Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2475,2,Mod(199,2475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2475.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2475.c (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: | \(19.7629745003\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 825) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(0.432320 + 0.432320i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2475.199 |
Dual form | 2475.2.c.q.199.6 |
$q$-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 \(\left(\mathbb{Z}/2475\mathbb{Z}\right)^\times\).
\(n\) | \(551\) | \(2026\) | \(2377\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.76156i | − 1.95272i | −0.216160 | − | 0.976358i | \(-0.569353\pi\) | ||||
0.216160 | − | 0.976358i | \(-0.430647\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.62620 | −2.81310 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.86464i | − 0.704768i | −0.935855 | − | 0.352384i | \(-0.885371\pi\) | ||||
0.935855 | − | 0.352384i | \(-0.114629\pi\) | |||||||
\(8\) | 10.0140i | 3.54047i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.62620i | 1.28308i | 0.767091 | + | 0.641538i | \(0.221703\pi\) | ||||
−0.767091 | + | 0.641538i | \(0.778297\pi\) | |||||||
\(14\) | −5.14931 | −1.37621 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.4017 | 4.10043 | ||||||||
\(17\) | 2.49084i | 0.604117i | 0.953289 | + | 0.302059i | \(0.0976738\pi\) | ||||
−0.953289 | + | 0.302059i | \(0.902326\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.38776 | 1.23604 | 0.618018 | − | 0.786164i | \(-0.287936\pi\) | ||||
0.618018 | + | 0.786164i | \(0.287936\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.76156i | 0.588766i | ||||||||
\(23\) | − 7.14931i | − 1.49073i | −0.666654 | − | 0.745367i | \(-0.732274\pi\) | ||||
0.666654 | − | 0.745367i | \(-0.267726\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 12.7755 | 2.50548 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 10.4908i | 1.98258i | ||||||||
\(29\) | −3.52311 | −0.654226 | −0.327113 | − | 0.944985i | \(-0.606076\pi\) | ||||
−0.327113 | + | 0.944985i | \(0.606076\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.62620 | 1.54931 | 0.774655 | − | 0.632384i | \(-0.217923\pi\) | ||||
0.774655 | + | 0.632384i | \(0.217923\pi\) | |||||||
\(32\) | − 25.2663i | − 4.46650i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.87859 | 1.17967 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.87859i | 1.45963i | 0.683644 | + | 0.729816i | \(0.260394\pi\) | ||||
−0.683644 | + | 0.729816i | \(0.739606\pi\) | |||||||
\(38\) | − 14.8786i | − 2.41363i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.761557 | 0.118935 | 0.0594676 | − | 0.998230i | \(-0.481060\pi\) | ||||
0.0594676 | + | 0.998230i | \(0.481060\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 7.40171i | − 1.12875i | −0.825519 | − | 0.564375i | \(-0.809117\pi\) | ||||
0.825519 | − | 0.564375i | \(-0.190883\pi\) | |||||||
\(44\) | 5.62620 | 0.848181 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −19.7432 | −2.91098 | ||||||||
\(47\) | − 0.373802i | − 0.0545246i | −0.999628 | − | 0.0272623i | \(-0.991321\pi\) | ||||
0.999628 | − | 0.0272623i | \(-0.00867894\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.52311 | 0.503302 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 26.0279i | − 3.60942i | ||||||||
\(53\) | 5.45856i | 0.749791i | 0.927067 | + | 0.374896i | \(0.122321\pi\) | ||||
−0.927067 | + | 0.374896i | \(0.877679\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 18.6724 | 2.49521 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.72928i | 1.27752i | ||||||||
\(59\) | 5.14931 | 0.670383 | 0.335192 | − | 0.942150i | \(-0.391199\pi\) | ||||
0.335192 | + | 0.942150i | \(0.391199\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.42003 | 0.565927 | 0.282963 | − | 0.959131i | \(-0.408682\pi\) | ||||
0.282963 | + | 0.959131i | \(0.408682\pi\) | |||||||
\(62\) | − 23.8217i | − 3.02536i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −36.9711 | −4.62138 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 11.9431i | − 1.45909i | −0.683934 | − | 0.729544i | \(-0.739732\pi\) | ||||
0.683934 | − | 0.729544i | \(-0.260268\pi\) | |||||||
\(68\) | − 14.0140i | − 1.69944i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.6262 | −1.37978 | −0.689888 | − | 0.723916i | \(-0.742340\pi\) | ||||
−0.689888 | + | 0.723916i | \(0.742340\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.77551i | 0.793014i | 0.918032 | + | 0.396507i | \(0.129778\pi\) | ||||
−0.918032 | + | 0.396507i | \(0.870222\pi\) | |||||||
\(74\) | 24.5187 | 2.85025 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −30.3126 | −3.47709 | ||||||||
\(77\) | 1.86464i | 0.212496i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.01395 | 0.676623 | 0.338311 | − | 0.941034i | \(-0.390144\pi\) | ||||
0.338311 | + | 0.941034i | \(0.390144\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 2.10308i | − 0.232247i | ||||||||
\(83\) | − 14.5693i | − 1.59919i | −0.600538 | − | 0.799597i | \(-0.705047\pi\) | ||||
0.600538 | − | 0.799597i | \(-0.294953\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −20.4402 | −2.20413 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 10.0140i | − 1.06749i | ||||||||
\(89\) | 9.04623 | 0.958898 | 0.479449 | − | 0.877570i | \(-0.340836\pi\) | ||||
0.479449 | + | 0.877570i | \(0.340836\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.62620 | 0.904271 | ||||||||
\(92\) | 40.2234i | 4.19358i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.03228 | −0.106471 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 16.3169i | − 1.65673i | −0.560185 | − | 0.828367i | \(-0.689270\pi\) | ||||
0.560185 | − | 0.828367i | \(-0.310730\pi\) | |||||||
\(98\) | − 9.72928i | − 0.982806i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.03228 | 0.102715 | 0.0513576 | − | 0.998680i | \(-0.483645\pi\) | ||||
0.0513576 | + | 0.998680i | \(0.483645\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.04623i | 0.300154i | 0.988674 | + | 0.150077i | \(0.0479521\pi\) | ||||
−0.988674 | + | 0.150077i | \(0.952048\pi\) | |||||||
