Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(157,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.ce (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 157.1 | ||
Character | \(\chi\) | \(=\) | 2100.157 |
Dual form | 2100.2.ce.c.1993.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.965926 | + | 0.258819i | −0.557678 | + | 0.149429i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.588711 | + | 2.57942i | −0.222512 | + | 0.974930i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.866025 | − | 0.500000i | 0.288675 | − | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.401047 | + | 0.694634i | −0.120920 | + | 0.209440i | −0.920131 | − | 0.391611i | \(-0.871918\pi\) |
0.799211 | + | 0.601051i | \(0.205251\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.60097 | + | 2.60097i | 0.721378 | + | 0.721378i | 0.968886 | − | 0.247508i | \(-0.0796115\pi\) |
−0.247508 | + | 0.968886i | \(0.579612\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.207597 | + | 0.774764i | 0.0503497 | + | 0.187908i | 0.986520 | − | 0.163638i | \(-0.0523229\pi\) |
−0.936171 | + | 0.351546i | \(0.885656\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.40765 | − | 2.43811i | −0.322936 | − | 0.559342i | 0.658156 | − | 0.752881i | \(-0.271337\pi\) |
−0.981092 | + | 0.193540i | \(0.938003\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0989528 | − | 2.64390i | −0.0215933 | − | 0.576946i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.12259 | + | 2.17644i | 1.69368 | + | 0.453819i | 0.971334 | − | 0.237717i | \(-0.0763991\pi\) |
0.722342 | + | 0.691536i | \(0.243066\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.14126 | − | 2.96831i | −0.923397 | − | 0.533123i | −0.0386796 | − | 0.999252i | \(-0.512315\pi\) |
−0.884717 | + | 0.466128i | \(0.845649\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.207597 | − | 0.774764i | 0.0361381 | − | 0.134869i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.448288 | − | 1.67303i | 0.0736980 | − | 0.275045i | −0.919237 | − | 0.393705i | \(-0.871193\pi\) |
0.992935 | + | 0.118660i | \(0.0378599\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.18552 | − | 1.83916i | −0.510092 | − | 0.294501i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.01985i | 1.09632i | 0.836375 | + | 0.548158i | \(0.184671\pi\) | ||||
−0.836375 | + | 0.548158i | \(0.815329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.23310 | + | 2.23310i | −0.340544 | + | 0.340544i | −0.856572 | − | 0.516028i | \(-0.827410\pi\) |
0.516028 | + | 0.856572i | \(0.327410\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.1949 | − | 2.73172i | −1.48708 | − | 0.398462i | −0.578331 | − | 0.815802i | \(-0.696296\pi\) |
−0.908750 | + | 0.417340i | \(0.862962\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.30684 | − | 3.03707i | −0.900977 | − | 0.433867i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.401047 | − | 0.694634i | −0.0561578 | − | 0.0972682i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.27417 | + | 12.2194i | 0.449742 | + | 1.67846i | 0.703102 | + | 0.711089i | \(0.251798\pi\) |
−0.253360 | + | 0.967372i | \(0.581536\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.99071 | + | 1.99071i | 0.263676 | + | 0.263676i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.50993 | + | 6.07937i | −0.456953 | + | 0.791466i | −0.998798 | − | 0.0490121i | \(-0.984393\pi\) |
0.541845 | + | 0.840479i | \(0.317726\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.78251 | − | 5.07059i | 1.12449 | − | 0.649222i | 0.181943 | − | 0.983309i | \(-0.441761\pi\) |
0.942542 | + | 0.334087i | \(0.108428\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.779873 | + | 2.52820i | 0.0982547 | + | 0.318523i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.71936 | + | 0.728651i | −0.332223 | + | 0.0890189i | −0.421075 | − | 0.907026i | \(-0.638347\pi\) |
0.0888516 | + | 0.996045i | \(0.471680\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.40912 | −1.01234 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.35664 | −0.635717 | −0.317858 | − | 0.948138i | \(-0.602964\pi\) | ||||
−0.317858 | + | 0.948138i | \(0.602964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.68957 | − | 2.06042i | 0.899997 | − | 0.241153i | 0.220982 | − | 0.975278i | \(-0.429074\pi\) |
0.679015 | + | 0.734125i | \(0.262407\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.55565 | − | 1.44341i | −0.177283 | − | 0.164492i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.85687 | + | 3.38146i | −0.658949 | + | 0.380444i | −0.791876 | − | 0.610681i | \(-0.790896\pi\) |
0.132927 | + | 0.991126i | \(0.457562\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.112245 | + | 0.112245i | 0.0123205 | + | 0.0123205i | 0.713240 | − | 0.700920i | \(-0.247227\pi\) |
−0.700920 | + | 0.713240i | \(0.747227\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.694634 | + | 1.20314i | 0.0736311 | + | 0.127533i | 0.900490 | − | 0.434876i | \(-0.143208\pi\) |
−0.826859 | + | 0.562409i | \(0.809875\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.24021 | + | 5.17777i | −0.863809 | + | 0.542778i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.73433 | + | 1.53651i | 0.594622 | + | 0.159328i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.53553 | + | 3.53553i | −0.358979 | + | 0.358979i | −0.863437 | − | 0.504457i | \(-0.831693\pi\) |
0.504457 | + | 0.863437i | \(0.331693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.802094i | 0.0806135i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.36188 | + | 2.51833i | 0.434023 | + | 0.250583i | 0.701059 | − | 0.713103i | \(-0.252711\pi\) |
−0.267036 | + | 0.963687i | \(0.586044\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.30329 | + | 12.3280i | −0.325483 | + | 1.21472i | 0.588343 | + | 0.808611i | \(0.299780\pi\) |
−0.913826 | + | 0.406107i | \(0.866886\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.30359 | + | 4.86505i | −0.126022 | + | 0.470322i | −0.999874 | − | 0.0158708i | \(-0.994948\pi\) |
0.873852 | + | 0.486193i | \(0.161615\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.48173 | − | 4.31958i | −0.716620 | − | 0.413741i | 0.0968876 | − | 0.995295i | \(-0.469111\pi\) |
−0.813507 | + | 0.581555i | \(0.802445\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.73205i | 0.164399i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.34847 | + | 7.34847i | −0.691286 | + | 0.691286i | −0.962515 | − | 0.271229i | \(-0.912570\pi\) |
