Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2025,2,Mod(649,2025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2025.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2025 = 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2025.b (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: | \(16.1697064093\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.34810603776.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 12x^{6} + 42x^{4} + 49x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 225) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.2 | ||
Root | \(-1.63372i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2025.649 |
Dual form | 2025.2.b.o.649.7 |
$q$-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 \(\left(\mathbb{Z}/2025\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(1702\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.63372i | − 1.15522i | −0.816314 | − | 0.577608i | \(-0.803986\pi\) | ||||
0.816314 | − | 0.577608i | \(-0.196014\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.669052 | −0.334526 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.505348i | 0.191004i | 0.995429 | + | 0.0955019i | \(0.0304456\pi\) | ||||
−0.995429 | + | 0.0955019i | \(0.969554\pi\) | |||||||
\(8\) | − 2.17440i | − 0.768767i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.10020 | −0.934746 | −0.467373 | − | 0.884060i | \(-0.654800\pi\) | ||||
−0.467373 | + | 0.884060i | \(0.654800\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.23927i | 1.73046i | 0.501372 | + | 0.865232i | \(0.332829\pi\) | ||||
−0.501372 | + | 0.865232i | \(0.667171\pi\) | |||||||
\(14\) | 0.825599 | 0.220651 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.89047 | −1.22262 | ||||||||
\(17\) | 6.10020i | 1.47952i | 0.672873 | + | 0.739758i | \(0.265060\pi\) | ||||
−0.672873 | + | 0.739758i | \(0.734940\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.57022 | 1.27790 | 0.638948 | − | 0.769250i | \(-0.279370\pi\) | ||||
0.638948 | + | 0.769250i | \(0.279370\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.06487i | 1.07983i | ||||||||
\(23\) | − 3.82560i | − 0.797693i | −0.917018 | − | 0.398846i | \(-0.869411\pi\) | ||||
0.917018 | − | 0.398846i | \(-0.130589\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 10.1932 | 1.99906 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 0.338104i | − 0.0638957i | ||||||||
\(29\) | 2.45932 | 0.456685 | 0.228342 | − | 0.973581i | \(-0.426669\pi\) | ||||
0.228342 | + | 0.973581i | \(0.426669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.22858 | 0.759475 | 0.379738 | − | 0.925094i | \(-0.376014\pi\) | ||||
0.379738 | + | 0.925094i | \(0.376014\pi\) | |||||||
\(32\) | 3.64088i | 0.643623i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.96604 | 1.70916 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.72677i | 1.10587i | 0.833223 | + | 0.552937i | \(0.186493\pi\) | ||||
−0.833223 | + | 0.552937i | \(0.813507\pi\) | |||||||
\(38\) | − 9.10020i | − 1.47625i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.44185 | 0.849874 | 0.424937 | − | 0.905223i | \(-0.360296\pi\) | ||||
0.424937 | + | 0.905223i | \(0.360296\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.32741i | − 0.202428i | −0.994865 | − | 0.101214i | \(-0.967727\pi\) | ||||
0.994865 | − | 0.101214i | \(-0.0322726\pi\) | |||||||
\(44\) | 2.07420 | 0.312697 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.24997 | −0.921508 | ||||||||
\(47\) | 3.70792i | 0.540856i | 0.962740 | + | 0.270428i | \(0.0871652\pi\) | ||||
−0.962740 | + | 0.270428i | \(0.912835\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.74462 | 0.963518 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 4.17440i | − 0.578885i | ||||||||
\(53\) | 2.54205i | 0.349177i | 0.984641 | + | 0.174589i | \(0.0558596\pi\) | ||||
−0.984641 | + | 0.174589i | \(0.944140\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.09883 | 0.146837 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 4.01785i | − 0.527570i | ||||||||
\(59\) | 2.88232 | 0.375246 | 0.187623 | − | 0.982241i | \(-0.439922\pi\) | ||||
0.187623 | + | 0.982241i | \(0.439922\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.84345 | −0.364067 | −0.182033 | − | 0.983292i | \(-0.558268\pi\) | ||||
−0.182033 | + | 0.983292i | \(0.558268\pi\) | |||||||
\(62\) | − 6.90833i | − 0.877358i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.83276 | −0.479095 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.40652i | 0.294003i | 0.989136 | + | 0.147002i | \(0.0469622\pi\) | ||||
−0.989136 | + | 0.147002i | \(0.953038\pi\) | |||||||
\(68\) | − 4.08135i | − 0.494937i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.54205 | −0.657720 | −0.328860 | − | 0.944379i | \(-0.606664\pi\) | ||||
−0.328860 | + | 0.944379i | \(0.606664\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.7988i | 1.38095i | 0.723359 | + | 0.690473i | \(0.242597\pi\) | ||||
−0.723359 | + | 0.690473i | \(0.757403\pi\) | |||||||
\(74\) | 10.9897 | 1.27752 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.72677 | −0.427490 | ||||||||
\(77\) | − 1.56668i | − 0.178540i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.40298 | −0.382865 | −0.191433 | − | 0.981506i | \(-0.561313\pi\) | ||||
−0.191433 | + | 0.981506i | \(0.561313\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 8.89047i | − 0.981789i | ||||||||
\(83\) | − 13.9012i | − 1.52585i | −0.646486 | − | 0.762926i | \(-0.723762\pi\) | ||||
0.646486 | − | 0.762926i | \(-0.276238\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.16862 | −0.233848 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.74108i | 0.718602i | ||||||||
\(89\) | 3.38513 | 0.358823 | 0.179411 | − | 0.983774i | \(-0.442581\pi\) | ||||
0.179411 | + | 0.983774i | \(0.442581\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.15301 | −0.330525 | ||||||||
\(92\) | 2.55953i | 0.266849i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.05772 | 0.624806 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0756i | 1.12455i | 0.826949 | + | 0.562277i | \(0.190074\pi\) | ||||
−0.826949 | + | 0.562277i | \(0.809926\pi\) | |||||||
\(98\) | − 11.0188i | − 1.11307i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.3690 | 1.72828 | 0.864141 | − | 0.503249i | \(-0.167862\pi\) | ||||
0.864141 | + | 0.503249i | \(0.167862\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 0.832756i | − 0.0820539i | −0.999158 | − | 0.0410269i | \(-0.986937\pi\) | ||||