\(104\) | −46.3265 | −4.54269 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.0741 | 1.46413 | ||||||||
\(107\) | − 8.50479i | − 0.822189i | −0.911593 | − | 0.411095i | \(-0.865147\pi\) | ||||
0.911593 | − | 0.411095i | \(-0.134853\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.14931 | 0.588997 | 0.294499 | − | 0.955652i | \(-0.404847\pi\) | ||||
0.294499 | + | 0.955652i | \(0.404847\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 30.5833i | − 2.88985i | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 19.8217 | 1.84040 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 14.2201i | − 1.30907i | ||||||||
\(119\) | 4.64452 | 0.425762 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − 12.2062i | − 1.10509i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −48.5327 | −4.35837 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.26635i | 0.822256i | 0.911578 | + | 0.411128i | \(0.134865\pi\) | ||||
−0.911578 | + | 0.411128i | \(0.865135\pi\) | |||||||
\(128\) | 51.5650i | 4.55774i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.06455 | −0.355121 | −0.177561 | − | 0.984110i | \(-0.556821\pi\) | ||||
−0.177561 | + | 0.984110i | \(0.556821\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 10.0462i | − 0.871119i | ||||||||
\(134\) | −32.9817 | −2.84918 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −24.9431 | −2.13886 | ||||||||
\(137\) | 5.93545i | 0.507100i | 0.967322 | + | 0.253550i | \(0.0815982\pi\) | ||||
−0.967322 | + | 0.253550i | \(0.918402\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.71096 | −0.569216 | −0.284608 | − | 0.958644i | \(-0.591863\pi\) | ||||
−0.284608 | + | 0.958644i | \(0.591863\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 32.1064i | 2.69431i | ||||||||
\(143\) | − 4.62620i | − 0.386862i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 18.7110 | 1.54853 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 49.9527i | − 4.10609i | ||||||||
\(149\) | 5.74324 | 0.470504 | 0.235252 | − | 0.971934i | \(-0.424408\pi\) | ||||
0.235252 | + | 0.971934i | \(0.424408\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.5616 | 0.859495 | 0.429747 | − | 0.902949i | \(-0.358603\pi\) | ||||
0.429747 | + | 0.902949i | \(0.358603\pi\) | |||||||
\(152\) | 53.9527i | 4.37614i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.14931 | 0.414943 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3.10308i | − 0.247653i | −0.992304 | − | 0.123827i | \(-0.960483\pi\) | ||||
0.992304 | − | 0.123827i | \(-0.0395166\pi\) | |||||||
\(158\) | − 16.6079i | − 1.32125i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.3309 | −1.05062 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.6724i | 1.22756i | 0.789477 | + | 0.613780i | \(0.210352\pi\) | ||||
−0.789477 | + | 0.613780i | \(0.789648\pi\) | |||||||
\(164\) | −4.28467 | −0.334577 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −40.2341 | −3.12277 | ||||||||
\(167\) | − 8.98168i | − 0.695023i | −0.937676 | − | 0.347512i | \(-0.887027\pi\) | ||||
0.937676 | − | 0.347512i | \(-0.112973\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.40171 | −0.646285 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 41.6435i | 3.17529i | ||||||||
\(173\) | 11.5092i | 0.875025i | 0.899212 | + | 0.437513i | \(0.144140\pi\) | ||||
−0.899212 | + | 0.437513i | \(0.855860\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.4017 | −1.23633 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 24.9817i | − 1.87246i | ||||||||
\(179\) | 10.3738 | 0.775374 | 0.387687 | − | 0.921791i | \(-0.373274\pi\) | ||||
0.387687 | + | 0.921791i | \(0.373274\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.66473 | −0.198068 | −0.0990339 | − | 0.995084i | \(-0.531575\pi\) | ||||
−0.0990339 | + | 0.995084i | \(0.531575\pi\) | |||||||
\(182\) | − 23.8217i | − 1.76578i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 71.5929 | 5.27790 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.49084i | − 0.182148i | ||||||||
\(188\) | 2.10308i | 0.153383i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.6724 | −1.06166 | −0.530830 | − | 0.847478i | \(-0.678120\pi\) | ||||
−0.530830 | + | 0.847478i | \(0.678120\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.10308i | 0.367328i | 0.982989 | + | 0.183664i | \(0.0587958\pi\) | ||||
−0.982989 | + | 0.183664i | \(0.941204\pi\) | |||||||
\(194\) | −45.0602 | −3.23513 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −19.8217 | −1.41584 | ||||||||
\(197\) | 3.74324i | 0.266694i | 0.991069 | + | 0.133347i | \(0.0425725\pi\) | ||||
−0.991069 | + | 0.133347i | \(0.957427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.08476 | 0.573114 | 0.286557 | − | 0.958063i | \(-0.407489\pi\) | ||||
0.286557 | + | 0.958063i | \(0.407489\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 2.85069i | − 0.200574i | ||||||||
\(203\) | 6.56934i | 0.461077i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.41233 | 0.586115 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 75.8776i | 5.26116i | ||||||||
\(209\) | −5.38776 | −0.372679 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9431 | −1.09757 | −0.548786 | − | 0.835963i | \(-0.684910\pi\) | ||||
−0.548786 | + | 0.835963i | \(0.684910\pi\) | |||||||
\(212\) | − 30.7110i | − 2.10924i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −23.4865 | −1.60550 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 16.0848i | − 1.09190i | ||||||||
\(218\) | − 16.9817i | − 1.15014i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.5231 | −0.775129 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 22.1772i | − 1.48510i | −0.669793 | − | 0.742548i | \(-0.733617\pi\) | ||||
0.669793 | − | 0.742548i | \(-0.266383\pi\) | |||||||
\(224\) | −47.1127 | −3.14785 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.5693 | 1.10218 | ||||||||
\(227\) | 5.93545i | 0.393950i | 0.980409 | + | 0.196975i | \(0.0631117\pi\) | ||||
−0.980409 | + | 0.196975i | \(0.936888\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.31695 | 0.549599 | 0.274800 | − | 0.961502i | \(-0.411388\pi\) | ||||
0.274800 | + | 0.961502i | \(0.411388\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 35.2803i | − 2.31627i | ||||||||