0.271229 | + | 0.962515i | \(0.412570\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.55299 | + | 0.952020i | 0.328474 | + | 0.0880143i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.12066 | + | 0.0793695i | −0.194400 | + | 0.00727579i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.17832 | + | 8.96912i | 0.470757 | + | 0.815374i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.81687 | − | 6.78066i | −0.163822 | − | 0.611391i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.15325 | + | 8.15325i | 0.723484 | + | 0.723484i | 0.969313 | − | 0.245829i | \(-0.0790602\pi\) |
−0.245829 | + | 0.969313i | \(0.579060\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.57904 | − | 2.73497i | 0.139026 | − | 0.240801i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.15874 | + | 1.82370i | −0.275980 | + | 0.159337i | −0.631602 | − | 0.775293i | \(-0.717602\pi\) |
0.355622 | + | 0.934630i | \(0.384269\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.11762 | − | 2.19557i | 0.617176 | − | 0.190380i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.6839 | + | 5.81018i | −1.85258 | + | 0.496397i | −0.999671 | − | 0.0256612i | \(-0.991831\pi\) |
−0.852910 | + | 0.522059i | \(0.825164\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.0131 | −1.69749 | −0.848743 | − | 0.528805i | \(-0.822640\pi\) | ||||
−0.848743 | + | 0.528805i | \(0.822640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.5546 | 0.888853 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.84983 | + | 0.763610i | −0.238315 | + | 0.0638563i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.87799 | + | 1.30125i | 0.567287 | + | 0.107325i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.28005 | − | 4.20314i | 0.596405 | − | 0.344335i | −0.171221 | − | 0.985233i | \(-0.554771\pi\) |
0.767626 | + | 0.640898i | \(0.221438\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.90105 | − | 6.75681i | 0.317463 | − | 0.549862i | −0.662495 | − | 0.749066i | \(-0.730503\pi\) |
0.979958 | + | 0.199205i | \(0.0638358\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.567166 | + | 0.567166i | 0.0458527 | + | 0.0458527i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.156376 | − | 0.583601i | −0.0124801 | − | 0.0465765i | 0.959405 | − | 0.282032i | \(-0.0910085\pi\) |
−0.971885 | + | 0.235456i | \(0.924342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.32522 | − | 10.9556i | −0.501622 | − | 0.868835i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.3958 | + | 19.6703i | −0.819305 | + | 1.55024i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3693 | + | 2.77845i | 0.812186 | + | 0.217625i | 0.640927 | − | 0.767601i | \(-0.278550\pi\) |
0.171259 | + | 0.985226i | \(0.445217\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.6539 | + | 14.6539i | −1.13395 | + | 1.13395i | −0.144440 | + | 0.989514i | \(0.546138\pi\) |
−0.989514 | + | 0.144440i | \(0.953862\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.530055i | 0.0407735i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.43811 | − | 1.40765i | −0.186447 | − | 0.107645i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.96811 | − | 7.34508i | 0.149633 | − | 0.558436i | −0.849873 | − | 0.526988i | \(-0.823321\pi\) |
0.999505 | − | 0.0314484i | \(-0.0100120\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.81687 | − | 6.78066i | 0.136564 | − | 0.509665i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.6672 | + | 6.15874i | 0.797308 | + | 0.460326i | 0.842529 | − | 0.538651i | \(-0.181066\pi\) |
−0.0452212 | + | 0.998977i | \(0.514399\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.91980i | 0.588674i | 0.955702 | + | 0.294337i | \(0.0950988\pi\) | ||||
−0.955702 | + | 0.294337i | \(0.904901\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.17089 | + | 7.17089i | −0.530087 | + | 0.530087i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.621434 | − | 0.166513i | −0.0454437 | − | 0.0121766i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.40765 | − | 2.24021i | −0.102391 | − | 0.162951i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.47518 | − | 12.9474i | −0.540885 | − | 0.936840i | −0.998853 | − | 0.0478720i | \(-0.984756\pi\) |
0.457968 | − | 0.888968i | \(-0.348577\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.53651 | + | 5.73433i | 0.110600 | + | 0.412766i | 0.998920 | − | 0.0464593i | \(-0.0147938\pi\) |
−0.888320 | + | 0.459225i | \(0.848127\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.56052 | − | 6.56052i | −0.467418 | − | 0.467418i | 0.433659 | − | 0.901077i | \(-0.357222\pi\) |
−0.901077 | + | 0.433659i | \(0.857222\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.45078 | − | 11.1731i | 0.457284 | − | 0.792039i | −0.541532 | − | 0.840680i | \(-0.682156\pi\) |
0.998816 | + | 0.0486408i | \(0.0154890\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.43811 | − | 1.40765i | 0.171971 | − | 0.0992877i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.12259 | − | 2.17644i | 0.564559 | − | 0.151273i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.25813 | 0.156198 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.1587 | 1.31894 | 0.659471 | − | 0.751730i | \(-0.270780\pi\) | ||||
0.659471 | + | 0.751730i | \(0.270780\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.17412 | − | 1.38640i | 0.354525 | − | 0.0949947i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.6832 | − | 11.5140i | 0.725225 | − | 0.781621i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.89428 | + | 3.98042i | −0.465873 | + | 0.268972i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.47518 | + | 2.55509i | −0.0992314 | + | 0.171874i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.7899 | − | 17.7899i | −1.19130 | − | 1.19130i | −0.976702 | − | 0.214598i | \(-0.931156\pi\) |
−0.214598 | − | 0.976702i | \(-0.568844\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.32262 | + | 19.8643i | 0.353275 | + | 1.31844i | 0.882642 | + | 0.470046i | \(0.155763\pi\) |
−0.529367 | + | 0.848393i | \(0.677571\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.49155 | − | 6.04754i | −0.230728 | − | 0.399633i | 0.727295 | − | 0.686325i | \(-0.240777\pi\) |
−0.958023 | + | 0.286693i | \(0.907444\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.87623 | + | 0.991593i | 0.123447 | + | 0.0652420i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.69627 | + | 2.33016i | 0.569711 | + | 0.152654i | 0.532164 | − | 0.846641i | \(-0.321379\pi\) |
0.0375471 | + | 0.999295i | \(0.488046\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.78211 | − | 4.78211i | 0.310632 | − | 0.310632i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.7525i | 1.79516i | 0.440855 | + | 0.897579i | \(0.354675\pi\) | ||||