0.999158 | − | 0.0410269i | \(-0.0130629\pi\) | |||||||
\(104\) | 13.5667 | 1.33032 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.15301 | 0.403376 | ||||||||
\(107\) | 11.0684i | 1.07002i | 0.844844 | + | 0.535012i | \(0.179693\pi\) | ||||
−0.844844 | + | 0.535012i | \(0.820307\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.65836 | 0.446190 | 0.223095 | − | 0.974797i | \(-0.428384\pi\) | ||||
0.223095 | + | 0.974797i | \(0.428384\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 2.47139i | − 0.233525i | ||||||||
\(113\) | − 11.9942i | − 1.12832i | −0.825665 | − | 0.564160i | \(-0.809200\pi\) | ||||
0.825665 | − | 0.564160i | \(-0.190800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.64542 | −0.152773 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 4.70892i | − 0.433491i | ||||||||
\(119\) | −3.08273 | −0.282593 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.38874 | −0.126249 | ||||||||
\(122\) | 4.64542i | 0.420576i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.82914 | −0.254064 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.22858i | 0.286490i | 0.989687 | + | 0.143245i | \(0.0457537\pi\) | ||||
−0.989687 | + | 0.143245i | \(0.954246\pi\) | |||||||
\(128\) | 13.5434i | 1.19708i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.38513 | 0.819982 | 0.409991 | − | 0.912090i | \(-0.365532\pi\) | ||||
0.409991 | + | 0.912090i | \(0.365532\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.81490i | 0.244083i | ||||||||
\(134\) | 3.93159 | 0.339637 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.2643 | 1.13740 | ||||||||
\(137\) | 2.30955i | 0.197319i | 0.995121 | + | 0.0986593i | \(0.0314554\pi\) | ||||
−0.995121 | + | 0.0986593i | \(0.968545\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.8940 | −0.924018 | −0.462009 | − | 0.886875i | \(-0.652871\pi\) | ||||
−0.462009 | + | 0.886875i | \(0.652871\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.05418i | 0.759810i | ||||||||
\(143\) | − 19.3430i | − 1.61754i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 19.2760 | 1.59529 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 4.50056i | − 0.369944i | ||||||||
\(149\) | −16.3430 | −1.33887 | −0.669436 | − | 0.742870i | \(-0.733464\pi\) | ||||
−0.669436 | + | 0.742870i | \(0.733464\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.7827 | 1.85403 | 0.927015 | − | 0.375025i | \(-0.122366\pi\) | ||||
0.927015 | + | 0.375025i | \(0.122366\pi\) | |||||||
\(152\) | − 12.1119i | − 0.982404i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.55953 | −0.206252 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 12.4607i | − 0.994472i | −0.867615 | − | 0.497236i | \(-0.834348\pi\) | ||||
0.867615 | − | 0.497236i | \(-0.165652\pi\) | |||||||
\(158\) | 5.55953i | 0.442292i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.93326 | 0.152362 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 7.57384i | − 0.593229i | −0.954997 | − | 0.296614i | \(-0.904142\pi\) | ||||
0.954997 | − | 0.296614i | \(-0.0958576\pi\) | |||||||
\(164\) | −3.64088 | −0.284305 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −22.7107 | −1.76269 | ||||||||
\(167\) | − 2.97674i | − 0.230347i | −0.993345 | − | 0.115174i | \(-0.963258\pi\) | ||||
0.993345 | − | 0.115174i | \(-0.0367424\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −25.9285 | −1.99450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.888105i | 0.0677174i | ||||||||
\(173\) | 15.8530i | 1.20528i | 0.798013 | + | 0.602640i | \(0.205884\pi\) | ||||
−0.798013 | + | 0.602640i | \(0.794116\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.1615 | 1.14284 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 5.53036i | − 0.414518i | ||||||||
\(179\) | 17.0841 | 1.27693 | 0.638463 | − | 0.769653i | \(-0.279571\pi\) | ||||
0.638463 | + | 0.769653i | \(0.279571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3690 | 0.993712 | 0.496856 | − | 0.867833i | \(-0.334488\pi\) | ||||
0.496856 | + | 0.867833i | \(0.334488\pi\) | |||||||
\(182\) | 5.15114i | 0.381828i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.31839 | −0.613240 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 18.9119i | − 1.38297i | ||||||||
\(188\) | − 2.48079i | − 0.180930i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.3372 | −1.83334 | −0.916669 | − | 0.399647i | \(-0.869133\pi\) | ||||
−0.916669 | + | 0.399647i | \(0.869133\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 9.55953i | − 0.688110i | −0.938950 | − | 0.344055i | \(-0.888199\pi\) | ||||
0.938950 | − | 0.344055i | \(-0.111801\pi\) | |||||||
\(194\) | 18.0944 | 1.29910 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.51250 | −0.322322 | ||||||||
\(197\) | − 2.06841i | − 0.147368i | −0.997282 | − | 0.0736842i | \(-0.976524\pi\) | ||||
0.997282 | − | 0.0736842i | \(-0.0234757\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.0970 | −0.928419 | −0.464210 | − | 0.885725i | \(-0.653662\pi\) | ||||
−0.464210 | + | 0.885725i | \(0.653662\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 28.3762i | − 1.99654i | ||||||||
\(203\) | 1.24281i | 0.0872285i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.36049 | −0.0947900 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 30.5130i | − 2.11570i | ||||||||
\(209\) | −17.2688 | −1.19451 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.1119 | 0.764974 | 0.382487 | − | 0.923961i | \(-0.375068\pi\) | ||||
0.382487 | + | 0.923961i | \(0.375068\pi\) | |||||||
\(212\) | − 1.70076i | − 0.116809i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.0827 | 1.23611 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.13690i | 0.145063i | ||||||||
\(218\) | − 7.61046i | − 0.515446i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −38.0608 | −2.56025 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3.89401i | − 0.260762i | −0.991464 | − | 0.130381i | \(-0.958380\pi\) | ||||
0.991464 | − | 0.130381i | \(-0.0416201\pi\) | |||||||
\(224\) | −1.83991 | −0.122934 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.5952 | −1.30346 | ||||||||
\(227\) | 12.8081i | 0.850105i | 0.905169 | + | 0.425053i | \(0.139744\pi\) | ||||
−0.905169 | + | 0.425053i | \(0.860256\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.65295 | −0.439639 | −0.219820 | − | 0.975541i | \(-0.570547\pi\) | ||||