\(233\) | − 28.5187i | − 1.86833i | −0.356848 | − | 0.934163i | \(-0.616148\pi\) | ||||
0.356848 | − | 0.934163i | \(-0.383852\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −28.9711 | −1.88585 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 12.8261i | − 0.831393i | ||||||||
\(239\) | 24.0925 | 1.55841 | 0.779206 | − | 0.626768i | \(-0.215623\pi\) | ||||
0.779206 | + | 0.626768i | \(0.215623\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.16763 | −0.332877 | −0.166438 | − | 0.986052i | \(-0.553227\pi\) | ||||
−0.166438 | + | 0.986052i | \(0.553227\pi\) | |||||||
\(242\) | − 2.76156i | − 0.177520i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −24.8680 | −1.59201 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.9248i | 1.58593i | ||||||||
\(248\) | 86.3823i | 5.48528i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.25240 | 0.584006 | 0.292003 | − | 0.956417i | \(-0.405678\pi\) | ||||
0.292003 | + | 0.956417i | \(0.405678\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.14931i | 0.449473i | ||||||||
\(254\) | 25.5896 | 1.60563 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 68.4575 | 4.27860 | ||||||||
\(257\) | − 25.2158i | − 1.57292i | −0.617644 | − | 0.786458i | \(-0.711913\pi\) | ||||
0.617644 | − | 0.786458i | \(-0.288087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.5554 | 1.02870 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.2245i | 0.693451i | ||||||||
\(263\) | − 5.45856i | − 0.336589i | −0.985737 | − | 0.168295i | \(-0.946174\pi\) | ||||
0.985737 | − | 0.168295i | \(-0.0538260\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −27.7432 | −1.70105 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 67.1945i | 4.10456i | ||||||||
\(269\) | 17.0741 | 1.04103 | 0.520514 | − | 0.853853i | \(-0.325740\pi\) | ||||
0.520514 | + | 0.853853i | \(0.325740\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.77988 | 0.594085 | 0.297043 | − | 0.954864i | \(-0.404000\pi\) | ||||
0.297043 | + | 0.954864i | \(0.404000\pi\) | |||||||
\(272\) | 40.8540i | 2.47714i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.3911 | 0.990221 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 5.91524i | − 0.355412i | −0.984084 | − | 0.177706i | \(-0.943132\pi\) | ||||
0.984084 | − | 0.177706i | \(-0.0568676\pi\) | |||||||
\(278\) | 18.5327i | 1.11152i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.76156 | 0.403361 | 0.201680 | − | 0.979451i | \(-0.435360\pi\) | ||||
0.201680 | + | 0.979451i | \(0.435360\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.81841i | 0.524200i | 0.965041 | + | 0.262100i | \(0.0844151\pi\) | ||||
−0.965041 | + | 0.262100i | \(0.915585\pi\) | |||||||
\(284\) | 65.4113 | 3.88145 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.7755 | −0.755432 | ||||||||
\(287\) | − 1.42003i | − 0.0838218i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.7957 | 0.635042 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 38.1204i | − 2.23083i | ||||||||
\(293\) | 30.4908i | 1.78129i | 0.454696 | + | 0.890647i | \(0.349748\pi\) | ||||
−0.454696 | + | 0.890647i | \(0.650252\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −88.9098 | −5.16778 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 15.8603i | − 0.918761i | ||||||||
\(299\) | 33.0741 | 1.91273 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.8015 | −0.795507 | ||||||||
\(302\) | − 29.1666i | − 1.67835i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 88.3684 | 5.06827 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 0.767815i | − 0.0438215i | −0.999760 | − | 0.0219107i | \(-0.993025\pi\) | ||||
0.999760 | − | 0.0219107i | \(-0.00697497\pi\) | |||||||
\(308\) | − 10.4908i | − 0.597771i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.8496 | 1.91944 | 0.959719 | − | 0.280963i | \(-0.0906538\pi\) | ||||
0.959719 | + | 0.280963i | \(0.0906538\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 8.11078i | − 0.458448i | −0.973374 | − | 0.229224i | \(-0.926381\pi\) | ||||
0.973374 | − | 0.229224i | \(-0.0736189\pi\) | |||||||
\(314\) | −8.56934 | −0.483596 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −33.8357 | −1.90341 | ||||||||
\(317\) | 8.06455i | 0.452950i | 0.974017 | + | 0.226475i | \(0.0727202\pi\) | ||||
−0.974017 | + | 0.226475i | \(0.927280\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.52311 | 0.197257 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 36.8140i | 2.05157i | ||||||||
\(323\) | 13.4200i | 0.746710i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 43.2803 | 2.39707 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.62620i | 0.421086i | ||||||||
\(329\) | −0.697006 | −0.0384272 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.4769 | 1.23544 | 0.617721 | − | 0.786398i | \(-0.288056\pi\) | ||||
0.617721 | + | 0.786398i | \(0.288056\pi\) | |||||||
\(332\) | 81.9700i | 4.49869i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24.8034 | −1.35718 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 6.32757i | − 0.344685i | −0.985037 | − | 0.172342i | \(-0.944866\pi\) | ||||
0.985037 | − | 0.172342i | \(-0.0551336\pi\) | |||||||
\(338\) | 23.2018i | 1.26201i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.62620 | −0.467135 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 19.6218i | − 1.05948i | ||||||||
\(344\) | 74.1204 | 3.99630 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 31.7832 | 1.70868 | ||||||||
\(347\) | − 0.178261i | − 0.00956954i | −0.999989 | − | 0.00478477i | \(-0.998477\pi\) | ||||
0.999989 | − | 0.00478477i | \(-0.00152305\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.7293 | 1.05608 | 0.528042 | − | 0.849218i | \(-0.322926\pi\) | ||||
0.528042 | + | 0.849218i | \(0.322926\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 25.2663i | 1.34670i | ||||||||
\(353\) | 19.5231i | 1.03911i | 0.854437 | + | 0.519555i | \(0.173902\pi\) | ||||
−0.854437 | + | 0.519555i | \(0.826098\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −50.8959 | −2.69748 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 28.6478i | − 1.51409i | ||||||||
\(359\) | 35.6926 | 1.88379 | 0.941893 | − | 0.335914i | \(-0.109045\pi\) | ||||