−0.440855 | + | 0.897579i | \(0.645325\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.50000 | − | 4.33013i | −0.483117 | − | 0.278928i | 0.238597 | − | 0.971119i | \(-0.423312\pi\) |
−0.721715 | + | 0.692191i | \(0.756646\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.258819 | + | 0.965926i | −0.0166032 | + | 0.0619642i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.68021 | − | 10.0027i | 0.170538 | − | 0.636456i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.137472 | − | 0.0793695i | −0.00871193 | − | 0.00502984i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.15099i | 0.388247i | 0.980977 | + | 0.194124i | \(0.0621863\pi\) | ||||
−0.980977 | + | 0.194124i | \(0.937814\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.76937 | + | 4.76937i | −0.299848 | + | 0.299848i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.2940 | − | 3.56211i | −0.829255 | − | 0.222198i | −0.180866 | − | 0.983508i | \(-0.557890\pi\) |
−0.648389 | + | 0.761310i | \(0.724557\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.05155 | + | 2.14126i | 0.251751 | + | 0.133051i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.86617 | + | 18.1608i | 0.300061 | + | 1.11984i | 0.937114 | + | 0.349022i | \(0.113486\pi\) |
−0.637054 | + | 0.770819i | \(0.719847\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.982361 | − | 0.982361i | −0.0601195 | − | 0.0601195i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.1321 | + | 17.5493i | −0.617765 | + | 1.07000i | 0.372127 | + | 0.928182i | \(0.378628\pi\) |
−0.989893 | + | 0.141819i | \(0.954705\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.688794 | + | 0.397675i | −0.0418413 | + | 0.0241571i | −0.520775 | − | 0.853694i | \(-0.674357\pi\) |
0.478933 | + | 0.877851i | \(0.341024\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.61932 | − | 7.13407i | 0.400620 | − | 0.431774i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.0613 | − | 6.17926i | 1.38562 | − | 0.371276i | 0.512461 | − | 0.858710i | \(-0.328734\pi\) |
0.873160 | + | 0.487434i | \(0.162067\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.93661 | −0.355416 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.4063 | 0.859407 | 0.429703 | − | 0.902970i | \(-0.358618\pi\) | ||||
0.429703 | + | 0.902970i | \(0.358618\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.9460 | + | 5.34452i | −1.18567 | + | 0.317699i | −0.797172 | − | 0.603752i | \(-0.793672\pi\) |
−0.388495 | + | 0.921451i | \(0.627005\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.1072 | − | 4.13266i | −1.06883 | − | 0.243943i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.1653 | − | 8.17832i | 0.833251 | − | 0.481078i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.50000 | − | 4.33013i | 0.146553 | − | 0.253837i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.6239 | − | 19.6239i | −1.14644 | − | 1.14644i | −0.987247 | − | 0.159196i | \(-0.949110\pi\) |
−0.159196 | − | 0.987247i | \(-0.550890\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.207597 | − | 0.774764i | −0.0120460 | − | 0.0449563i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.4657 | + | 26.7874i | 0.894406 | + | 1.54916i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.44545 | − | 7.07474i | −0.256231 | − | 0.407781i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.86505 | − | 1.30359i | −0.279490 | − | 0.0748890i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.46843 | − | 2.46843i | 0.140881 | − | 0.140881i | −0.633149 | − | 0.774030i | \(-0.718238\pi\) |
0.774030 | + | 0.633149i | \(0.218238\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 12.7629i | − | 0.726058i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.4413 | − | 11.2244i | −1.10241 | − | 0.636478i | −0.165559 | − | 0.986200i | \(-0.552943\pi\) |
−0.936854 | + | 0.349722i | \(0.886276\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.98054 | − | 18.5876i | 0.281517 | − | 1.05064i | −0.669830 | − | 0.742514i | \(-0.733633\pi\) |
0.951347 | − | 0.308121i | \(-0.0997003\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.60433 | − | 20.9156i | 0.314771 | − | 1.17474i | −0.609432 | − | 0.792838i | \(-0.708603\pi\) |
0.924203 | − | 0.381902i | \(-0.124731\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 5.03667i | − | 0.281119i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.59674 | − | 1.59674i | 0.0888449 | − | 0.0888449i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.34478 | + | 2.23598i | 0.461468 | + | 0.123650i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.0481 | − | 24.6888i | 0.719366 | − | 1.36114i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0598 | − | 27.8164i | −0.882726 | − | 1.52893i | −0.848298 | − | 0.529519i | \(-0.822373\pi\) |
−0.0344273 | − | 0.999407i | \(-0.510961\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.448288 | − | 1.67303i | −0.0245660 | − | 0.0916816i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.76022 | − | 4.76022i | −0.259305 | − | 0.259305i | 0.565466 | − | 0.824772i | \(-0.308696\pi\) |
−0.824772 | + | 0.565466i | \(0.808696\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.19615 | − | 9.00000i | 0.282216 | − | 0.488813i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.12377 | − | 2.38086i | 0.223315 | − | 0.128931i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.5468 | − | 14.4800i | 0.623468 | − | 0.781849i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.46452 | − | 2.53601i | 0.508082 | − | 0.136140i | 0.00433355 | − | 0.999991i | \(-0.498621\pi\) |
0.503748 | + | 0.863850i | \(0.331954\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.11432 | −0.0596484 | −0.0298242 | − | 0.999555i | \(-0.509495\pi\) | ||||
−0.0298242 | + | 0.999555i | \(0.509495\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.67832 | −0.196334 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.0624 | − | 4.03595i | 0.801689 | − | 0.214812i | 0.165364 | − | 0.986233i | \(-0.447120\pi\) |
0.636326 | + | 0.771421i | \(0.280454\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.02786 | − | 0.625532i | 0.107325 | − | 0.0331066i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.5893 | − | 18.2381i | 1.66722 | − | 0.962571i | 0.698095 | − | 0.716005i | \(-0.254031\pi\) |
0.969126 | − | 0.246565i | \(-0.0793020\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.53707 | − | 9.59048i | 0.291425 | − | 0.504762i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.32325 | − | 7.32325i | −0.384371 | − | 0.384371i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.28139 | + | 12.2463i | 0.171287 | + | 0.639253i | 0.997154 | + | 0.0753878i | \(0.0240195\pi\) |