−0.219820 | + | 0.975541i | \(0.570547\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 5.34755i | − 0.351084i | ||||||||
\(233\) | 3.65836i | 0.239667i | 0.992794 | + | 0.119833i | \(0.0382360\pi\) | ||||
−0.992794 | + | 0.119833i | \(0.961764\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.92842 | −0.125530 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.03632i | 0.326456i | ||||||||
\(239\) | −15.6915 | −1.01500 | −0.507500 | − | 0.861652i | \(-0.669430\pi\) | ||||
−0.507500 | + | 0.861652i | \(0.669430\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.2250 | 0.723063 | 0.361532 | − | 0.932360i | \(-0.382254\pi\) | ||||
0.361532 | + | 0.932360i | \(0.382254\pi\) | |||||||
\(242\) | 2.26882i | 0.145845i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.90242 | 0.121790 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.7541i | 2.21135i | ||||||||
\(248\) | − 9.19462i | − 0.583859i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.94042 | −0.438075 | −0.219038 | − | 0.975716i | \(-0.570292\pi\) | ||||
−0.219038 | + | 0.975716i | \(0.570292\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.8601i | 0.745640i | ||||||||
\(254\) | 5.27460 | 0.330958 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.4607 | 0.903794 | ||||||||
\(257\) | 18.3327i | 1.14356i | 0.820406 | + | 0.571781i | \(0.193747\pi\) | ||||
−0.820406 | + | 0.571781i | \(0.806253\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.39936 | −0.211226 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 15.3327i | − 0.947257i | ||||||||
\(263\) | − 16.0766i | − 0.991328i | −0.868514 | − | 0.495664i | \(-0.834925\pi\) | ||||
0.868514 | − | 0.495664i | \(-0.165075\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.59877 | 0.281969 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 1.61009i | − 0.0983517i | ||||||||
\(269\) | −18.2004 | −1.10970 | −0.554849 | − | 0.831951i | \(-0.687224\pi\) | ||||
−0.554849 | + | 0.831951i | \(0.687224\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.48571 | −0.150996 | −0.0754979 | − | 0.997146i | \(-0.524055\pi\) | ||||
−0.0754979 | + | 0.997146i | \(0.524055\pi\) | |||||||
\(272\) | − 29.8329i | − 1.80888i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.77317 | 0.227946 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 7.66726i | − 0.460681i | −0.973110 | − | 0.230341i | \(-0.926016\pi\) | ||||
0.973110 | − | 0.230341i | \(-0.0739840\pi\) | |||||||
\(278\) | 17.7978i | 1.06744i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.273230 | −0.0162996 | −0.00814978 | − | 0.999967i | \(-0.502594\pi\) | ||||
−0.00814978 | + | 0.999967i | \(0.502594\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.37089i | 0.200379i | 0.994968 | + | 0.100189i | \(0.0319448\pi\) | ||||
−0.994968 | + | 0.100189i | \(0.968055\pi\) | |||||||
\(284\) | 3.70792 | 0.220025 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −31.6011 | −1.86861 | ||||||||
\(287\) | 2.75003i | 0.162329i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.2125 | −1.18897 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 7.89401i | − 0.461962i | ||||||||
\(293\) | 5.64404i | 0.329728i | 0.986316 | + | 0.164864i | \(0.0527186\pi\) | ||||
−0.986316 | + | 0.164864i | \(0.947281\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 14.6267 | 0.850159 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 26.7000i | 1.54669i | ||||||||
\(299\) | 23.8690 | 1.38038 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.670803 | 0.0386645 | ||||||||
\(302\) | − 37.2206i | − 2.14181i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −27.2410 | −1.56238 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 5.44105i | − 0.310537i | −0.987872 | − | 0.155269i | \(-0.950376\pi\) | ||||
0.987872 | − | 0.155269i | \(-0.0496243\pi\) | |||||||
\(308\) | 1.04819i | 0.0597263i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.0797 | 1.08191 | 0.540955 | − | 0.841052i | \(-0.318063\pi\) | ||||
0.540955 | + | 0.841052i | \(0.318063\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 9.14231i | − 0.516754i | −0.966044 | − | 0.258377i | \(-0.916812\pi\) | ||||
0.966044 | − | 0.258377i | \(-0.0831877\pi\) | |||||||
\(314\) | −20.3573 | −1.14883 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.27677 | 0.128078 | ||||||||
\(317\) | 14.2367i | 0.799614i | 0.916599 | + | 0.399807i | \(0.130923\pi\) | ||||
−0.916599 | + | 0.399807i | \(0.869077\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.62440 | −0.426884 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 3.15841i | − 0.176011i | ||||||||
\(323\) | 33.9795i | 1.89067i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.3736 | −0.685308 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 11.8328i | − 0.653355i | ||||||||
\(329\) | −1.87379 | −0.103305 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.2000 | −0.670574 | −0.335287 | − | 0.942116i | \(-0.608833\pi\) | ||||
−0.335287 | + | 0.942116i | \(0.608833\pi\) | |||||||
\(332\) | 9.30061i | 0.510437i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.86317 | −0.266101 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 4.58986i | − 0.250026i | −0.992155 | − | 0.125013i | \(-0.960103\pi\) | ||||
0.992155 | − | 0.125013i | \(-0.0398972\pi\) | |||||||
\(338\) | 42.3601i | 2.30408i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.1094 | −0.709917 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.94582i | 0.375039i | ||||||||
\(344\) | −2.88632 | −0.155620 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 25.8994 | 1.39236 | ||||||||
\(347\) | 33.4603i | 1.79624i | 0.439748 | + | 0.898121i | \(0.355068\pi\) | ||||
−0.439748 | + | 0.898121i | \(0.644932\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.0816 | 1.50317 | 0.751586 | − | 0.659636i | \(-0.229289\pi\) | ||||
0.751586 | + | 0.659636i | \(0.229289\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 11.2875i | − 0.601624i | ||||||||
\(353\) | 1.84170i | 0.0980239i | 0.998798 | + | 0.0490119i | \(0.0156072\pi\) | ||||
−0.998798 | + | 0.0490119i | \(0.984393\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.26483 | −0.120036 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 27.9107i | − 1.47513i | ||||||||
\(359\) | −12.1119 | −0.639241 | −0.319621 | − | 0.947546i | \(-0.603555\pi\) | ||||
−0.319621 | + | 0.947546i | \(0.603555\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.0274 | 0.633020 | ||||||||