0.941893 | + | 0.335914i | \(0.109045\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.0279 | 0.527785 | ||||||||
\(362\) | 7.35881i | 0.386770i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −48.5327 | −2.54380 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 20.1127i | − 1.04987i | −0.851141 | − | 0.524936i | \(-0.824089\pi\) | ||||
0.851141 | − | 0.524936i | \(-0.175911\pi\) | |||||||
\(368\) | − 117.261i | − 6.11265i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.1783 | 0.528429 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 2.56165i | − 0.132637i | −0.997799 | − | 0.0663185i | \(-0.978875\pi\) | ||||
0.997799 | − | 0.0663185i | \(-0.0211253\pi\) | |||||||
\(374\) | −6.87859 | −0.355684 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.74324 | 0.193043 | ||||||||
\(377\) | − 16.2986i | − 0.839422i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.2601 | −1.19479 | −0.597395 | − | 0.801947i | \(-0.703798\pi\) | ||||
−0.597395 | + | 0.801947i | \(0.703798\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 40.5187i | 2.07312i | ||||||||
\(383\) | − 25.7938i | − 1.31800i | −0.752142 | − | 0.659002i | \(-0.770979\pi\) | ||||
0.752142 | − | 0.659002i | \(-0.229021\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.0925 | 0.717287 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 91.8024i | 4.66056i | ||||||||
\(389\) | 2.33527 | 0.118403 | 0.0592014 | − | 0.998246i | \(-0.481145\pi\) | ||||
0.0592014 | + | 0.998246i | \(0.481145\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.8078 | 0.900578 | ||||||||
\(392\) | 35.2803i | 1.78192i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.3372 | 0.520778 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 17.1955i | − 0.863019i | −0.902108 | − | 0.431510i | \(-0.857981\pi\) | ||||
0.902108 | − | 0.431510i | \(-0.142019\pi\) | |||||||
\(398\) | − 22.3265i | − 1.11913i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.5693 | 1.32681 | 0.663405 | − | 0.748261i | \(-0.269111\pi\) | ||||
0.663405 | + | 0.748261i | \(0.269111\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 39.9065i | 1.98788i | ||||||||
\(404\) | −5.80779 | −0.288948 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.1416 | 0.900353 | ||||||||
\(407\) | − 8.87859i | − 0.440096i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.4200 | 1.00971 | 0.504853 | − | 0.863205i | \(-0.331547\pi\) | ||||
0.504853 | + | 0.863205i | \(0.331547\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 17.1387i | − 0.844362i | ||||||||
\(413\) | − 9.60162i | − 0.472465i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 116.887 | 5.73086 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.8786i | 0.727736i | ||||||||
\(419\) | −13.5896 | −0.663893 | −0.331947 | − | 0.943298i | \(-0.607705\pi\) | ||||
−0.331947 | + | 0.943298i | \(0.607705\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.6175 | −1.93084 | −0.965418 | − | 0.260705i | \(-0.916045\pi\) | ||||
−0.965418 | + | 0.260705i | \(0.916045\pi\) | |||||||
\(422\) | 44.0279i | 2.14324i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −54.6618 | −2.65461 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 8.24177i | − 0.398847i | ||||||||
\(428\) | 47.8496i | 2.31290i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.56934 | 0.316434 | 0.158217 | − | 0.987404i | \(-0.449425\pi\) | ||||
0.158217 | + | 0.987404i | \(0.449425\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 36.4113i | − 1.74982i | −0.484290 | − | 0.874908i | \(-0.660922\pi\) | ||||
0.484290 | − | 0.874908i | \(-0.339078\pi\) | |||||||
\(434\) | −44.4190 | −2.13218 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −34.5972 | −1.65691 | ||||||||
\(437\) | − 38.5187i | − 1.84260i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.3878 | −1.21169 | −0.605846 | − | 0.795582i | \(-0.707165\pi\) | ||||
−0.605846 | + | 0.795582i | \(0.707165\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 31.8217i | 1.51361i | ||||||||
\(443\) | 20.9065i | 0.993298i | 0.867952 | + | 0.496649i | \(0.165436\pi\) | ||||
−0.867952 | + | 0.496649i | \(0.834564\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −61.2437 | −2.89997 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 68.9377i | 3.25700i | ||||||||
\(449\) | −34.9450 | −1.64916 | −0.824579 | − | 0.565747i | \(-0.808588\pi\) | ||||
−0.824579 | + | 0.565747i | \(0.808588\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.761557 | −0.0358603 | ||||||||
\(452\) | − 33.7572i | − 1.58780i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.3911 | 0.769272 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 7.31695i | − 0.342272i | −0.985247 | − | 0.171136i | \(-0.945256\pi\) | ||||
0.985247 | − | 0.171136i | \(-0.0547438\pi\) | |||||||
\(458\) | − 22.9677i | − 1.07321i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0279 | 0.653345 | 0.326672 | − | 0.945138i | \(-0.394073\pi\) | ||||
0.326672 | + | 0.945138i | \(0.394073\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 4.33527i | − 0.201477i | −0.994913 | − | 0.100739i | \(-0.967879\pi\) | ||||
0.994913 | − | 0.100739i | \(-0.0321206\pi\) | |||||||
\(464\) | −57.7851 | −2.68261 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −78.7561 | −3.64831 | ||||||||
\(467\) | − 3.70138i | − 0.171279i | −0.996326 | − | 0.0856396i | \(-0.972707\pi\) | ||||
0.996326 | − | 0.0856396i | \(-0.0272934\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.2697 | −1.02832 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 51.5650i | 2.37347i | ||||||||
\(473\) | 7.40171i | 0.340331i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −26.1310 | −1.19771 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 66.5327i | − 3.04313i | ||||||||
\(479\) | −22.8680 | −1.04486 | −0.522432 | − | 0.852681i | \(-0.674975\pi\) | ||||
−0.522432 | + | 0.852681i | \(0.674975\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.0741 | −1.87282 | ||||||||
\(482\) | 14.2707i | 0.650013i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.62620 | −0.255736 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 5.42962i | − 0.246039i | −0.992404 | − | 0.123020i | \(-0.960742\pi\) | ||||
0.992404 | − | 0.123020i | \(-0.0392578\pi\) | |||||||