−0.825867 | + | 0.563865i | \(0.809314\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.50993 | + | 6.07937i | 0.182719 | + | 0.316479i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −33.4465 | + | 1.25180i | −1.73646 | + | 0.0649900i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.1377 | + | 6.46767i | 1.24980 | + | 0.334883i | 0.822260 | − | 0.569112i | \(-0.192713\pi\) |
0.427542 | + | 0.903996i | \(0.359380\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.9154i | 0.714786i | 0.933954 | + | 0.357393i | \(0.116334\pi\) | ||||
−0.933954 | + | 0.357393i | \(0.883666\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.98565 | − | 5.76522i | −0.511580 | − | 0.295361i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.93932 | + | 10.9697i | −0.150192 | + | 0.560524i | 0.849277 | + | 0.527947i | \(0.177038\pi\) |
−0.999469 | + | 0.0325771i | \(0.989629\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.817370 | + | 3.05047i | −0.0415492 | + | 0.155064i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.9756 | + | 13.8423i | 1.21561 | + | 0.701832i | 0.963976 | − | 0.265990i | \(-0.0856989\pi\) |
0.251634 | + | 0.967823i | \(0.419032\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.74491i | 0.341105i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.57910 | − | 2.57910i | 0.130098 | − | 0.130098i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.35171 | + | 0.898088i | 0.168217 | + | 0.0450737i | 0.341945 | − | 0.939720i | \(-0.388914\pi\) |
−0.173727 | + | 0.984794i | \(0.555581\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.30684 | + | 3.96293i | −0.315737 | + | 0.198395i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.0402 | + | 22.5863i | 0.651197 | + | 1.12791i | 0.982833 | + | 0.184498i | \(0.0590660\pi\) |
−0.331636 | + | 0.943407i | \(0.607601\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.65177 | − | 21.0927i | −0.281535 | − | 1.05070i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.982361 | + | 0.982361i | 0.0486938 | + | 0.0486938i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.49155 | − | 6.04754i | 0.172646 | − | 0.299032i | −0.766698 | − | 0.642008i | \(-0.778102\pi\) |
0.939344 | + | 0.342976i | \(0.111435\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.4413 | − | 11.2244i | 0.958966 | − | 0.553659i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.6149 | − | 12.6326i | −0.669947 | − | 0.621608i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.3311 | − | 5.17976i | 0.946650 | − | 0.253654i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.2640 | 1.47849 | 0.739247 | − | 0.673434i | \(-0.235182\pi\) | ||||
0.739247 | + | 0.673434i | \(0.235182\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.3566 | 1.47949 | 0.739746 | − | 0.672886i | \(-0.234946\pi\) | ||||
0.739746 | + | 0.672886i | \(0.234946\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.1949 | + | 2.73172i | −0.495694 | + | 0.132821i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.90882 | + | 25.6389i | 0.382735 | + | 1.24075i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.55509 | − | 1.47518i | 0.123361 | − | 0.0712224i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.46994 | − | 14.6704i | 0.407983 | − | 0.706647i | −0.586681 | − | 0.809818i | \(-0.699566\pi\) |
0.994664 | + | 0.103171i | \(0.0328990\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.25962 | − | 9.25962i | −0.444989 | − | 0.444989i | 0.448696 | − | 0.893685i | \(-0.351889\pi\) |
−0.893685 | + | 0.448696i | \(0.851889\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.12731 | − | 22.8674i | −0.293109 | − | 1.09390i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.45919 | − | 9.45560i | −0.260553 | − | 0.451291i | 0.705836 | − | 0.708375i | \(-0.250572\pi\) |
−0.966389 | + | 0.257084i | \(0.917238\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.98042 | + | 0.523243i | −0.332401 | + | 0.0249163i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.20698 | − | 1.66315i | −0.294902 | − | 0.0790188i | 0.108335 | − | 0.994114i | \(-0.465448\pi\) |
−0.403237 | + | 0.915096i | \(0.632115\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.94414 | + | 5.94414i | −0.281148 | + | 0.281148i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.9504i | 0.705551i | 0.935708 | + | 0.352776i | \(0.114762\pi\) | ||||
−0.935708 | + | 0.352776i | \(0.885238\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.87623 | − | 2.81529i | −0.229613 | − | 0.132567i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.01933 | + | 7.53624i | −0.0948764 | + | 0.354084i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.41033 | − | 12.7275i | 0.159529 | − | 0.595369i | −0.839146 | − | 0.543906i | \(-0.816945\pi\) |
0.998675 | − | 0.0514631i | \(-0.0163885\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.694634 | − | 0.401047i | −0.0324227 | − | 0.0187193i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.6932i | 1.66240i | 0.555976 | + | 0.831198i | \(0.312345\pi\) | ||||
−0.555976 | + | 0.831198i | \(0.687655\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.9259 | + | 28.9259i | −1.34430 | + | 1.34430i | −0.452578 | + | 0.891725i | \(0.649495\pi\) |
−0.891725 | + | 0.452578i | \(0.850505\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.89461 | + | 2.38330i | 0.411593 | + | 0.110286i | 0.458673 | − | 0.888605i | \(-0.348325\pi\) |
−0.0470798 | + | 0.998891i | \(0.514992\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.278581 | − | 7.44335i | −0.0128637 | − | 0.343702i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.302094 | + | 0.523243i | 0.0139198 | + | 0.0241098i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.655608 | − | 2.44676i | −0.0301449 | − | 0.112502i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.94521 | + | 8.94521i | 0.409573 | + | 0.409573i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.9473 | − | 31.0856i | 0.820033 | − | 1.42034i | −0.0856235 | − | 0.996328i | \(-0.527288\pi\) |
0.905657 | − | 0.424012i | \(-0.139378\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.51748 | − | 3.18552i | 0.251576 | − | 0.145247i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.95054 | − | 21.6907i | 0.225257 | − | 0.986960i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.74260 | − | 2.61052i | 0.441479 | − | 0.118294i | −0.0312305 | − | 0.999512i | \(-0.509943\pi\) |
0.472710 | + | 0.881218i | \(0.343276\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.7351 | −0.485457 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.83079 | 0.353399 | 0.176699 | − | 0.984265i | \(-0.443458\pi\) | ||||