\(362\) | − 21.8413i | − 1.14795i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.10953 | 0.110569 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.5738i | 0.760744i | 0.924834 | + | 0.380372i | \(0.124204\pi\) | ||||
−0.924834 | + | 0.380372i | \(0.875796\pi\) | |||||||
\(368\) | 18.7090i | 0.975274i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.28462 | −0.0666942 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 9.44646i | − 0.489119i | −0.969634 | − | 0.244560i | \(-0.921357\pi\) | ||||
0.969634 | − | 0.244560i | \(-0.0786434\pi\) | |||||||
\(374\) | −30.8968 | −1.59763 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.06251 | 0.415792 | ||||||||
\(377\) | 15.3444i | 0.790276i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.5541 | 1.46673 | 0.733363 | − | 0.679837i | \(-0.237949\pi\) | ||||
0.733363 | + | 0.679837i | \(0.237949\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 41.3940i | 2.11790i | ||||||||
\(383\) | − 1.46541i | − 0.0748788i | −0.999299 | − | 0.0374394i | \(-0.988080\pi\) | ||||
0.999299 | − | 0.0374394i | \(-0.0119201\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.6176 | −0.794916 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 7.41014i | − 0.376193i | ||||||||
\(389\) | −12.9101 | −0.654569 | −0.327284 | − | 0.944926i | \(-0.606134\pi\) | ||||
−0.327284 | + | 0.944926i | \(0.606134\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.3369 | 1.18020 | ||||||||
\(392\) | − 14.6655i | − 0.740720i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.37922 | −0.170242 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.868386i | 0.0435831i | 0.999763 | + | 0.0217915i | \(0.00693701\pi\) | ||||
−0.999763 | + | 0.0217915i | \(0.993063\pi\) | |||||||
\(398\) | 21.3968i | 1.07253i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.4125 | −1.66854 | −0.834270 | − | 0.551356i | \(-0.814111\pi\) | ||||
−0.834270 | + | 0.551356i | \(0.814111\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.3833i | 1.31424i | ||||||||
\(404\) | −11.6208 | −0.578156 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.03042 | 0.100768 | ||||||||
\(407\) | − 20.8544i | − 1.03371i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.05535 | −0.249971 | −0.124985 | − | 0.992159i | \(-0.539888\pi\) | ||||
−0.124985 | + | 0.992159i | \(0.539888\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.557157i | 0.0274492i | ||||||||
\(413\) | 1.45658i | 0.0716734i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −22.7165 | −1.11377 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 28.2125i | 1.37992i | ||||||||
\(419\) | 10.9576 | 0.535313 | 0.267657 | − | 0.963514i | \(-0.413751\pi\) | ||||
0.267657 | + | 0.963514i | \(0.413751\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.6386 | −0.518495 | −0.259248 | − | 0.965811i | \(-0.583475\pi\) | ||||
−0.259248 | + | 0.965811i | \(0.583475\pi\) | |||||||
\(422\) | − 18.1538i | − 0.883711i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.52744 | 0.268436 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.43693i | − 0.0695381i | ||||||||
\(428\) | − 7.40535i | − 0.357951i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.3529 | 1.79923 | 0.899613 | − | 0.436687i | \(-0.143848\pi\) | ||||
0.899613 | + | 0.436687i | \(0.143848\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 17.2125i | − 0.827179i | −0.910464 | − | 0.413589i | \(-0.864275\pi\) | ||||
0.910464 | − | 0.413589i | \(-0.135725\pi\) | |||||||
\(434\) | 3.49111 | 0.167579 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.11668 | −0.149262 | ||||||||
\(437\) | − 21.3094i | − 1.01937i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.7487 | 1.51528 | 0.757642 | − | 0.652670i | \(-0.226351\pi\) | ||||
0.757642 | + | 0.652670i | \(0.226351\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 62.1809i | 2.95764i | ||||||||
\(443\) | 0.355958i | 0.0169121i | 0.999964 | + | 0.00845603i | \(0.00269167\pi\) | ||||
−0.999964 | + | 0.00845603i | \(0.997308\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.36174 | −0.301237 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 1.93688i | − 0.0915088i | ||||||||
\(449\) | −7.85632 | −0.370762 | −0.185381 | − | 0.982667i | \(-0.559352\pi\) | ||||
−0.185381 | + | 0.982667i | \(0.559352\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.8708 | −0.794416 | ||||||||
\(452\) | 8.02476i | 0.377453i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 20.9249 | 0.982056 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 21.4910i | − 1.00531i | −0.864488 | − | 0.502654i | \(-0.832357\pi\) | ||||
0.864488 | − | 0.502654i | \(-0.167643\pi\) | |||||||
\(458\) | 10.8691i | 0.507879i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −40.9927 | −1.90922 | −0.954611 | − | 0.297856i | \(-0.903729\pi\) | ||||
−0.954611 | + | 0.297856i | \(0.903729\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 42.1339i | 1.95813i | 0.203555 | + | 0.979063i | \(0.434750\pi\) | ||||
−0.203555 | + | 0.979063i | \(0.565250\pi\) | |||||||
\(464\) | −12.0273 | −0.558351 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.97674 | 0.276867 | ||||||||
\(467\) | − 22.5376i | − 1.04292i | −0.853276 | − | 0.521459i | \(-0.825388\pi\) | ||||
0.853276 | − | 0.521459i | \(-0.174612\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.21613 | −0.0561557 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 6.26732i | − 0.288477i | ||||||||
\(473\) | 4.11523i | 0.189219i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.06251 | 0.0945348 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25.6356i | 1.17255i | ||||||||
\(479\) | −33.2880 | −1.52097 | −0.760483 | − | 0.649358i | \(-0.775038\pi\) | ||||
−0.760483 | + | 0.649358i | \(0.775038\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.9702 | −1.91367 | ||||||||
\(482\) | − 18.3385i | − 0.835295i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.929141 | 0.0422337 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 23.7703i | − 1.07713i | −0.842583 | − | 0.538566i | \(-0.818966\pi\) | ||||
0.842583 | − | 0.538566i | \(-0.181034\pi\) | |||||||
\(488\) | 6.18281i | 0.279882i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.60563 | 0.207849 | 0.103925 | − | 0.994585i | \(-0.466860\pi\) | ||||
0.103925 | + | 0.994585i | \(0.466860\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.0024i | 0.675673i | ||||||||
\(494\) | 56.7787 | 2.55459 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20.6797 | −0.928548 | ||||||||
