Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(176,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.176");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.4433380710\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-59})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 14x^{2} - 15x + 225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 176.2 | ||
Root | \(3.57603 + 1.48727i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.176 |
Dual form | 177.4.d.b.176.1 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | −5.07603 | + | 1.11080i | −0.976883 | + | 0.213774i | ||||
\(4\) | −8.00000 | −1.00000 | ||||||||
\(5\) | 22.0271i | 1.97016i | 0.172085 | + | 0.985082i | \(0.444950\pi\) | ||||
−0.172085 | + | 0.985082i | \(0.555050\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −34.4562 | −1.86046 | −0.930230 | − | 0.366977i | \(-0.880393\pi\) | ||||
−0.930230 | + | 0.366977i | \(0.880393\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 24.5322 | − | 11.2769i | 0.908601 | − | 0.417665i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 40.6083 | − | 8.88642i | 0.976883 | − | 0.213774i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −24.4678 | − | 111.810i | −0.421170 | − | 1.92462i | ||||
\(16\) | 64.0000 | 1.00000 | ||||||||
\(17\) | 61.4492i | 0.876683i | 0.898808 | + | 0.438342i | \(0.144434\pi\) | ||||
−0.898808 | + | 0.438342i | \(0.855566\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 40.2810 | 0.486374 | 0.243187 | − | 0.969979i | \(-0.421807\pi\) | ||||
0.243187 | + | 0.969979i | \(0.421807\pi\) | |||||||
\(20\) | − | 176.217i | − | 1.97016i | ||||||
\(21\) | 174.901 | − | 38.2740i | 1.81745 | − | 0.397718i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −360.193 | −2.88155 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −112.000 | + | 84.4926i | −0.798311 | + | 0.602245i | ||||
\(28\) | 275.650 | 1.86046 | ||||||||
\(29\) | − | 272.118i | − | 1.74245i | −0.490884 | − | 0.871225i | \(-0.663326\pi\) | ||
0.490884 | − | 0.871225i | \(-0.336674\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 758.970i | − | 3.66541i | ||||||
\(36\) | −196.258 | + | 90.2155i | −0.908601 | + | 0.417665i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 458.504i | 1.74649i | 0.487277 | + | 0.873247i | \(0.337990\pi\) | ||||
−0.487277 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 248.398 | + | 540.374i | 0.822868 | + | 1.79009i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −324.866 | + | 71.0914i | −0.976883 | + | 0.213774i | ||||
\(49\) | 844.230 | 2.46131 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −68.2579 | − | 311.918i | −0.187412 | − | 0.856417i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 632.682i | 1.63973i | 0.572558 | + | 0.819864i | \(0.305951\pi\) | ||||
−0.572558 | + | 0.819864i | \(0.694049\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −204.468 | + | 44.7442i | −0.475130 | + | 0.103974i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 453.188i | − | 1.00000i | ||||||
\(60\) | 195.742 | + | 894.483i | 0.421170 | + | 1.92462i | ||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −845.288 | + | 388.561i | −1.69042 | + | 0.777048i | ||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | − | 491.593i | − | 0.876683i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1182.90i | − | 1.97724i | −0.150437 | − | 0.988620i | \(-0.548068\pi\) | ||
0.150437 | − | 0.988620i | \(-0.451932\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1828.35 | − | 400.104i | 2.81493 | − | 0.616000i | ||||
\(76\) | −322.248 | −0.486374 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −560.354 | −0.798035 | −0.399017 | − | 0.916943i | \(-0.630649\pi\) | ||||
−0.399017 | + | 0.916943i | \(0.630649\pi\) | |||||||
\(80\) | 1409.73i | 1.97016i | ||||||||
\(81\) | 474.661 | − | 553.297i | 0.651113 | − | 0.758981i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | −1399.21 | + | 306.192i | −1.81745 | + | 0.397718i | ||||