0.176699 | + | 0.984265i | \(0.443458\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.15351 | − | 13.8170i | 0.141454 | − | 0.619779i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.5121 | − | 6.64649i | 0.515351 | − | 0.297538i | −0.219680 | − | 0.975572i | \(-0.570501\pi\) |
0.735030 | + | 0.678034i | \(0.237168\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.3619 | − | 17.9473i | 0.462935 | − | 0.801826i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.4558 | − | 25.4558i | −1.13502 | − | 1.13502i | −0.989330 | − | 0.145690i | \(-0.953460\pi\) |
−0.145690 | − | 0.989330i | \(-0.546540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.137188 | − | 0.511994i | −0.00609275 | − | 0.0227384i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.4206 | + | 28.4413i | 0.727829 | + | 1.26064i | 0.957799 | + | 0.287439i | \(0.0928037\pi\) |
−0.229970 | + | 0.973198i | \(0.573863\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.787747 | + | 21.0476i | 0.0348479 | + | 0.931093i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.71936 | + | 0.728651i | 0.120063 | + | 0.0321707i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.98619 | − | 5.98619i | 0.263272 | − | 0.263272i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.60419i | 0.333787i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.56502 | + | 3.21297i | 0.243808 | + | 0.140763i | 0.616926 | − | 0.787021i | \(-0.288378\pi\) |
−0.373118 | + | 0.927784i | \(0.621711\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.30288 | − | 23.5227i | 0.275606 | − | 1.02857i | −0.679829 | − | 0.733371i | \(-0.737946\pi\) |
0.955434 | − | 0.295203i | \(-0.0953873\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.23242 | − | 4.59947i | 0.0536852 | − | 0.200356i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.3209 | + | 23.8566i | 1.79656 | + | 1.03725i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.01985i | 0.304636i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.2584 | + | 18.2584i | −0.790859 | + | 0.790859i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.8978 | − | 3.18800i | −0.513427 | − | 0.137572i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.63899 | − | 3.16294i | 0.199815 | − | 0.136237i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.9979 | − | 38.1015i | −0.945764 | − | 1.63811i | −0.754215 | − | 0.656627i | \(-0.771982\pi\) |
−0.191549 | − | 0.981483i | \(-0.561351\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.04979 | − | 7.64994i | −0.0879651 | − | 0.328290i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.4881 | + | 16.4881i | 0.704980 | + | 0.704980i | 0.965475 | − | 0.260495i | \(-0.0838858\pi\) |
−0.260495 | + | 0.965475i | \(0.583886\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.07059 | − | 8.78251i | 0.216407 | − | 0.374828i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.27422 | − | 17.0980i | −0.224283 | − | 0.727083i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.7221 | + | 8.49991i | −1.34411 | + | 0.360153i | −0.857957 | − | 0.513722i | \(-0.828266\pi\) |
−0.486151 | + | 0.873875i | \(0.661600\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.6164 | −0.491322 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.643355 | 0.0271625 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 42.7973 | − | 11.4675i | 1.80369 | − | 0.483297i | 0.809146 | − | 0.587608i | \(-0.199930\pi\) |
0.994545 | + | 0.104311i | \(0.0332637\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.93949 | + | 1.79955i | 0.0814509 | + | 0.0755740i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.77646 | + | 2.75769i | −0.200240 | + | 0.115608i | −0.596767 | − | 0.802414i | \(-0.703548\pi\) |
0.396528 | + | 0.918023i | \(0.370215\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.6465 | − | 18.4403i | 0.445542 | − | 0.771701i | −0.552548 | − | 0.833481i | \(-0.686344\pi\) |
0.998090 | + | 0.0617801i | \(0.0196777\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.5715 | + | 10.5715i | 0.441631 | + | 0.441631i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.60401 | − | 32.1106i | −0.358190 | − | 1.33678i | −0.876423 | − | 0.481543i | \(-0.840077\pi\) |
0.518233 | − | 0.855239i | \(-0.326590\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.96831 | − | 5.14126i | −0.123359 | − | 0.213663i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.355608 | + | 0.223448i | −0.0147531 | + | 0.00927020i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.80110 | − | 2.62620i | −0.405920 | − | 0.108766i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.5720 | − | 22.5720i | 0.931647 | − | 0.931647i | −0.0661617 | − | 0.997809i | \(-0.521075\pi\) |
0.997809 | + | 0.0661617i | \(0.0210753\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.7133i | 0.688659i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.03497 | + | 4.63899i | 0.330514 | + | 0.190823i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.96917 | − | 14.8131i | 0.162994 | − | 0.608303i | −0.835293 | − | 0.549805i | \(-0.814702\pi\) |
0.998288 | − | 0.0584983i | \(-0.0186312\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.33917 | + | 12.4620i | −0.136663 | + | 0.510034i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.5104 | − | 23.9661i | −1.69607 | − | 0.979227i | −0.949419 | − | 0.314012i | \(-0.898327\pi\) |
−0.746652 | − | 0.665215i | \(-0.768340\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.2503i | 1.47868i | 0.673331 | + | 0.739341i | \(0.264863\pi\) | ||||
−0.673331 | + | 0.739341i | \(0.735137\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.99071 | + | 1.99071i | −0.0810680 | + | 0.0810680i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.955811 | − | 0.256109i | −0.0387952 | − | 0.0103951i | 0.239369 | − | 0.970929i | \(-0.423059\pi\) |
−0.278164 | + | 0.960533i | \(0.589726\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.4115 | − | 33.6217i | −0.785306 | − | 1.36019i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.61472 | − | 13.4903i | −0.145997 | − | 0.544868i | −0.999709 | − | 0.0241228i | \(-0.992321\pi\) |
0.853712 | − | 0.520745i | \(-0.174346\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.2946 | + | 13.2946i | 0.535221 | + | 0.535221i | 0.922121 | − | 0.386900i | \(-0.126454\pi\) |
−0.386900 | + | 0.922121i | \(0.626454\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.23484 | + | 7.33496i | −0.170213 | + | 0.294817i | −0.938494 | − | 0.345295i | \(-0.887779\pi\) |
