.f.113.11 | 20 | 1.1 | even | 1 | trivial | ||
1368.5.o.a.721.15 | 20 | 12.11 | even | 2 | |||
1368.5.o.a.721.16 | 20 | 228.227 | odd | 2 |