\(85\) | −1353.55 | −1.72721 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 302.269 | + | 1381.28i | 0.372491 | + | 1.70217i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 887.274i | 0.958236i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2881.55 | 2.88155 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 843.066 | + | 3852.56i | 0.783570 | + | 3.58068i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 928.173i | − | 0.838597i | −0.907848 | − | 0.419299i | \(-0.862276\pi\) | ||
0.907848 | − | 0.419299i | \(-0.137724\pi\) | |||||||
\(108\) | 896.000 | − | 675.941i | 0.798311 | − | 0.602245i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2205.20 | −1.86046 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2176.94i | 1.74245i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2117.30i | − | 1.63103i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1331.00 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −509.307 | − | 2327.38i | −0.373355 | − | 1.70612i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 5180.63i | − | 3.70696i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1964.29 | 1.37246 | 0.686230 | − | 0.727385i | \(-0.259264\pi\) | ||||
0.686230 | + | 0.727385i | \(0.259264\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1387.93 | −0.904879 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1861.13 | − | 2467.04i | −1.18652 | − | 1.57280i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1178.26i | − | 0.734784i | −0.930066 | − | 0.367392i | \(-0.880251\pi\) | ||
0.930066 | − | 0.367392i | \(-0.119749\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1960.00 | −1.19601 | −0.598004 | − | 0.801493i | \(-0.704039\pi\) | ||||
−0.598004 | + | 0.801493i | \(0.704039\pi\) | |||||||
\(140\) | 6071.76i | 3.66541i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1570.06 | − | 721.724i | 0.908601 | − | 0.417665i | ||||
\(145\) | 5993.97 | 3.43291 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4285.34 | + | 937.773i | −2.40441 | + | 0.526165i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 692.959 | + | 1507.49i | 0.366159 | + | 0.796555i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −702.785 | − | 3211.52i | −0.350531 | − | 1.60182i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4048.00 | −1.94518 | −0.972588 | − | 0.232533i | \(-0.925299\pi\) | ||||
−0.972588 | + | 0.232533i | \(0.925299\pi\) | |||||||
\(164\) | − | 3668.03i | − | 1.74649i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 719.468i | − | 0.333378i | −0.986010 | − | 0.166689i | \(-0.946692\pi\) | ||
0.986010 | − | 0.166689i | \(-0.0533076\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2197.00 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 988.183 | − | 454.247i | 0.441920 | − | 0.203141i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12410.9 | 5.36100 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 503.402 | + | 2300.40i | 0.213774 | + | 0.976883i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | −1987.19 | − | 4322.99i | −0.822868 | − | 1.79009i | ||||
\(181\) | 1659.12 | 0.681334 | 0.340667 | − | 0.940184i | \(-0.389347\pi\) | ||||
0.340667 | + | 0.940184i | \(0.389347\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3859.09 | − | 2911.29i | 1.48523 | − | 1.12045i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 2598.93 | − | 568.731i | 0.976883 | − | 0.213774i | ||||
\(193\) | −5299.00 | −1.97632 | −0.988161 | − | 0.153422i | \(-0.950971\pi\) | ||||
−0.988161 | + | 0.153422i | \(0.950971\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6753.84 | −2.46131 | ||||||||
\(197\) | − | 4086.37i | − | 1.47788i | −0.673773 | − | 0.738939i | \(-0.735327\pi\) | ||
0.673773 | − | 0.738939i | \(-0.264673\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1408.35 | −0.501684 | −0.250842 | − | 0.968028i | \(-0.580707\pi\) | ||||
−0.250842 | + | 0.968028i | \(0.580707\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9376.16i | 3.24176i | ||||||||
\(204\) | 546.063 | + | 2495.34i | 0.187412 | + | 0.856417i | ||||
\(205\) | −10099.5 | −3.44088 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | − | 5061.46i | − | 1.63973i | ||||||