0.768281 | + | 0.640112i | \(0.221112\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.28251 | + | 4.20456i | −0.292237 | + | 0.168723i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.51235 | + | 1.08345i | −0.140719 | + | 0.0434076i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.18119 | + | 0.584447i | −0.0871082 | + | 0.0233406i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.38927 | 0.0553937 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.4371 | −1.05244 | −0.526221 | − | 0.850348i | \(-0.676392\pi\) | ||||
−0.526221 | + | 0.850348i | \(0.676392\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.5059 | + | 4.95865i | −0.735544 | + | 0.197089i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.50457 | − | 24.3032i | −0.336963 | − | 0.962927i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.63899 | + | 2.67832i | −0.183516 | + | 0.105953i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.2329 | + | 22.9200i | −0.522667 | + | 0.905286i | 0.476985 | + | 0.878911i | \(0.341730\pi\) |
−0.999652 | + | 0.0263745i | \(0.991604\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.4173 | − | 22.4173i | −0.884051 | − | 0.884051i | 0.109892 | − | 0.993943i | \(-0.464949\pi\) |
−0.993943 | + | 0.109892i | \(0.964949\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.06784 | + | 7.71729i | 0.0812953 | + | 0.303398i | 0.994587 | − | 0.103908i | \(-0.0331348\pi\) |
−0.913292 | + | 0.407306i | \(0.866468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.81529 | − | 4.87623i | −0.110510 | − | 0.191409i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.33916 | + | 13.8867i | −0.287644 | + | 0.544262i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.41828 | + | 0.647977i | 0.0946348 | + | 0.0253573i | 0.305826 | − | 0.952088i | \(-0.401068\pi\) |
−0.211191 | + | 0.977445i | \(0.567734\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.62916 | − | 5.62916i | 0.219614 | − | 0.219614i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.5937i | 0.841172i | 0.907253 | + | 0.420586i | \(0.138175\pi\) | ||||
−0.907253 | + | 0.420586i | \(0.861825\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.8524 | + | 14.3486i | 0.966648 | + | 0.558095i | 0.898213 | − | 0.439561i | \(-0.144866\pi\) |
0.0684353 | + | 0.997656i | \(0.478199\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.763610 | − | 2.84983i | 0.0296561 | − | 0.110678i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.7881 | + | 12.5794i | 0.842377 | + | 0.486347i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.13418i | 0.314016i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.9403 | + | 11.9403i | −0.460263 | + | 0.460263i | −0.898742 | − | 0.438478i | \(-0.855518\pi\) |
0.438478 | + | 0.898742i | \(0.355518\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.0113 | + | 5.62995i | 0.807528 | + | 0.216377i | 0.638887 | − | 0.769301i | \(-0.279395\pi\) |
0.168642 | + | 0.985677i | \(0.446062\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.03823 | − | 11.2010i | −0.270102 | − | 0.429857i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.2825 | − | 17.8098i | −0.394027 | − | 0.682474i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.76559 | + | 25.2495i | 0.258878 | + | 0.966147i | 0.965892 | + | 0.258947i | \(0.0833754\pi\) |
−0.707013 | + | 0.707200i | \(0.749958\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.93779 | + | 4.93779i | 0.188389 | + | 0.188389i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23.2662 | + | 40.2982i | −0.886371 | + | 1.53524i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.86188 | − | 3.38436i | 0.222996 | − | 0.128747i | −0.384341 | − | 0.923191i | \(-0.625571\pi\) |
0.607337 | + | 0.794444i | \(0.292238\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.06894 | − | 0.472201i | −0.0785925 | − | 0.0179375i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.43873 | + | 1.45730i | −0.206006 | + | 0.0551993i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.00304 | −0.340526 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.7238 | 1.46258 | 0.731288 | − | 0.682069i | \(-0.238919\pi\) | ||||
0.731288 | + | 0.682069i | \(0.238919\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.71007 | + | 1.26206i | −0.177644 | + | 0.0475995i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.06373 | + | 9.76856i | −0.340877 | + | 0.367385i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.2866 | − | 9.98042i | 0.649211 | − | 0.374822i | −0.138943 | − | 0.990300i | \(-0.544370\pi\) |
0.788154 | + | 0.615478i | \(0.211037\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.38146 | + | 5.85687i | −0.126815 | + | 0.219650i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.2999 | − | 35.2999i | −1.32199 | − | 1.32199i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.18286 | − | 26.8068i | −0.268249 | − | 1.00112i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.68623 | + | 2.92063i | 0.0628856 | + | 0.108921i | 0.895754 | − | 0.444550i | \(-0.146636\pi\) |
−0.832868 | + | 0.553471i | \(0.813303\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.8545 | − | 15.7782i | −1.11184 | − | 0.587612i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.36516 | + | 2.24144i | 0.311104 | + | 0.0833600i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.0642 | + | 10.0642i | −0.373259 | + | 0.373259i | −0.868663 | − | 0.495404i | \(-0.835020\pi\) |
0.495404 | + | 0.868663i | \(0.335020\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.19371 | − | 1.26654i | −0.0811371 | − | 0.0468446i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.8753 | + | 44.3191i | −0.438623 | + | 1.63696i | 0.293622 | + | 0.955922i | \(0.405139\pi\) |
−0.732245 | + | 0.681041i | \(0.761527\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.584447 | − | 2.18119i | 0.0215284 | − | 0.0803450i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.94993 | + | 1.70314i | 0.108515 | + | 0.0626511i | 0.553275 | − | 0.832999i | \(-0.313378\pi\) |
−0.444760 | + | 0.895650i | \(0.646711\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.3555i | 0.380421i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.8718 | + | 21.8718i | −0.802400 | + | 0.802400i | −0.983470 | − | 0.181070i | \(-0.942044\pi\) |
0.181070 | + | 0.983470i | \(0.442044\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.153330 | + | 0.0410847i | 0.00561005 | + | 0.00150321i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.7816 | − | 6.22660i | −0.430489 | − | 0.227515i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.4164 | + | 21.5059i | 0.453082 | + | 0.784761i | 0.998576 | − | 0.0533539i | \(-0.0169911\pi\) |
−0.545494 | + | 0.838115i | \(0.683658\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.59199 | − | 5.94140i | −0.0580155 | − | 0.216517i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.662347 | + | 0.662347i | 0.0240734 | + | 0.0240734i | 0.719041 | − | 0.694968i | \(-0.244581\pi\) |