\(497\) | − 2.80067i | − 0.125627i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.8976 | 0.845971 | 0.422985 | − | 0.906137i | \(-0.360982\pi\) | ||||
0.422985 | + | 0.906137i | \(0.360982\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.3387i | 0.506072i | ||||||||
\(503\) | − 35.7581i | − 1.59438i | −0.603731 | − | 0.797188i | \(-0.706320\pi\) | ||||
0.603731 | − | 0.797188i | \(-0.293680\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 19.3762 | 0.861376 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 2.16009i | − 0.0958384i | ||||||||
\(509\) | 24.4067 | 1.08181 | 0.540904 | − | 0.841084i | \(-0.318082\pi\) | ||||
0.540904 | + | 0.841084i | \(0.318082\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.96250 | −0.263766 | ||||||||
\(512\) | 3.46207i | 0.153003i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 29.9506 | 1.32106 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 11.4953i | − 0.505563i | ||||||||
\(518\) | 5.55362i | 0.244012i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.3968 | −1.46314 | −0.731571 | − | 0.681766i | \(-0.761212\pi\) | ||||
−0.731571 | + | 0.681766i | \(0.761212\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 37.3654i | − 1.63388i | −0.576726 | − | 0.816938i | \(-0.695670\pi\) | ||||
0.576726 | − | 0.816938i | \(-0.304330\pi\) | |||||||
\(524\) | −6.27914 | −0.274305 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26.2648 | −1.14520 | ||||||||
\(527\) | 25.7952i | 1.12366i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.36479 | 0.363686 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 1.88332i | − 0.0816521i | ||||||||
\(533\) | 33.9532i | 1.47068i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.23274 | 0.226020 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 29.7344i | 1.28194i | ||||||||
\(539\) | −20.9097 | −0.900645 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.2560 | 1.21482 | 0.607409 | − | 0.794389i | \(-0.292209\pi\) | ||||
0.607409 | + | 0.794389i | \(0.292209\pi\) | |||||||
\(542\) | 4.06096i | 0.174433i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −22.2101 | −0.952250 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.5452i | 1.64807i | 0.566537 | + | 0.824036i | \(0.308283\pi\) | ||||
−0.566537 | + | 0.824036i | \(0.691717\pi\) | |||||||
\(548\) | − 1.54521i | − 0.0660082i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.6990 | 0.583596 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1.71969i | − 0.0731286i | ||||||||
\(554\) | −12.5262 | −0.532187 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.28866 | 0.309108 | ||||||||
\(557\) | − 27.4125i | − 1.16151i | −0.814080 | − | 0.580753i | \(-0.802758\pi\) | ||||
0.814080 | − | 0.580753i | \(-0.197242\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.28206 | 0.350294 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.446383i | 0.0188295i | ||||||||
\(563\) | 27.6392i | 1.16485i | 0.812883 | + | 0.582427i | \(0.197897\pi\) | ||||
−0.812883 | + | 0.582427i | \(0.802103\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.50710 | 0.231481 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.0506i | 0.505634i | ||||||||
\(569\) | −14.7161 | −0.616933 | −0.308467 | − | 0.951235i | \(-0.599816\pi\) | ||||
−0.308467 | + | 0.951235i | \(0.599816\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.3006 | −1.18434 | −0.592172 | − | 0.805812i | \(-0.701729\pi\) | ||||
−0.592172 | + | 0.805812i | \(0.701729\pi\) | |||||||
\(572\) | 12.9415i | 0.541111i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.49279 | 0.187525 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.7976i | 1.69843i | 0.528049 | + | 0.849214i | \(0.322924\pi\) | ||||
−0.528049 | + | 0.849214i | \(0.677076\pi\) | |||||||
\(578\) | 33.0216i | 1.37352i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.02493 | 0.291443 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 7.88087i | − 0.326392i | ||||||||
\(584\) | 25.6553 | 1.06162 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.22080 | 0.380908 | ||||||||
\(587\) | 2.78033i | 0.114756i | 0.998353 | + | 0.0573782i | \(0.0182741\pi\) | ||||
−0.998353 | + | 0.0573782i | \(0.981726\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.5541 | 0.970531 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 32.8971i | − 1.35206i | ||||||||
\(593\) | 14.8084i | 0.608109i | 0.952655 | + | 0.304055i | \(0.0983405\pi\) | ||||
−0.952655 | + | 0.304055i | \(0.901659\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.9343 | 0.447888 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 38.9953i | − 1.59464i | ||||||||
\(599\) | −16.3430 | −0.667758 | −0.333879 | − | 0.942616i | \(-0.608358\pi\) | ||||
−0.333879 | + | 0.942616i | \(0.608358\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.62371 | −0.270187 | −0.135093 | − | 0.990833i | \(-0.543133\pi\) | ||||
−0.135093 | + | 0.990833i | \(0.543133\pi\) | |||||||
\(602\) | − 1.09591i | − 0.0446658i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.2428 | −0.620221 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 30.3094i | − 1.23022i | −0.788442 | − | 0.615110i | \(-0.789112\pi\) | ||||
0.788442 | − | 0.615110i | \(-0.210888\pi\) | |||||||
\(608\) | 20.2805i | 0.822483i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.1347 | −0.935931 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.7803i | 0.596969i | 0.954415 | + | 0.298484i | \(0.0964811\pi\) | ||||
−0.954415 | + | 0.298484i | \(0.903519\pi\) | |||||||
\(614\) | −8.88918 | −0.358738 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.40660 | −0.137256 | ||||||||
\(617\) | − 33.8512i | − 1.36280i | −0.731912 | − | 0.681399i | \(-0.761372\pi\) | ||||
0.731912 | − | 0.681399i | \(-0.238628\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.6887 | −0.469807 | −0.234903 | − | 0.972019i | \(-0.575477\pi\) | ||||
−0.234903 | + | 0.972019i | \(0.575477\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 31.1709i | − 1.24984i | ||||||||
\(623\) | 1.71067i | 0.0685364i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.9360 | −0.596963 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.33686i | 0.332677i | ||||||||
\(629\) | −41.0347 | −1.63616 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.1357 | −1.51816 | −0.759078 | − | 0.650999i | \(-0.774350\pi\) | ||||
−0.759078 | + | 0.650999i | \(0.774350\pi\) | |||||||