\(488\) | 44.2620i | 2.00365i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.2803 | −0.960367 | −0.480183 | − | 0.877168i | \(-0.659430\pi\) | ||||
−0.480183 | + | 0.877168i | \(0.659430\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 8.77551i | − 0.395229i | ||||||||
\(494\) | 68.8313 | 3.09687 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 141.484 | 6.35284 | ||||||||
\(497\) | 21.6787i | 0.972422i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0077 | 0.716603 | 0.358301 | − | 0.933606i | \(-0.383356\pi\) | ||||
0.358301 | + | 0.933606i | \(0.383356\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 25.5510i | − 1.14040i | ||||||||
\(503\) | 12.0925i | 0.539176i | 0.962976 | + | 0.269588i | \(0.0868875\pi\) | ||||
−0.962976 | + | 0.269588i | \(0.913112\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 19.7432 | 0.877694 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 52.1343i | − 2.31309i | ||||||||
\(509\) | 14.7110 | 0.652052 | 0.326026 | − | 0.945361i | \(-0.394290\pi\) | ||||
0.326026 | + | 0.945361i | \(0.394290\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.6339 | 0.558891 | ||||||||
\(512\) | − 85.9194i | − 3.79714i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −69.6347 | −3.07146 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.373802i | 0.0164398i | ||||||||
\(518\) | − 45.7187i | − 2.00876i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.2803 | 0.757064 | 0.378532 | − | 0.925588i | \(-0.376429\pi\) | ||||
0.378532 | + | 0.925588i | \(0.376429\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.7326i | 1.86857i | 0.356532 | + | 0.934283i | \(0.383959\pi\) | ||||
−0.356532 | + | 0.934283i | \(0.616041\pi\) | |||||||
\(524\) | 22.8680 | 0.998992 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.0741 | −0.657264 | ||||||||
\(527\) | 21.4865i | 0.935965i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.1127 | −1.22229 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 56.5221i | 2.45054i | ||||||||
\(533\) | 3.52311i | 0.152603i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 119.598 | 5.16585 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 47.1512i | − 2.03283i | ||||||||
\(539\) | −3.52311 | −0.151751 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.69075 | 0.373644 | 0.186822 | − | 0.982394i | \(-0.440181\pi\) | ||||
0.186822 | + | 0.982394i | \(0.440181\pi\) | |||||||
\(542\) | − 27.0077i | − 1.16008i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 62.9344 | 2.69829 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.1064i | 1.88585i | 0.333000 | + | 0.942927i | \(0.391939\pi\) | ||||
−0.333000 | + | 0.942927i | \(0.608061\pi\) | |||||||
\(548\) | − 33.3940i | − 1.42652i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.9817 | −0.808647 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 11.2139i | − 0.476862i | ||||||||
\(554\) | −16.3353 | −0.694019 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 37.7572 | 1.60126 | ||||||||
\(557\) | − 7.69264i | − 0.325948i | −0.986630 | − | 0.162974i | \(-0.947891\pi\) | ||||
0.986630 | − | 0.162974i | \(-0.0521086\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.2418 | 1.44827 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 18.6724i | − 0.787649i | ||||||||
\(563\) | − 9.25240i | − 0.389942i | −0.980809 | − | 0.194971i | \(-0.937539\pi\) | ||||
0.980809 | − | 0.194971i | \(-0.0624613\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.3525 | 1.02361 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 116.424i | − 4.88505i | ||||||||
\(569\) | 4.96772 | 0.208258 | 0.104129 | − | 0.994564i | \(-0.466795\pi\) | ||||
0.104129 | + | 0.994564i | \(0.466795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.02021 | 0.251938 | 0.125969 | − | 0.992034i | \(-0.459796\pi\) | ||||
0.125969 | + | 0.992034i | \(0.459796\pi\) | |||||||
\(572\) | 26.0279i | 1.08828i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.92150 | −0.163680 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 8.25240i | − 0.343552i | −0.985136 | − | 0.171776i | \(-0.945050\pi\) | ||||
0.985136 | − | 0.171776i | \(-0.0549505\pi\) | |||||||
\(578\) | − 29.8130i | − 1.24006i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.1666 | −1.12706 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 5.45856i | − 0.226071i | ||||||||
\(584\) | −67.8496 | −2.80764 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 84.2022 | 3.47836 | ||||||||
\(587\) | − 11.4846i | − 0.474019i | −0.971507 | − | 0.237010i | \(-0.923833\pi\) | ||||
0.971507 | − | 0.237010i | \(-0.0761673\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 46.4758 | 1.91500 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 145.624i | 5.98511i | ||||||||
\(593\) | 39.0375i | 1.60308i | 0.597943 | + | 0.801539i | \(0.295985\pi\) | ||||
−0.597943 | + | 0.801539i | \(0.704015\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −32.3126 | −1.32357 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 91.3361i | − 3.73501i | ||||||||
\(599\) | −30.1589 | −1.23226 | −0.616130 | − | 0.787645i | \(-0.711300\pi\) | ||||
−0.616130 | + | 0.787645i | \(0.711300\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.1310 | 0.780369 | 0.390185 | − | 0.920737i | \(-0.372411\pi\) | ||||
0.390185 | + | 0.920737i | \(0.372411\pi\) | |||||||
\(602\) | 38.1137i | 1.55340i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −59.4219 | −2.41784 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 4.20617i | − 0.170723i | −0.996350 | − | 0.0853615i | \(-0.972795\pi\) | ||||
0.996350 | − | 0.0853615i | \(-0.0272045\pi\) | |||||||
\(608\) | − 136.129i | − 5.52076i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.72928 | 0.0699593 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.45856i | 0.220469i | 0.993906 | + | 0.110235i | \(0.0351602\pi\) | ||||
−0.993906 | + | 0.110235i | \(0.964840\pi\) | |||||||
\(614\) | −2.12036 | −0.0855709 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −18.6724 | −0.752334 | ||||||||
\(617\) | 30.1974i | 1.21570i | 0.794051 | + | 0.607851i | \(0.207968\pi\) | ||||