\(213\) | 1313.96 | + | 6004.42i | 0.422682 | + | 1.93153i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5852.00 | 1.75730 | 0.878652 | − | 0.477462i | \(-0.158443\pi\) | ||||
0.878652 | + | 0.477462i | \(0.158443\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8836.35 | + | 4061.88i | −2.61818 | + | 1.20352i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 1635.74 | − | 357.954i | 0.475130 | − | 0.103974i | ||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3625.50i | 1.00000i | ||||||||
\(237\) | 2844.38 | − | 622.442i | 0.779587 | − | 0.170599i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1586.24i | − | 0.429311i | −0.976690 | − | 0.214655i | \(-0.931137\pi\) | ||
0.976690 | − | 0.214655i | \(-0.0688628\pi\) | |||||||
\(240\) | −1565.94 | − | 7155.86i | −0.421170 | − | 1.92462i | ||||
\(241\) | −1189.52 | −0.317941 | −0.158971 | − | 0.987283i | \(-0.550817\pi\) | ||||
−0.158971 | + | 0.987283i | \(0.550817\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1794.79 | + | 3335.81i | −0.473811 | + | 0.880627i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18595.9i | 4.84919i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5420.99i | 1.36323i | 0.731712 | + | 0.681614i | \(0.238722\pi\) | ||||
−0.731712 | + | 0.681614i | \(0.761278\pi\) | |||||||
\(252\) | 6762.30 | − | 3108.48i | 1.69042 | − | 0.777048i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6870.65 | − | 1503.52i | 1.68728 | − | 0.369233i | ||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | − | 4866.00i | − | 1.18106i | −0.807015 | − | 0.590530i | \(-0.798919\pi\) | ||
0.807015 | − | 0.590530i | \(-0.201081\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3068.66 | − | 6675.67i | −0.727760 | − | 1.58319i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5283.40i | 1.23874i | 0.785099 | + | 0.619370i | \(0.212612\pi\) | ||||
−0.785099 | + | 0.619370i | \(0.787388\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13936.2 | −3.23053 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6422.81 | 1.43970 | 0.719849 | − | 0.694131i | \(-0.244211\pi\) | ||||
0.719849 | + | 0.694131i | \(0.244211\pi\) | |||||||
\(272\) | 3932.75i | 0.876683i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3597.65 | 0.780367 | 0.390183 | − | 0.920737i | \(-0.372412\pi\) | ||||
0.390183 | + | 0.920737i | \(0.372412\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8020.94i | 1.70281i | 0.524510 | + | 0.851404i | \(0.324249\pi\) | ||||
−0.524510 | + | 0.851404i | \(0.675751\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | 9463.17i | 1.97724i | ||||||||
\(285\) | −985.586 | − | 4503.83i | −0.204846 | − | 0.936084i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 15798.3i | − | 3.24928i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1137.00 | 0.231427 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4636.93i | 0.924548i | 0.886737 | + | 0.462274i | \(0.152966\pi\) | ||||
−0.886737 | + | 0.462274i | \(0.847034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9982.41 | 1.97016 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −14626.8 | + | 3200.83i | −2.81493 | + | 0.616000i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2577.98 | 0.486374 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6930.27 | −1.28838 | −0.644188 | − | 0.764867i | \(-0.722805\pi\) | ||||
−0.644188 | + | 0.764867i | \(0.722805\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1406.08i | − | 0.256371i | −0.991750 | − | 0.128186i | \(-0.959085\pi\) | ||
0.991750 | − | 0.128186i | \(-0.0409154\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8558.87 | − | 18619.2i | −1.53091 | − | 3.33040i | ||||
\(316\) | 4482.83 | 0.798035 | ||||||||
\(317\) | − | 215.072i | − | 0.0381062i | −0.999818 | − | 0.0190531i | \(-0.993935\pi\) | ||
0.999818 | − | 0.0190531i | \(-0.00606515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 11277.9i | − | 1.97016i | ||||||
\(321\) | 1031.02 | + | 4711.44i | 0.179270 | + | 0.819211i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2475.23i | 0.426395i | ||||||||