\(632\) | 7.39944i | 0.294334i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 23.2589 | 0.923728 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 42.0816i | 1.66733i | ||||||||
\(638\) | 12.4562i | 0.493144i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.7654 | 1.37315 | 0.686576 | − | 0.727058i | \(-0.259113\pi\) | ||||
0.686576 | + | 0.727058i | \(0.259113\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.68515i | 0.105892i | 0.998597 | + | 0.0529461i | \(0.0168611\pi\) | ||||
−0.998597 | + | 0.0529461i | \(0.983139\pi\) | |||||||
\(644\) | −1.29345 | −0.0509692 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 55.5131 | 2.18413 | ||||||||
\(647\) | 40.5103i | 1.59262i | 0.604887 | + | 0.796311i | \(0.293218\pi\) | ||||
−0.604887 | + | 0.796311i | \(0.706782\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.93578 | −0.350760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.06729i | 0.198451i | ||||||||
\(653\) | − 13.3354i | − 0.521856i | −0.965358 | − | 0.260928i | \(-0.915971\pi\) | ||||
0.965358 | − | 0.260928i | \(-0.0840286\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −26.6132 | −1.03907 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.06126i | 0.119340i | ||||||||
\(659\) | 31.1543 | 1.21360 | 0.606800 | − | 0.794855i | \(-0.292453\pi\) | ||||
0.606800 | + | 0.794855i | \(0.292453\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.31788 | 0.245737 | 0.122869 | − | 0.992423i | \(-0.460791\pi\) | ||||
0.122869 | + | 0.992423i | \(0.460791\pi\) | |||||||
\(662\) | 19.9315i | 0.774659i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −30.2267 | −1.17302 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 9.40838i | − 0.364294i | ||||||||
\(668\) | 1.99160i | 0.0770571i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.81528 | 0.340310 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 6.59220i | − 0.254110i | −0.991896 | − | 0.127055i | \(-0.959447\pi\) | ||||
0.991896 | − | 0.127055i | \(-0.0405525\pi\) | |||||||
\(674\) | −7.49857 | −0.288834 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.3476 | 0.667214 | ||||||||
\(677\) | 34.8947i | 1.34111i | 0.741859 | + | 0.670556i | \(0.233944\pi\) | ||||
−0.741859 | + | 0.670556i | \(0.766056\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.59702 | −0.214794 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 21.4172i | 0.820108i | ||||||||
\(683\) | − 26.0958i | − 0.998528i | −0.866450 | − | 0.499264i | \(-0.833604\pi\) | ||||
0.866450 | − | 0.499264i | \(-0.166396\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 11.3476 | 0.433252 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.49165i | 0.247492i | ||||||||
\(689\) | −15.8606 | −0.604239 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.3058 | −1.11485 | −0.557423 | − | 0.830229i | \(-0.688210\pi\) | ||||
−0.557423 | + | 0.830229i | \(0.688210\pi\) | |||||||
\(692\) | − 10.6065i | − 0.403197i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 54.6648 | 2.07505 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.1964i | 1.25740i | ||||||||
\(698\) | − 45.8775i | − 1.73649i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.3891 | −0.581239 | −0.290620 | − | 0.956839i | \(-0.593861\pi\) | ||||
−0.290620 | + | 0.956839i | \(0.593861\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.4696i | 1.41319i | ||||||||
\(704\) | 11.8823 | 0.447832 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.00883 | 0.113239 | ||||||||
\(707\) | 8.77741i | 0.330108i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.73991 | 0.290678 | 0.145339 | − | 0.989382i | \(-0.453573\pi\) | ||||
0.145339 | + | 0.989382i | \(0.453573\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 7.36062i | − 0.275851i | ||||||||
\(713\) | − 16.1768i | − 0.605828i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.4302 | −0.427165 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.7875i | 0.738462i | ||||||||
\(719\) | −15.1316 | −0.564313 | −0.282156 | − | 0.959368i | \(-0.591050\pi\) | ||||
−0.282156 | + | 0.959368i | \(0.591050\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.420832 | 0.0156726 | ||||||||
\(722\) | − 19.6494i | − 0.731275i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.94457 | −0.332422 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 0.161876i | − 0.00600366i | −0.999995 | − | 0.00300183i | \(-0.999044\pi\) | ||||
0.999995 | − | 0.00300183i | \(-0.000955513\pi\) | |||||||
\(728\) | 6.85590i | 0.254097i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.09746 | 0.299495 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 50.0332i | − 1.84802i | −0.382371 | − | 0.924009i | \(-0.624893\pi\) | ||||
0.382371 | − | 0.924009i | \(-0.375107\pi\) | |||||||
\(734\) | 23.8095 | 0.878825 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.9285 | 0.513413 | ||||||||
\(737\) | − 7.46070i | − 0.274818i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.5505 | −1.12382 | −0.561909 | − | 0.827199i | \(-0.689933\pi\) | ||||
−0.561909 | + | 0.827199i | \(0.689933\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.09872i | 0.0770463i | ||||||||
\(743\) | − 5.96684i | − 0.218902i | −0.993992 | − | 0.109451i | \(-0.965091\pi\) | ||||
0.993992 | − | 0.109451i | \(-0.0349093\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.4329 | −0.565039 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.6530i | 0.462640i | ||||||||
\(749\) | −5.59340 | −0.204379 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.3976 | 1.25519 | 0.627593 | − | 0.778542i | \(-0.284040\pi\) | ||||
0.627593 | + | 0.778542i | \(0.284040\pi\) | |||||||
\(752\) | − 18.1335i | − 0.661260i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 25.0685 | 0.912941 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 40.6873i | − 1.47881i | −0.673263 | − | 0.739403i | \(-0.735108\pi\) | ||||
0.673263 | − | 0.739403i | \(-0.264892\pi\) | |||||||
\(758\) | − 46.6495i | − 1.69439i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.2596 | −1.02441 | −0.512204 | − | 0.858864i | \(-0.671171\pi\) | ||||
−0.512204 | + | 0.858864i | \(0.671171\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.35409i | 0.0852239i | ||||||||
\(764\) | 16.9519 | 0.613299 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.39407 | −0.0865013 | ||||||||
\(767\) | 17.9836i | 0.649350i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.9036 | 1.69139 | 0.845694 | − | 0.533668i | \(-0.179187\pi\) | ||||