−0.794051 | + | 0.607851i | \(0.792032\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.1955 | −0.932308 | −0.466154 | − | 0.884704i | \(-0.654361\pi\) | ||||
−0.466154 | + | 0.884704i | \(0.654361\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 93.4777i | − 3.74812i | ||||||||
\(623\) | − 16.8680i | − 0.675801i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −22.3984 | −0.895219 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.4586i | 0.696673i | ||||||||
\(629\) | −22.1151 | −0.881789 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.19554 | −0.127212 | −0.0636062 | − | 0.997975i | \(-0.520260\pi\) | ||||
−0.0636062 | + | 0.997975i | \(0.520260\pi\) | |||||||
\(632\) | 60.2234i | 2.39556i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22.2707 | 0.884483 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.2986i | 0.645775i | ||||||||
\(638\) | − 9.72928i | − 0.385186i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.1974 | −1.11373 | −0.556866 | − | 0.830603i | \(-0.687996\pi\) | ||||
−0.556866 | + | 0.830603i | \(0.687996\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.9634i | 0.708406i | 0.935169 | + | 0.354203i | \(0.115248\pi\) | ||||
−0.935169 | + | 0.354203i | \(0.884752\pi\) | |||||||
\(644\) | 75.0023 | 2.95550 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 37.0602 | 1.45811 | ||||||||
\(647\) | − 40.9990i | − 1.61184i | −0.592028 | − | 0.805918i | \(-0.701672\pi\) | ||||
0.592028 | − | 0.805918i | \(-0.298328\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.14931 | −0.202128 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 88.1762i | − 3.45325i | ||||||||
\(653\) | − 11.6926i | − 0.457568i | −0.973477 | − | 0.228784i | \(-0.926525\pi\) | ||||
0.973477 | − | 0.228784i | \(-0.0734750\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 12.4908 | 0.487685 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.92482i | 0.0750374i | ||||||||
\(659\) | −1.72928 | −0.0673633 | −0.0336816 | − | 0.999433i | \(-0.510723\pi\) | ||||
−0.0336816 | + | 0.999433i | \(0.510723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.232185 | 0.00903096 | 0.00451548 | − | 0.999990i | \(-0.498563\pi\) | ||||
0.00451548 | + | 0.999990i | \(0.498563\pi\) | |||||||
\(662\) | − 62.0712i | − 2.41247i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 145.897 | 5.66189 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.1878i | 0.975277i | ||||||||
\(668\) | 50.5327i | 1.95517i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.42003 | −0.170633 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.5144i | 1.29188i | 0.763386 | + | 0.645942i | \(0.223535\pi\) | ||||
−0.763386 | + | 0.645942i | \(0.776465\pi\) | |||||||
\(674\) | −17.4740 | −0.673072 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 47.2697 | 1.81806 | ||||||||
\(677\) | − 13.0183i | − 0.500335i | −0.968203 | − | 0.250167i | \(-0.919514\pi\) | ||||
0.968203 | − | 0.250167i | \(-0.0804857\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.4252 | −1.16761 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 23.8217i | 0.912182i | ||||||||
\(683\) | 4.54333i | 0.173846i | 0.996215 | + | 0.0869228i | \(0.0277033\pi\) | ||||
−0.996215 | + | 0.0869228i | \(0.972297\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −54.1868 | −2.06886 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 121.401i | − 4.62836i | ||||||||
\(689\) | −25.2524 | −0.962040 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.8988 | −0.756986 | −0.378493 | − | 0.925604i | \(-0.623558\pi\) | ||||
−0.378493 | + | 0.925604i | \(0.623558\pi\) | |||||||
\(692\) | − 64.7528i | − 2.46153i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.492277 | −0.0186866 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.89692i | 0.0718508i | ||||||||
\(698\) | − 54.4835i | − 2.06223i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.8444 | 0.598436 | 0.299218 | − | 0.954185i | \(-0.403274\pi\) | ||||
0.299218 | + | 0.954185i | \(0.403274\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 47.8357i | 1.80416i | ||||||||
\(704\) | 36.9711 | 1.39340 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 53.9142 | 2.02909 | ||||||||
\(707\) | − 1.92482i | − 0.0723904i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.82174 | −0.331307 | −0.165654 | − | 0.986184i | \(-0.552973\pi\) | ||||
−0.165654 | + | 0.986184i | \(0.552973\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 90.5885i | 3.39495i | ||||||||
\(713\) | − 61.6714i | − 2.30961i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −58.3651 | −2.18120 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 98.5673i | − 3.67850i | ||||||||
\(719\) | 36.7668 | 1.37117 | 0.685585 | − | 0.727993i | \(-0.259547\pi\) | ||||
0.685585 | + | 0.727993i | \(0.259547\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.68012 | 0.211539 | ||||||||
\(722\) | − 27.6926i | − 1.03061i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.9923 | 0.557185 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.27261i | 0.195550i | 0.995209 | + | 0.0977751i | \(0.0311726\pi\) | ||||
−0.995209 | + | 0.0977751i | \(0.968827\pi\) | |||||||
\(728\) | 86.3823i | 3.20154i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.4365 | 0.681897 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.9508i | 1.40175i | 0.713286 | + | 0.700873i | \(0.247206\pi\) | ||||
−0.713286 | + | 0.700873i | \(0.752794\pi\) | |||||||
\(734\) | −55.5423 | −2.05010 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −180.637 | −6.65837 | ||||||||
\(737\) | 11.9431i | 0.439931i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.2943 | −1.37189 | −0.685946 | − | 0.727653i | \(-0.740611\pi\) | ||||
−0.685946 | + | 0.727653i | \(0.740611\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 28.1078i | − 1.03187i | ||||||||
\(743\) | − 22.5693i | − 0.827989i | −0.910279 | − | 0.413994i | \(-0.864133\pi\) | ||||
0.910279 | − | 0.413994i | \(-0.135867\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.07414 | −0.259002 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 14.0140i | 0.512401i | ||||||||
\(749\) | −15.8584 | −0.579453 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.55102 | −0.348522 | −0.174261 | − | 0.984700i | \(-0.555754\pi\) | ||||