\(324\) | −3797.29 | + | 4426.38i | −0.651113 | + | 0.758981i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5310.03 | −0.881770 | −0.440885 | − | 0.897564i | \(-0.645335\pi\) | ||||
−0.440885 | + | 0.897564i | \(0.645335\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 11193.7 | − | 2449.54i | 1.81745 | − | 0.397718i | ||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10828.4 | 1.72721 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17270.5 | −2.71871 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | −2418.16 | − | 11050.2i | −0.372491 | − | 1.70217i | ||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26055.8 | 3.89549 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2351.91 | + | 10747.5i | 0.348673 | + | 1.59333i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 13527.7i | − | 1.98875i | −0.105895 | − | 0.994377i | \(-0.533771\pi\) | ||
0.105895 | − | 0.994377i | \(-0.466229\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5236.44 | −0.763441 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6756.20 | − | 1478.48i | 0.976883 | − | 0.213774i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5170.52 | + | 11248.1i | 0.729449 | + | 1.58687i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 21799.8i | − | 3.05065i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4898.00 | 0.679916 | 0.339958 | − | 0.940441i | \(-0.389587\pi\) | ||||
0.339958 | + | 0.940441i | \(0.389587\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5754.66 | + | 26297.1i | 0.792451 | + | 3.62126i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12519.3 | −1.69677 | −0.848383 | − | 0.529383i | \(-0.822423\pi\) | ||||
−0.848383 | + | 0.529383i | \(0.822423\pi\) | |||||||
\(380\) | − | 7098.19i | − | 0.958236i | ||||||
\(381\) | −9970.79 | + | 2181.94i | −1.34073 | + | 0.293396i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14025.8i | 1.87124i | 0.353014 | + | 0.935618i | \(0.385157\pi\) | ||||
−0.353014 | + | 0.935618i | \(0.614843\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 11829.0i | − | 1.54178i | −0.636968 | − | 0.770890i | \(-0.719812\pi\) | ||
0.636968 | − | 0.770890i | \(-0.280188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 12343.0i | − | 1.57226i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7045.18 | − | 1541.72i | 0.883961 | − | 0.193440i | ||||
\(400\) | −23052.4 | −2.88155 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12187.5 | + | 10455.4i | 1.49532 | + | 1.28280i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1308.81 | + | 5980.88i | 0.157078 | + | 0.717798i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15615.1i | 1.86046i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9949.03 | − | 2177.17i | 1.16836 | − | 0.255675i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | −6744.53 | − | 30820.5i | −0.783570 | − | 3.58068i | ||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 22133.6i | − | 2.52620i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7425.39i | 0.838597i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | −7168.00 | + | 5407.53i | −0.798311 | + | 0.602245i | ||||
\(433\) | −1808.48 | −0.200716 | −0.100358 | − | 0.994951i | \(-0.531999\pi\) | ||||
−0.100358 | + | 0.994951i | \(0.531999\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −30425.6 | + | 6658.12i | −3.35356 | + | 0.733868i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3220.00 | −0.350073 | −0.175037 | − | 0.984562i | \(-0.556004\pi\) | ||||
−0.175037 | + | 0.984562i | \(0.556004\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20710.8 | − | 9520.33i | 2.23635 | − | 1.02800i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 17641.6 | 1.86046 | ||||||||
\(449\) | − | 9618.49i | − | 1.01097i | −0.862836 | − | 0.505484i | \(-0.831314\pi\) | ||
0.862836 | − | 0.505484i | \(-0.168686\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5192.00 | − | 6882.31i | −0.527978 | − | 0.699866i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13488.1i | − | 1.36270i | −0.731959 | − | 0.681348i | \(-0.761394\pi\) | ||
0.731959 | − | 0.681348i | \(-0.238606\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | − | 17415.6i | − | 1.74245i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14509.0 | −1.40151 | ||||||||