0.845694 | + | 0.533668i | \(0.179187\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.39582i | 0.230191i | ||||||||
\(773\) | − 9.19641i | − 0.330772i | −0.986229 | − | 0.165386i | \(-0.947113\pi\) | ||||
0.986229 | − | 0.165386i | \(-0.0528870\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 24.0827 | 0.864520 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21.0916i | 0.756169i | ||||||||
\(779\) | 30.3123 | 1.08605 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.1815 | 0.614802 | ||||||||
\(782\) | − 38.1261i | − 1.36339i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −32.9844 | −1.17801 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 5.74637i | − 0.204836i | −0.994741 | − | 0.102418i | \(-0.967342\pi\) | ||||
0.994741 | − | 0.102418i | \(-0.0326579\pi\) | |||||||
\(788\) | 1.38388i | 0.0492986i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.06126 | 0.215514 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 17.7411i | − 0.630004i | ||||||||
\(794\) | 1.41870 | 0.0503479 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.76255 | 0.310580 | ||||||||
\(797\) | − 7.07450i | − 0.250592i | −0.992119 | − | 0.125296i | \(-0.960012\pi\) | ||||
0.992119 | − | 0.125296i | \(-0.0399880\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.6191 | −0.800205 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 54.5868i | 1.92753i | ||||||||
\(803\) | − 36.5787i | − 1.29083i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 43.1029 | 1.51824 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 37.7672i | − 1.32865i | ||||||||
\(809\) | 38.1075 | 1.33979 | 0.669894 | − | 0.742457i | \(-0.266340\pi\) | ||||
0.669894 | + | 0.742457i | \(0.266340\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.44105 | −0.0506022 | −0.0253011 | − | 0.999680i | \(-0.508054\pi\) | ||||
−0.0253011 | + | 0.999680i | \(0.508054\pi\) | |||||||
\(812\) | − 0.831508i | − 0.0291802i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −34.0702 | −1.19416 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 7.39396i | − 0.258682i | ||||||||
\(818\) | 8.25904i | 0.288771i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.5143 | −0.785753 | −0.392876 | − | 0.919591i | \(-0.628520\pi\) | ||||
−0.392876 | + | 0.919591i | \(0.628520\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 41.4589i | − 1.44517i | −0.691284 | − | 0.722583i | \(-0.742955\pi\) | ||||
0.691284 | − | 0.722583i | \(-0.257045\pi\) | |||||||
\(824\) | −1.81075 | −0.0630803 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.37964 | 0.0827984 | ||||||||
\(827\) | 27.8133i | 0.967164i | 0.875299 | + | 0.483582i | \(0.160664\pi\) | ||||
−0.875299 | + | 0.483582i | \(0.839336\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.7232 | −0.719745 | −0.359872 | − | 0.933002i | \(-0.617180\pi\) | ||||
−0.359872 | + | 0.933002i | \(0.617180\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 23.9136i | − 0.829056i | ||||||||
\(833\) | 41.1436i | 1.42554i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.5537 | 0.399595 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 17.9017i | − 0.618403i | ||||||||
\(839\) | 18.1451 | 0.626437 | 0.313218 | − | 0.949681i | \(-0.398593\pi\) | ||||
0.313218 | + | 0.949681i | \(0.398593\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.9517 | −0.791439 | ||||||||
\(842\) | 17.3806i | 0.598975i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.43444 | −0.255904 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 0.701798i | − 0.0241141i | ||||||||
\(848\) | − 12.4318i | − 0.426911i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.7339 | 0.882148 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 4.00708i | − 0.137200i | −0.997644 | − | 0.0685999i | \(-0.978147\pi\) | ||||
0.997644 | − | 0.0685999i | \(-0.0218532\pi\) | |||||||
\(854\) | −2.34755 | −0.0803316 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 24.0672 | 0.822599 | ||||||||
\(857\) | − 9.08971i | − 0.310499i | −0.987875 | − | 0.155249i | \(-0.950382\pi\) | ||||
0.987875 | − | 0.155249i | \(-0.0496181\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.3870 | −0.559116 | −0.279558 | − | 0.960129i | \(-0.590188\pi\) | ||||
−0.279558 | + | 0.960129i | \(0.590188\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 61.0243i | − 2.07850i | ||||||||
\(863\) | − 23.7967i | − 0.810050i | −0.914306 | − | 0.405025i | \(-0.867263\pi\) | ||||
0.914306 | − | 0.405025i | \(-0.132737\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −28.1204 | −0.955571 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 1.42970i | − 0.0485272i | ||||||||
\(869\) | 10.5499 | 0.357882 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.0149 | −0.508762 | ||||||||
\(872\) | − 10.1291i | − 0.343016i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −34.8137 | −1.17759 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 36.0744i | − 1.21815i | −0.793114 | − | 0.609073i | \(-0.791542\pi\) | ||||
0.793114 | − | 0.609073i | \(-0.208458\pi\) | |||||||
\(878\) | − 51.8687i | − 1.75048i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.4575 | 1.19459 | 0.597297 | − | 0.802020i | \(-0.296241\pi\) | ||||
0.597297 | + | 0.802020i | \(0.296241\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 39.1320i | − 1.31690i | −0.752626 | − | 0.658448i | \(-0.771213\pi\) | ||||
0.752626 | − | 0.658448i | \(-0.228787\pi\) | |||||||
\(884\) | 25.4647 | 0.856470 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.581537 | 0.0195371 | ||||||||
\(887\) | 51.2833i | 1.72192i | 0.508670 | + | 0.860962i | \(0.330137\pi\) | ||||
−0.508670 | + | 0.860962i | \(0.669863\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.63156 | −0.0547207 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.60530i | 0.0872318i | ||||||||
\(893\) | 20.6539i | 0.691158i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.84415 | −0.228647 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.8350i | 0.428311i | ||||||||
\(899\) | 10.3994 | 0.346841 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.5070 | −0.516614 | ||||||||
\(902\) | 27.5623i | 0.917723i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −26.0802 | −0.867416 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 47.8588i | − 1.58913i | −0.607181 | − | 0.794563i | \(-0.707700\pi\) | ||||
0.607181 | − | 0.794563i | \(-0.292300\pi\) | |||||||