−0.174261 | + | 0.984700i | \(0.555754\pi\) | |||||||
\(752\) | − 6.13099i | − 0.223574i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −45.0096 | −1.63915 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 30.3188i | − 1.10196i | −0.834519 | − | 0.550978i | \(-0.814255\pi\) | ||||
0.834519 | − | 0.550978i | \(-0.185745\pi\) | |||||||
\(758\) | 64.2341i | 2.33309i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.43066 | 0.0518613 | 0.0259306 | − | 0.999664i | \(-0.491745\pi\) | ||||
0.0259306 | + | 0.999664i | \(0.491745\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 11.4663i | − 0.415106i | ||||||||
\(764\) | 82.5500 | 2.98655 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −71.2311 | −2.57369 | ||||||||
\(767\) | 23.8217i | 0.860153i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.4017 | 1.27662 | 0.638309 | − | 0.769780i | \(-0.279634\pi\) | ||||
0.638309 | + | 0.769780i | \(0.279634\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 28.7110i | − 1.03333i | ||||||||
\(773\) | 13.4094i | 0.482303i | 0.970488 | + | 0.241151i | \(0.0775250\pi\) | ||||
−0.970488 | + | 0.241151i | \(0.922475\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 163.397 | 5.86562 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 6.44898i | − 0.231207i | ||||||||
\(779\) | 4.10308 | 0.147008 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.6262 | 0.416018 | ||||||||
\(782\) | − 49.1772i | − 1.75857i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 57.7851 | 2.06375 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.3232i | 1.33043i | 0.746653 | + | 0.665214i | \(0.231660\pi\) | ||||
−0.746653 | + | 0.665214i | \(0.768340\pi\) | |||||||
\(788\) | − 21.0602i | − 0.750238i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.1878 | 0.397794 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.4479i | 0.726128i | ||||||||
\(794\) | −47.4865 | −1.68523 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −45.4865 | −1.61223 | ||||||||
\(797\) | − 8.05581i | − 0.285352i | −0.989769 | − | 0.142676i | \(-0.954429\pi\) | ||||
0.989769 | − | 0.142676i | \(-0.0455706\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.931080 | 0.0329393 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 73.3728i | − 2.59088i | ||||||||
\(803\) | − 6.77551i | − 0.239103i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 110.204 | 3.88177 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.3372i | 0.363660i | ||||||||
\(809\) | −42.3771 | −1.48990 | −0.744950 | − | 0.667120i | \(-0.767527\pi\) | ||||
−0.744950 | + | 0.667120i | \(0.767527\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.3878 | −0.751026 | −0.375513 | − | 0.926817i | \(-0.622533\pi\) | ||||
−0.375513 | + | 0.926817i | \(0.622533\pi\) | |||||||
\(812\) | − 36.9604i | − 1.29706i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −24.5187 | −0.859382 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 39.8786i | − 1.39518i | ||||||||
\(818\) | − 56.3911i | − 1.97167i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.8776 | 1.67094 | 0.835469 | − | 0.549537i | \(-0.185196\pi\) | ||||
0.835469 | + | 0.549537i | \(0.185196\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.3555i | 0.570116i | 0.958510 | + | 0.285058i | \(0.0920129\pi\) | ||||
−0.958510 | + | 0.285058i | \(0.907987\pi\) | |||||||
\(824\) | −30.5048 | −1.06268 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −26.5154 | −0.922589 | ||||||||
\(827\) | − 44.7110i | − 1.55475i | −0.629036 | − | 0.777376i | \(-0.716550\pi\) | ||||
0.629036 | − | 0.777376i | \(-0.283450\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.5972 | 1.34054 | 0.670269 | − | 0.742118i | \(-0.266179\pi\) | ||||
0.670269 | + | 0.742118i | \(0.266179\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 171.035i | − 5.92959i | ||||||||
\(833\) | 8.77551i | 0.304053i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 30.3126 | 1.04838 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 37.5283i | 1.29639i | ||||||||
\(839\) | −0.710960 | −0.0245451 | −0.0122725 | − | 0.999925i | \(-0.503907\pi\) | ||||
−0.0122725 | + | 0.999925i | \(0.503907\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.5877 | −0.571988 | ||||||||
\(842\) | 109.406i | 3.77038i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 89.6993 | 3.08758 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1.86464i | − 0.0640698i | ||||||||
\(848\) | 89.5298i | 3.07446i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 63.4758 | 2.17592 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 52.7187i | 1.80505i | 0.430635 | + | 0.902526i | \(0.358290\pi\) | ||||
−0.430635 | + | 0.902526i | \(0.641710\pi\) | |||||||
\(854\) | −22.7601 | −0.778835 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 85.1666 | 2.91093 | ||||||||
\(857\) | 16.7124i | 0.570885i | 0.958396 | + | 0.285442i | \(0.0921405\pi\) | ||||
−0.958396 | + | 0.285442i | \(0.907859\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.9142 | 1.43009 | 0.715047 | − | 0.699076i | \(-0.246405\pi\) | ||||
0.715047 | + | 0.699076i | \(0.246405\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 18.1416i | − 0.617906i | ||||||||
\(863\) | 41.4219i | 1.41002i | 0.709198 | + | 0.705009i | \(0.249057\pi\) | ||||
−0.709198 | + | 0.705009i | \(0.750943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −100.552 | −3.41689 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 90.4961i | 3.07164i | ||||||||
\(869\) | −6.01395 | −0.204009 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.2514 | 1.87212 | ||||||||
\(872\) | 61.5789i | 2.08533i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −106.372 | −3.59808 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.0848i | 0.408073i | 0.978963 | + | 0.204037i | \(0.0654062\pi\) | ||||
−0.978963 | + | 0.204037i | \(0.934594\pi\) | |||||||
\(878\) | 70.1097i | 2.36609i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.8130 | 1.07181 | 0.535904 | − | 0.844279i | \(-0.319971\pi\) | ||||
0.535904 | + | 0.844279i | \(0.319971\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 20.9894i | − 0.706349i | −0.935558 | − | 0.353174i | \(-0.885102\pi\) | ||||