\(476\) | 16938.4i | 1.63103i | ||||||||
\(477\) | 7134.72 | + | 15521.1i | 0.684856 | + | 1.48986i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 1459.42i | − | 0.139212i | −0.997575 | − | 0.0696059i | \(-0.977826\pi\) | ||
0.997575 | − | 0.0696059i | \(-0.0221742\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10648.0 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2456.75 | −0.228595 | −0.114298 | − | 0.993447i | \(-0.536462\pi\) | ||||
−0.114298 | + | 0.993447i | \(0.536462\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20547.8 | − | 4496.53i | 1.90021 | − | 0.415828i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11786.6i | 1.08335i | 0.840589 | + | 0.541674i | \(0.182209\pi\) | ||||
−0.840589 | + | 0.541674i | \(0.817791\pi\) | |||||||
\(492\) | 4074.46 | + | 18619.1i | 0.373355 | + | 1.70612i | ||||
\(493\) | 16721.4 | 1.52758 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 40758.1i | 3.67857i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22217.2 | 1.99314 | 0.996571 | − | 0.0827472i | \(-0.0263694\pi\) | ||||
0.996571 | + | 0.0827472i | \(0.0263694\pi\) | |||||||
\(500\) | 41445.0i | 3.70696i | ||||||||
\(501\) | 799.187 | + | 3652.04i | 0.0712675 | + | 0.325671i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11152.0 | + | 2440.43i | −0.976883 | + | 0.213774i | ||||
\(508\) | −15714.3 | −1.37246 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4511.47 | + | 3403.45i | −0.388278 | + | 0.292916i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 11552.4i | − | 0.971443i | −0.874114 | − | 0.485721i | \(-0.838557\pi\) | ||
0.874114 | − | 0.485721i | \(-0.161443\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23099.6 | −1.93131 | −0.965654 | − | 0.259833i | \(-0.916333\pi\) | ||||
−0.965654 | + | 0.259833i | \(0.916333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −62998.1 | + | 13786.1i | −5.23707 | + | 1.14604i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12167.0 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5110.57 | − | 11117.7i | −0.417665 | − | 0.908601i | ||||
\(532\) | 11103.4 | 0.904879 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20445.0 | 1.65217 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 14889.0 | + | 19736.3i | 1.18652 | + | 1.57280i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8421.75 | + | 1842.96i | −0.665584 | + | 0.145652i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12616.0 | −0.986145 | −0.493072 | − | 0.869988i | \(-0.664126\pi\) | ||||
−0.493072 | + | 0.869988i | \(0.664126\pi\) | |||||||
\(548\) | 9426.07i | 0.734784i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10961.2i | − | 0.847482i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19307.7 | 1.48471 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15680.0 | 1.19601 | ||||||||
\(557\) | 17680.4i | 1.34496i | 0.740115 | + | 0.672481i | \(0.234771\pi\) | ||||
−0.740115 | + | 0.672481i | \(0.765229\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | − | 48574.1i | − | 3.66541i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16355.0 | + | 19064.5i | −1.21137 | + | 1.41205i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12560.5 | + | 5773.79i | −0.908601 | + | 0.417665i | ||||
\(577\) | −27315.1 | −1.97078 | −0.985390 | − | 0.170311i | \(-0.945523\pi\) | ||||
−0.985390 | + | 0.170311i | \(0.945523\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26897.9 | − | 5886.14i | 1.93064 | − | 0.422486i | ||||
\(580\) | −47951.8 | −3.43291 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 34282.7 | − | 7502.18i | 2.40441 | − | 0.526165i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4539.15 | + | 20742.5i | 0.315932 | + | 1.44371i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 27698.9i | − | 1.91814i | −0.283163 | − | 0.959072i | \(-0.591384\pi\) | ||
0.283163 | − | 0.959072i | \(-0.408616\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 46638.1 | 3.21340 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7148.82 | − | 1564.40i | 0.490086 | − | 0.107247i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 26228.1i | − | 1.78906i | −0.447004 | − | 0.894532i | \(-0.647509\pi\) | ||