\(908\) | − 8.56930i | − 0.284382i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.0431 | −0.597793 | −0.298897 | − | 0.954285i | \(-0.596619\pi\) | ||||
−0.298897 | + | 0.954285i | \(0.596619\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.0964i | 1.42628i | ||||||||
\(914\) | −35.1104 | −1.16135 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.45117 | 0.147071 | ||||||||
\(917\) | 4.74276i | 0.156620i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.3976 | −0.342984 | −0.171492 | − | 0.985185i | \(-0.554859\pi\) | ||||
−0.171492 | + | 0.985185i | \(0.554859\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 66.9708i | 2.20557i | ||||||||
\(923\) | − 34.5784i | − 1.13816i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 68.8351 | 2.26206 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.95410i | 0.293933i | ||||||||
\(929\) | −36.0216 | −1.18183 | −0.590915 | − | 0.806734i | \(-0.701233\pi\) | ||||
−0.590915 | + | 0.806734i | \(0.701233\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.5691 | 1.23128 | ||||||||
\(932\) | − 2.44763i | − 0.0801748i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −36.8203 | −1.20480 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 24.0326i | − 0.785111i | −0.919728 | − | 0.392555i | \(-0.871591\pi\) | ||||
0.919728 | − | 0.392555i | \(-0.128409\pi\) | |||||||
\(938\) | 1.98682i | 0.0648720i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.6676 | −0.543348 | −0.271674 | − | 0.962389i | \(-0.587577\pi\) | ||||
−0.271674 | + | 0.962389i | \(0.587577\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 20.8183i | − 0.677938i | ||||||||
\(944\) | −14.0959 | −0.458783 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.72315 | 0.218589 | ||||||||
\(947\) | − 27.5400i | − 0.894928i | −0.894302 | − | 0.447464i | \(-0.852327\pi\) | ||||
0.894302 | − | 0.447464i | \(-0.147673\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −73.6160 | −2.38968 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.70308i | 0.217248i | ||||||||
\(953\) | 18.1344i | 0.587432i | 0.955893 | + | 0.293716i | \(0.0948920\pi\) | ||||
−0.955893 | + | 0.293716i | \(0.905108\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.4984 | 0.339544 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 54.3833i | 1.75705i | ||||||||
\(959\) | −1.16713 | −0.0376886 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.1191 | −0.423198 | ||||||||
\(962\) | 68.5676i | 2.21071i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.51009 | −0.241884 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 36.1875i | − 1.16371i | −0.813292 | − | 0.581855i | \(-0.802327\pi\) | ||||
0.813292 | − | 0.581855i | \(-0.197673\pi\) | |||||||
\(968\) | 3.01968i | 0.0970562i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.6173 | 1.11092 | 0.555461 | − | 0.831542i | \(-0.312542\pi\) | ||||
0.555461 | + | 0.831542i | \(0.312542\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 5.50527i | − 0.176491i | ||||||||
\(974\) | −38.8340 | −1.24432 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.9058 | 0.445115 | ||||||||
\(977\) | − 29.4331i | − 0.941650i | −0.882227 | − | 0.470825i | \(-0.843956\pi\) | ||||
0.882227 | − | 0.470825i | \(-0.156044\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.4946 | −0.335408 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 7.52432i | − 0.240111i | ||||||||
\(983\) | − 24.4911i | − 0.781145i | −0.920572 | − | 0.390573i | \(-0.872277\pi\) | ||||
0.920572 | − | 0.390573i | \(-0.127723\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 24.5097 | 0.780549 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 23.2523i | − 0.739755i | ||||||||
\(989\) | −5.07813 | −0.161475 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.2821 | −0.421919 | −0.210959 | − | 0.977495i | \(-0.567659\pi\) | ||||
−0.210959 | + | 0.977495i | \(0.567659\pi\) | |||||||
\(992\) | 15.3957i | 0.488815i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.57551 | −0.145126 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 39.1530i | − 1.23999i | −0.784606 | − | 0.619994i | \(-0.787135\pi\) | ||||
0.784606 | − | 0.619994i | \(-0.212865\pi\) | |||||||
\(998\) | − 30.8734i | − 0.977280i | ||||||||
\(999\) | 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 | 2025.2.b.o.649.2 | 8 | ||
3.2 | odd | 2 | 2025.2.b.n.649.7 | 8 | |||
5.2 | odd | 4 | 2025.2.a.p.1.4 | 4 | |||
5.3 | odd | 4 | 2025.2.a.z.1.1 | 4 | |||
5.4 | even | 2 | inner | 2025.2.b.o.649.7 | 8 | ||
9.2 | odd | 6 | 225.2.k.c.49.7 | 16 | |||
9.4 | even | 3 | 675.2.k.c.424.7 | 16 | |||
9.5 | odd | 6 | 225.2.k.c.124.2 | 16 | |||
9.7 | even | 3 | 675.2.k.c.199.2 | 16 | |||
15.2 | even | 4 | 2025.2.a.y.1.1 | 4 | |||
15.8 | even | 4 | 2025.2.a.q.1.4 | 4 | |||
15.14 | odd | 2 | 2025.2.b.n.649.2 | 8 | |||
45.2 | even | 12 | 225.2.e.c.76.4 | ✓ | 8 | ||
45.4 | even | 6 | 675.2.k.c.424.2 | 16 | |||
45.7 | odd | 12 | 675.2.e.e.226.1 | 8 | |||
45.13 | odd | 12 | 675.2.e.c.451.4 | 8 | |||
45.14 | odd | 6 | 225.2.k.c.124.7 | 16 | |||
45.22 | odd | 12 | 675.2.e.e.451.1 | 8 | |||
45.23 | even | 12 | 225.2.e.e.151.1 | yes | 8 | ||
45.29 | odd | 6 | 225.2.k.c.49.2 | 16 | |||
45.32 | even | 12 | 225.2.e.c.151.4 | yes | 8 | ||
45.34 | even | 6 | 675.2.k.c.199.7 | 16 | |||
45.38 | even | 12 | 225.2.e.e.76.1 | yes | 8 | ||
45.43 | odd | 12 | 675.2.e.c.226.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.e.c.76.4 | ✓ | 8 | 45.2 | even | 12 | ||
225.2.e.c.151.4 | yes | 8 | 45.32 | even | 12 | ||
225.2.e.e.76.1 | yes | 8 | 45.38 | even | 12 | ||
225.2.e.e.151.1 | yes | 8 | 45.23 | even | 12 | ||
225.2.k.c.49.2 | 16 | 45.29 | odd | 6 | |||
225.2.k.c.49.7 | 16 | 9.2 | odd | 6 | |||
225.2.k.c.124.2 | 16 | 9.5 | odd | 6 | |||
225.2.k.c.124.7 | 16 | 45.14 | odd | 6 | |||
675.2.e.c.226.4 | 8 | 45.43 | odd | 12 | |||
675.2.e.c.451.4 | 8 | 45.13 | odd | 12 | |||
675.2.e.e.226.1 | 8 | 45.7 | odd | 12 | |||
675.2.e.e.451.1 | 8 | 45.22 | odd | 12 | |||
675.2.k.c.199.2 | 16 | 9.7 | even | 3 | |||
675.2.k.c.199.7 | 16 | 45.34 | even | 6 | |||
675.2.k.c.424.2 | 16 | 45.4 | even | 6 | |||
675.2.k.c.424.7 | 16 | 9.4 | even | 3 | |||
2025.2.a.p.1.4 | 4 | 5.2 | odd | 4 | |||
2025.2.a.q.1.4 | 4 | 15.8 | even | 4 | |||
2025.2.a.y.1.1 | 4 | 15.2 | even | 4 | |||
2025.2.a.z.1.1 | 4 | 5.3 | odd | 4 | |||
2025.2.b.n.649.2 | 8 | 15.14 | odd | 2 | |||
2025.2.b.n.649.7 | 8 | 3.2 | odd | 2 | |||
2025.2.b.o.649.2 | 8 | 1.1 | even | 1 | trivial | ||
2025.2.b.o.649.7 | 8 | 5.4 | even | 2 | inner |