0.935558 | − | 0.353174i | \(-0.114898\pi\) | |||||||
\(884\) | 64.8313 | 2.18051 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 57.7345 | 1.93963 | ||||||||
\(887\) | 49.2032i | 1.65208i | 0.563609 | + | 0.826042i | \(0.309412\pi\) | ||||
−0.563609 | + | 0.826042i | \(0.690588\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.2784 | 0.579499 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 124.773i | 4.17772i | ||||||||
\(893\) | − 2.01395i | − 0.0673944i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 96.1502 | 3.21215 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 96.5027i | 3.22034i | ||||||||
\(899\) | −30.3911 | −1.01360 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.5964 | −0.452962 | ||||||||
\(902\) | 2.10308i | 0.0700250i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −60.0837 | −1.99835 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.8526i | 0.825216i | 0.910909 | + | 0.412608i | \(0.135382\pi\) | ||||
−0.910909 | + | 0.412608i | \(0.864618\pi\) | |||||||
\(908\) | − 33.3940i | − 1.10822i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.4758 | −1.50668 | −0.753341 | − | 0.657630i | \(-0.771559\pi\) | ||||
−0.753341 | + | 0.657630i | \(0.771559\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.5693i | 0.482175i | ||||||||
\(914\) | −20.2062 | −0.668361 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −46.7928 | −1.54608 | ||||||||
\(917\) | 7.57893i | 0.250278i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.7355 | 0.519068 | 0.259534 | − | 0.965734i | \(-0.416431\pi\) | ||||
0.259534 | + | 0.965734i | \(0.416431\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 38.7389i | − 1.27580i | ||||||||
\(923\) | − 53.7851i | − 1.77036i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −11.9721 | −0.393427 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 89.0162i | 2.92210i | ||||||||
\(929\) | −2.06455 | −0.0677357 | −0.0338679 | − | 0.999426i | \(-0.510783\pi\) | ||||
−0.0338679 | + | 0.999426i | \(0.510783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.9817 | 0.622099 | ||||||||
\(932\) | 160.452i | 5.25578i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.2216 | −0.334460 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 40.1493i | − 1.31162i | −0.754926 | − | 0.655810i | \(-0.772327\pi\) | ||||
0.754926 | − | 0.655810i | \(-0.227673\pi\) | |||||||
\(938\) | 61.4990i | 2.00801i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.4050 | −0.860780 | −0.430390 | − | 0.902643i | \(-0.641624\pi\) | ||||
−0.430390 | + | 0.902643i | \(0.641624\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 5.44461i | − 0.177301i | ||||||||
\(944\) | 84.4575 | 2.74886 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.4402 | 0.664570 | ||||||||
\(947\) | 8.67243i | 0.281816i | 0.990023 | + | 0.140908i | \(0.0450022\pi\) | ||||
−0.990023 | + | 0.140908i | \(0.954998\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.3449 | −1.01750 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 46.5100i | 1.50740i | ||||||||
\(953\) | 26.8540i | 0.869887i | 0.900458 | + | 0.434943i | \(0.143232\pi\) | ||||
−0.900458 | + | 0.434943i | \(0.856768\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −135.549 | −4.38397 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 63.1512i | 2.04032i | ||||||||
\(959\) | 11.0675 | 0.357388 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43.4113 | 1.40036 | ||||||||
\(962\) | 113.429i | 3.65708i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 29.0741 | 0.936415 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55.8496i | 1.79600i | 0.439992 | + | 0.898002i | \(0.354981\pi\) | ||||
−0.439992 | + | 0.898002i | \(0.645019\pi\) | |||||||
\(968\) | 10.0140i | 0.321861i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.0664 | −0.964878 | −0.482439 | − | 0.875930i | \(-0.660249\pi\) | ||||
−0.482439 | + | 0.875930i | \(0.660249\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.5135i | 0.401165i | ||||||||
\(974\) | −14.9942 | −0.480445 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 72.4961 | 2.32054 | ||||||||
\(977\) | 15.7014i | 0.502331i | 0.967944 | + | 0.251166i | \(0.0808139\pi\) | ||||
−0.967944 | + | 0.251166i | \(0.919186\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.04623 | −0.289119 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 58.7668i | 1.87532i | ||||||||
\(983\) | 51.9894i | 1.65820i | 0.559098 | + | 0.829102i | \(0.311148\pi\) | ||||
−0.559098 | + | 0.829102i | \(0.688852\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −24.2341 | −0.771770 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 140.232i | − 4.46137i | ||||||||
\(989\) | −52.9171 | −1.68267 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.6445 | 0.878157 | 0.439079 | − | 0.898449i | \(-0.355305\pi\) | ||||
0.439079 | + | 0.898449i | \(0.355305\pi\) | |||||||
\(992\) | − 217.953i | − 6.92000i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 59.8669 | 1.89886 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 40.5048i | − 1.28280i | −0.767207 | − | 0.641400i | \(-0.778354\pi\) | ||||
0.767207 | − | 0.641400i | \(-0.221646\pi\) | |||||||
\(998\) | − 44.2062i | − 1.39932i | ||||||||
\(999\) | 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 | 2475.2.c.q.199.1 | 6 | ||
3.2 | odd | 2 | 825.2.c.f.199.6 | 6 | |||
5.2 | odd | 4 | 2475.2.a.bd.1.3 | 3 | |||
5.3 | odd | 4 | 2475.2.a.z.1.1 | 3 | |||
5.4 | even | 2 | inner | 2475.2.c.q.199.6 | 6 | ||
15.2 | even | 4 | 825.2.a.i.1.1 | ✓ | 3 | ||
15.8 | even | 4 | 825.2.a.m.1.3 | yes | 3 | ||
15.14 | odd | 2 | 825.2.c.f.199.1 | 6 | |||
165.32 | odd | 4 | 9075.2.a.cj.1.3 | 3 | |||
165.98 | odd | 4 | 9075.2.a.cd.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.a.i.1.1 | ✓ | 3 | 15.2 | even | 4 | ||
825.2.a.m.1.3 | yes | 3 | 15.8 | even | 4 | ||
825.2.c.f.199.1 | 6 | 15.14 | odd | 2 | |||
825.2.c.f.199.6 | 6 | 3.2 | odd | 2 | |||
2475.2.a.z.1.1 | 3 | 5.3 | odd | 4 | |||
2475.2.a.bd.1.3 | 3 | 5.2 | odd | 4 | |||
2475.2.c.q.199.1 | 6 | 1.1 | even | 1 | trivial | ||
2475.2.c.q.199.6 | 6 | 5.4 | even | 2 | inner | ||
9075.2.a.cd.1.1 | 3 | 165.98 | odd | 4 | |||
9075.2.a.cj.1.3 | 3 | 165.32 | odd | 4 |