0.447004 | − | 0.894532i | \(-0.352491\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 29318.1i | − | 1.97016i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26449.2 | −1.76860 | −0.884301 | − | 0.466917i | \(-0.845365\pi\) | ||||
−0.884301 | + | 0.466917i | \(0.845365\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10415.1 | − | 47593.7i | −0.693004 | − | 3.16682i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −5543.67 | − | 12059.9i | −0.366159 | − | 0.796555i | ||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 51265.5 | − | 11218.6i | 3.36134 | − | 0.735571i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30635.6i | 1.99893i | 0.0326376 | + | 0.999467i | \(0.489609\pi\) | ||||
−0.0326376 | + | 0.999467i | \(0.510391\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11430.9 | −0.742238 | −0.371119 | − | 0.928585i | \(-0.621026\pi\) | ||||
−0.371119 | + | 0.928585i | \(0.621026\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 69090.1 | 4.42177 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29860.0 | −1.88385 | −0.941924 | − | 0.335827i | \(-0.890984\pi\) | ||||
−0.941924 | + | 0.335827i | \(0.890984\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 43267.6i | 2.70397i | ||||||||
\(636\) | 5622.28 | + | 25692.1i | 0.350531 | + | 1.60182i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13339.5 | − | 29019.1i | −0.825823 | − | 1.79652i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17205.8i | 1.06020i | 0.847936 | + | 0.530099i | \(0.177845\pi\) | ||||
−0.847936 | + | 0.530099i | \(0.822155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13556.0 | −0.831410 | −0.415705 | − | 0.909500i | \(-0.636465\pi\) | ||||
−0.415705 | + | 0.909500i | \(0.636465\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 15558.0i | − | 0.945362i | −0.881234 | − | 0.472681i | \(-0.843286\pi\) | ||
0.881234 | − | 0.472681i | \(-0.156714\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32384.0 | 1.94518 | ||||||||
\(653\) | − | 6801.85i | − | 0.407622i | −0.979010 | − | 0.203811i | \(-0.934667\pi\) | ||
0.979010 | − | 0.203811i | \(-0.0653328\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 29344.3i | 1.74649i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5355.58 | −0.315141 | −0.157570 | − | 0.987508i | \(-0.550366\pi\) | ||||
−0.157570 | + | 0.987508i | \(0.550366\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 30572.1i | − | 1.78276i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 5755.74i | 0.333378i | ||||||||
\(669\) | −29704.9 | + | 6500.42i | −1.71668 | + | 0.375666i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 40341.7 | − | 30433.7i | 2.30037 | − | 1.73540i | ||||
\(676\) | −17576.0 | −1.00000 | ||||||||
\(677\) | − | 33397.6i | − | 1.89597i | −0.318308 | − | 0.947987i | \(-0.603115\pi\) | ||
0.318308 | − | 0.947987i | \(-0.396885\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | −7905.47 | + | 3633.97i | −0.441920 | + | 0.203141i | ||||
\(685\) | 25953.6 | 1.44765 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 43173.1i | − | 2.35633i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28174.7 | −1.53112 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −99287.2 | −5.36100 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4027.22 | − | 18403.2i | −0.213774 | − | 0.976883i | ||||
\(709\) | 37498.6 | 1.98630 | 0.993152 | − | 0.116833i | \(-0.0372743\pi\) | ||||
0.993152 | + | 0.116833i | \(0.0372743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13746.7 | + | 6319.08i | −0.725095 | + | 0.333311i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1762.00 | + | 8051.80i | 0.0917755 | + | 0.419386i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 15897.5 | + | 34583.9i | 0.822868 | + | 1.79009i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6038.05 | − | 1321.32i | 0.310591 | − | 0.0679676i | ||||
\(724\) | −13273.0 | −0.681334 | ||||||||