−0.694968 | + | 0.719041i | \(0.744581\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.37245 | − | 5.84126i | 0.122412 | − | 0.212024i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.0507 | − | 8.11216i | 0.509337 | − | 0.294066i | −0.223224 | − | 0.974767i | \(-0.571658\pi\) |
0.732561 | + | 0.680701i | \(0.238325\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.5466 | − | 16.7556i | 0.562824 | − | 0.606592i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.9414 | + | 6.68304i | −0.900583 | + | 0.241311i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −54.1886 | −1.95409 | −0.977045 | − | 0.213033i | \(-0.931666\pi\) | ||||
−0.977045 | + | 0.213033i | \(0.931666\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.7629 | 0.495660 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.1822 | − | 6.21166i | 0.833806 | − | 0.223418i | 0.183433 | − | 0.983032i | \(-0.441279\pi\) |
0.650374 | + | 0.759614i | \(0.274612\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.46769 | − | 1.01968i | −0.160278 | − | 0.0365807i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.1152 | − | 9.88146i | 0.613216 | − | 0.354040i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.14827 | − | 3.72091i | 0.0768710 | − | 0.133145i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.41425 | + | 9.01011i | 0.0860588 | + | 0.321176i | 0.995513 | − | 0.0946293i | \(-0.0301666\pi\) |
−0.909454 | + | 0.415805i | \(0.863500\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.40071 | − | 16.2825i | −0.334674 | − | 0.579673i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.6287 | − | 23.2809i | −0.520136 | − | 0.827775i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.0314 | + | 9.65460i | 1.27951 | + | 0.342845i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.4334 | + | 11.4334i | −0.404990 | + | 0.404990i | −0.879987 | − | 0.474997i | \(-0.842449\pi\) |
0.474997 | + | 0.879987i | \(0.342449\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 8.46575i | − | 0.299497i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.20314 | + | 0.694634i | 0.0425109 | + | 0.0245437i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.65265 | + | 6.16776i | −0.0583207 | + | 0.217656i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.24476 | − | 19.5737i | 0.184624 | − | 0.689027i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.2809 | − | 13.4413i | −0.818514 | − | 0.472569i | 0.0313899 | − | 0.999507i | \(-0.490007\pi\) |
−0.849904 | + | 0.526938i | \(0.823340\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.3319i | 1.06510i | 0.846400 | + | 0.532548i | \(0.178765\pi\) | ||||
−0.846400 | + | 0.532548i | \(0.821235\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.562398 | − | 0.562398i | 0.0197242 | − | 0.0197242i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.58795 | + | 2.30113i | 0.300454 | + | 0.0805065i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.54734 | + | 8.60419i | −0.158897 | + | 0.300655i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.59895 | − | 14.8938i | −0.300106 | − | 0.519798i | 0.676054 | − | 0.736852i | \(-0.263689\pi\) |
−0.976160 | + | 0.217054i | \(0.930355\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.89036 | + | 25.7152i | 0.240183 | + | 0.896374i | 0.975744 | + | 0.218916i | \(0.0702520\pi\) |
−0.735561 | + | 0.677459i | \(0.763081\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.59580 | + | 4.59580i | 0.159812 | + | 0.159812i | 0.782483 | − | 0.622672i | \(-0.213953\pi\) |
−0.622672 | + | 0.782483i | \(0.713953\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.1555 | − | 31.4462i | 0.630565 | − | 1.09217i | −0.356872 | − | 0.934153i | \(-0.616157\pi\) |
0.987436 | − | 0.158017i | \(-0.0505100\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.6762 | + | 11.9374i | −0.717250 | + | 0.414105i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.04373 | − | 5.51680i | 0.0361630 | − | 0.191146i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.73433 | − | 1.53651i | 0.198207 | − | 0.0531095i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.7207 | −0.473692 | −0.236846 | − | 0.971547i | \(-0.576114\pi\) | ||||
−0.236846 | + | 0.971547i | \(0.576114\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.9154 | + | 3.72862i | −0.479272 | + | 0.128421i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.1837 | + | 8.07687i | −0.899682 | + | 0.277524i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.8831 | − | 10.3248i | 0.613746 | − | 0.354347i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.28251 | − | 12.6137i | 0.249641 | − | 0.432391i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.1341 | + | 27.1341i | 0.929053 | + | 0.929053i | 0.997645 | − | 0.0685915i | \(-0.0218505\pi\) |
−0.0685915 | + | 0.997645i | \(0.521851\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.4787 | + | 39.1071i | 0.357946 | + | 1.33587i | 0.876736 | + | 0.480972i | \(0.159716\pi\) |
−0.518789 | + | 0.854902i | \(0.673617\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.6419 | + | 32.2888i | 0.636055 | + | 1.10168i | 0.986291 | + | 0.165018i | \(0.0527681\pi\) |
−0.350236 | + | 0.936662i | \(0.613899\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.5598 | − | 0.694634i | 0.632516 | − | 0.0236731i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.5107 | + | 4.42404i | 0.562032 | + | 0.150596i | 0.528640 | − | 0.848846i | \(-0.322702\pi\) |
0.0333925 | + | 0.999442i | \(0.489369\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.5659 | + | 11.5659i | −0.392798 | + | 0.392798i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 5.42451i | − | 0.184014i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.96817 | − | 5.17777i | −0.303875 | − | 0.175442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.29410 | + | 4.82963i | −0.0437985 | + | 0.163458i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.6304 | + | 39.6731i | −0.358962 | + | 1.33967i | 0.516462 | + | 0.856310i | \(0.327249\pi\) |
−0.875424 | + | 0.483355i | \(0.839418\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.0343 | + | 13.8762i | 0.810658 | + | 0.468034i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.8014i | 0.633436i | 0.948520 | + | 0.316718i | \(0.102581\pi\) | ||||
−0.948520 | + | 0.316718i | \(0.897419\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.9855 | − | 30.9855i | 1.04274 | − | 1.04274i | 0.0436994 | − | 0.999045i | \(-0.486086\pi\) |