\(725\) | 98015.1i | 5.02095i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39116.0 | 1.99551 | 0.997753 | − | 0.0670071i | \(-0.0213450\pi\) | ||||
0.997753 | + | 0.0670071i | \(0.0213450\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5405.00 | − | 18926.3i | 0.274602 | − | 0.961558i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9898.00 | −0.498760 | −0.249380 | − | 0.968406i | \(-0.580227\pi\) | ||||
−0.249380 | + | 0.968406i | \(0.580227\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20656.4 | − | 94393.6i | −1.03663 | − | 4.73709i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35594.4i | 1.75751i | 0.477269 | + | 0.878757i | \(0.341627\pi\) | ||||
−0.477269 | + | 0.878757i | \(0.658373\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31981.3i | 1.56018i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6021.65 | − | 27517.1i | −0.291423 | − | 1.33171i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −30872.8 | + | 23290.4i | −1.48523 | + | 1.12045i | ||||
\(757\) | 41640.9 | 1.99929 | 0.999646 | − | 0.0265962i | \(-0.00846682\pi\) | ||||
0.999646 | + | 0.0265962i | \(0.00846682\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 38033.2i | − | 1.81170i | −0.423601 | − | 0.905849i | \(-0.639234\pi\) | ||
0.423601 | − | 0.905849i | \(-0.360766\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −33205.5 | + | 15263.9i | −1.56934 | + | 0.721394i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −20791.4 | + | 4549.85i | −0.976883 | + | 0.213774i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5405.16 | + | 24700.0i | 0.252480 | + | 1.15376i | ||||
\(772\) | 42392.0 | 1.97632 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18469.0i | 0.849449i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22992.0 | + | 30477.2i | 1.04938 | + | 1.39102i | ||||
\(784\) | 54030.7 | 2.46131 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42784.0 | −1.93785 | −0.968923 | − | 0.247362i | \(-0.920436\pi\) | ||||
−0.968923 | + | 0.247362i | \(0.920436\pi\) | |||||||
\(788\) | 32691.0i | 1.47788i | ||||||||
\(789\) | −5868.82 | − | 26818.7i | −0.264810 | − | 1.21010i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 70740.4 | − | 15480.3i | 3.15585 | − | 0.690604i | ||||
\(796\) | 11266.8 | 0.501684 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | − | 75009.2i | − | 3.24176i | ||||||
\(813\) | −32602.4 | + | 7134.48i | −1.40642 | + | 0.307770i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 89165.7i | − | 3.83232i | ||||||
\(816\) | −4368.50 | − | 19962.8i | −0.187412 | − | 0.856417i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 80796.1 | 3.44088 | ||||||||
\(821\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18603.7i | − | 0.782243i | −0.920339 | − | 0.391122i | \(-0.872087\pi\) | ||
0.920339 | − | 0.391122i | \(-0.127913\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47472.1 | −1.98887 | −0.994436 | − | 0.105339i | \(-0.966407\pi\) | ||||
−0.994436 | + | 0.105339i | \(0.966407\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18261.8 | + | 3996.27i | −0.762327 | + | 0.166822i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 51877.2i | 2.15779i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15847.8 | 0.656809 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −49659.3 | −2.03613 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8909.68 | − | 40714.6i | −0.364016 | − | 1.66345i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 48393.6i | 1.97016i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 45861.2 | 1.86046 | ||||||||
\(848\) | 40491.7i | 1.63973i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −10511.7 | − | 48035.4i | −0.422682 | − | 1.93153i | ||||
\(853\) | −48375.5 | −1.94179 | −0.970895 | − | 0.239506i | \(-0.923015\pi\) | ||||
−0.970895 | + | 0.239506i | \(0.923015\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10005.7 | + | 21766.8i | 0.400221 | + | 0.870654i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17548.8 | + | 80192.7i | 0.694612 | + | 3.17417i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5771.45 | + | 1262.98i | −0.226077 | + | 0.0494730i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 178505.i | 6.89665i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35493.1 | −1.36661 | −0.683305 | − | 0.730133i | \(-0.739458\pi\) | ||||
−0.683305 | + | 0.730133i | \(0.739458\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5150.71 | − | 23537.2i | −0.197644 | − | 0.903175i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26098.8 | 0.994671 | 0.497336 | − | 0.867558i | \(-0.334312\pi\) | ||||
0.497336 | + | 0.867558i | \(0.334312\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −50671.1 | + | 11088.5i | −1.92462 | + | 0.421170i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −67681.9 | −2.55341 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −46816.0 | −1.75730 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 70690.8 | − | 32495.0i | 2.61818 | − | 1.20352i | ||||
\(901\) | −38877.8 | −1.43752 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36545.6i | 1.34234i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33289.5 | −1.21870 | −0.609350 | − | 0.792901i | \(-0.708570\pi\) | ||||
−0.609350 | + | 0.792901i | \(0.708570\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42496.6i | 1.54553i | 0.634695 | + | 0.772763i | \(0.281126\pi\) | ||||
−0.634695 | + | 0.772763i | \(0.718874\pi\) | |||||||
\(912\) | −13085.9 | + | 2863.63i | −0.475130 | + | 0.103974i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 35178.3 | − | 7698.16i | 1.25859 | − | 0.275421i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34006.4 | 1.19712 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1561.88 | + | 7137.31i | 0.0548056 | + | 0.250445i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 29004.0i | − | 1.00000i | ||||||
\(945\) | 64127.4 | + | 85004.7i | 2.20748 | + | 2.92614i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10490.9i | 0.359989i | 0.983668 | + | 0.179994i | \(0.0576080\pi\) | ||||
−0.983668 | + | 0.179994i | \(0.942392\pi\) | |||||||
\(948\) | −22755.0 | + | 4979.54i | −0.779587 | + | 0.170599i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 238.903 | + | 1091.71i | 0.00814611 | + | 0.0372253i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 56348.9i | − | 1.91534i | −0.287868 | − | 0.957670i | \(-0.592946\pi\) | ||
0.287868 | − | 0.957670i | \(-0.407054\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12689.9i | 0.429311i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 40598.3i | 1.36704i | ||||||||
\(960\) | 12527.5 | + | 57246.9i | 0.421170 | + | 1.92462i | ||||
\(961\) | 29791.0 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10467.0 | − | 22770.2i | −0.350252 | − | 0.761951i | ||||
\(964\) | 9516.17 | 0.317941 | ||||||||
\(965\) | − | 116722.i | − | 3.89368i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2749.50 | − | 12564.4i | −0.0911523 | − | 0.416539i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11222.9i | 0.370916i | 0.982652 | + | 0.185458i | \(0.0593769\pi\) | ||||
−0.982652 | + | 0.185458i | \(0.940623\pi\) | |||||||
\(972\) | 14358.3 | − | 26686.5i | 0.473811 | − | 0.880627i | ||||
\(973\) | 67534.2 | 2.22512 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 148768.i | − | 4.84919i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 90010.9 | 2.91166 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26953.9 | − | 5898.40i | 0.861386 | − | 0.188499i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 31021.8i | − | 0.988399i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20771.8 | −0.659829 | −0.329914 | − | 0.944011i | \(-0.607020\pi\) | ||||
−0.329914 | + | 0.944011i | \(0.607020\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.4.d.b.176.2 | yes | 4 | |
3.2 | odd | 2 | inner | 177.4.d.b.176.1 | ✓ | 4 | |
59.58 | odd | 2 | CM | 177.4.d.b.176.2 | yes | 4 | |
177.176 | even | 2 | inner | 177.4.d.b.176.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.d.b.176.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
177.4.d.b.176.1 | ✓ | 4 | 177.176 | even | 2 | inner | |
177.4.d.b.176.2 | yes | 4 | 1.1 | even | 1 | trivial | |
177.4.d.b.176.2 | yes | 4 | 59.58 | odd | 2 | CM |