0.999045 | − | 0.0436994i | \(-0.0139144\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.08950 | + | 2.16758i | 0.271619 | + | 0.0727801i | 0.392057 | − | 0.919941i | \(-0.371763\pi\) |
−0.120439 | + | 0.992721i | \(0.538430\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.8306 | + | 16.2308i | −0.866330 | + | 0.544363i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.401047 | + | 0.694634i | 0.0134356 | + | 0.0232711i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.69058 | + | 28.7017i | 0.257356 | + | 0.960464i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.8718 | − | 21.8718i | −0.730279 | − | 0.730279i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.78742 | + | 5.07342i | −0.292752 | + | 0.169020i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.12505 | + | 5.68311i | 0.203829 | + | 0.189122i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.2222 | − | 9.43776i | 1.16953 | − | 0.313376i | 0.378767 | − | 0.925492i | \(-0.376348\pi\) |
0.790768 | + | 0.612116i | \(0.209682\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.03667 | 0.167056 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.0699 | 1.52637 | 0.763183 | − | 0.646183i | \(-0.223636\pi\) | ||||
0.763183 | + | 0.646183i | \(0.223636\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.122985 | + | 0.0329538i | −0.00407022 | + | 0.00109061i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.84451 | − | 9.22135i | −0.0939339 | − | 0.304516i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.0828 | + | 13.9042i | −0.794417 | + | 0.458657i | −0.841515 | − | 0.540234i | \(-0.818336\pi\) |
0.0470984 | + | 0.998890i | \(0.485003\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.74544 | + | 3.02320i | −0.0575143 | + | 0.0996178i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.9325 | − | 13.9325i | −0.458592 | − | 0.458592i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.30329 | + | 12.3280i | 0.108494 | + | 0.404906i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.6061 | − | 51.2793i | −0.971346 | − | 1.68242i | −0.691501 | − | 0.722376i | \(-0.743050\pi\) |
−0.279845 | − | 0.960045i | \(-0.590283\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.47308 | + | 19.6519i | 0.0482783 | + | 0.644065i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.6839 | + | 5.81018i | 0.709899 | + | 0.190217i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.5855 | + | 24.5855i | −0.803174 | + | 0.803174i | −0.983590 | − | 0.180416i | \(-0.942256\pi\) |
0.180416 | + | 0.983590i | \(0.442256\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.2433i | 0.627983i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.9713 | − | 14.9945i | −0.846640 | − | 0.488808i | 0.0128755 | − | 0.999917i | \(-0.495901\pi\) |
−0.859516 | + | 0.511109i | \(0.829235\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.2783 | + | 57.0193i | −0.497529 | + | 1.85681i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.88519 | + | 18.2318i | −0.158747 | + | 0.592453i | 0.840008 | + | 0.542574i | \(0.182550\pi\) |
−0.998755 | + | 0.0498792i | \(0.984116\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.3594 | + | 14.6413i | 0.823201 | + | 0.475275i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.6535i | 0.702162i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.3642 | + | 12.3642i | −0.400517 | + | 0.400517i | −0.878415 | − | 0.477898i | \(-0.841399\pi\) |
0.477898 | + | 0.878415i | \(0.341399\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.22137 | − | 59.3524i | −0.0717319 | − | 1.91659i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.12167 | + | 3.67484i | 0.0684410 | + | 0.118543i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.30359 | + | 4.86505i | 0.0420074 | + | 0.156774i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.6395 | − | 30.6395i | −0.985299 | − | 0.985299i | 0.0145946 | − | 0.999893i | \(-0.495354\pi\) |
−0.999893 | + | 0.0145946i | \(0.995354\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.12906 | + | 1.95560i | −0.0362708 | + | 0.0628228i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.1395 | + | 5.85403i | −0.325391 | + | 0.187865i | −0.653793 | − | 0.756673i | \(-0.726823\pi\) |
0.328402 | + | 0.944538i | \(0.393490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.7819 | − | 51.6222i | 0.377711 | − | 1.65493i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.5951 | − | 3.91076i | 0.466940 | − | 0.125116i | −0.0176751 | − | 0.999844i | \(-0.505626\pi\) |
0.484615 | + | 0.874728i | \(0.338960\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.11432 | −0.0356140 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.63916 | −0.275827 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.0225 | − | 14.2073i | 1.69116 | − | 0.453144i | 0.720469 | − | 0.693488i | \(-0.243927\pi\) |
0.970688 | + | 0.240344i | \(0.0772601\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.21358 | + | 27.2246i | −0.197780 | + | 0.866570i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.9987 | + | 13.2783i | −0.731316 | + | 0.422226i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.58251 | + | 9.66918i | −0.177334 | + | 0.307152i | −0.940967 | − | 0.338499i | \(-0.890081\pi\) |
0.763632 | + | 0.645651i | \(0.223414\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.7120 | + | 22.7120i | 0.720743 | + | 0.720743i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.64347 | − | 32.2579i | −0.273742 | − | 1.02162i | −0.956680 | − | 0.291141i | \(-0.905965\pi\) |
0.682939 | − | 0.730476i | \(-0.260702\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.866025 | + | 1.50000i | 0.0273998 | + | 0.0474579i |
(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 | 2100.2.ce.c.157.1 | ✓ | 24 | |
5.2 | odd | 4 | inner | 2100.2.ce.c.493.5 | yes | 24 | |
5.3 | odd | 4 | inner | 2100.2.ce.c.493.3 | yes | 24 | |
5.4 | even | 2 | inner | 2100.2.ce.c.157.6 | yes | 24 | |
7.5 | odd | 6 | inner | 2100.2.ce.c.1657.3 | yes | 24 | |
35.12 | even | 12 | inner | 2100.2.ce.c.1993.6 | yes | 24 | |
35.19 | odd | 6 | inner | 2100.2.ce.c.1657.5 | yes | 24 | |
35.33 | even | 12 | inner | 2100.2.ce.c.1993.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.ce.c.157.1 | ✓ | 24 | 1.1 | even | 1 | trivial | |
2100.2.ce.c.157.6 | yes | 24 | 5.4 | even | 2 | inner | |
2100.2.ce.c.493.3 | yes | 24 | 5.3 | odd | 4 | inner | |
2100.2.ce.c.493.5 | yes | 24 | 5.2 | odd | 4 | inner | |
2100.2.ce.c.1657.3 | yes | 24 | 7.5 | odd | 6 | inner | |
2100.2.ce.c.1657.5 | yes | 24 | 35.19 | odd | 6 | inner | |
2100.2.ce.c.1993.1 | yes | 24 | 35.33 | even | 12 | inner | |
2100.2.ce.c.1993.6 | yes | 24 | 35.12 | even | 12 | inner |