Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,2,Mod(81,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.l (of order \(4\), degree \(2\), 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: | \(2.55521286468\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 241.1 | ||
Root | \(1.21331 - 0.726558i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.241 |
Dual form | 320.2.l.a.81.1 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | −1.82762 | + | 1.82762i | −1.05518 | + | 1.05518i | −0.0567890 | + | 0.998386i | \(0.518086\pi\) |
−0.998386 | + | 0.0567890i | \(0.981914\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | − | 0.707107i | −0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.50961i | − | 1.70447i | −0.523158 | − | 0.852236i | \(-0.675246\pi\) | ||
0.523158 | − | 0.852236i | \(-0.324754\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.68037i | − | 1.22679i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.64080 | + | 1.64080i | 0.494721 | + | 0.494721i | 0.909790 | − | 0.415069i | \(-0.136243\pi\) |
−0.415069 | + | 0.909790i | \(0.636243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.51857 | − | 1.51857i | 0.421176 | − | 0.421176i | −0.464432 | − | 0.885609i | \(-0.653742\pi\) |
0.885609 | + | 0.464432i | \(0.153742\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.58464 | 0.667351 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.45616 | 0.353170 | 0.176585 | − | 0.984285i | \(-0.443495\pi\) | ||||
0.176585 | + | 0.984285i | \(0.443495\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.67964 | − | 2.67964i | 0.614752 | − | 0.614752i | −0.329428 | − | 0.944181i | \(-0.606856\pi\) |
0.944181 | + | 0.329428i | \(0.106856\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.24183 | + | 8.24183i | 1.79852 | + | 1.79852i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.37423i | − | 0.495061i | −0.968880 | − | 0.247530i | \(-0.920381\pi\) | ||
0.968880 | − | 0.247530i | \(-0.0796190\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.24345 | + | 1.24345i | 0.239303 | + | 0.239303i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.924966 | − | 0.924966i | 0.171762 | − | 0.171762i | −0.615991 | − | 0.787753i | \(-0.711244\pi\) |
0.787753 | + | 0.615991i | \(0.211244\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.20435 | 1.29394 | 0.646970 | − | 0.762515i | \(-0.276036\pi\) | ||||
0.646970 | + | 0.762515i | \(0.276036\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.99752 | −1.04403 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.18877 | + | 3.18877i | −0.539001 | + | 0.539001i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.21123 | − | 5.21123i | −0.856720 | − | 0.856720i | 0.134230 | − | 0.990950i | \(-0.457144\pi\) |
−0.990950 | + | 0.134230i | \(0.957144\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.55074i | 0.888830i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.41166i | − | 1.00133i | −0.865640 | − | 0.500667i | \(-0.833088\pi\) | ||
0.865640 | − | 0.500667i | \(-0.166912\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.65800 | − | 7.65800i | −1.16783 | − | 1.16783i | −0.982716 | − | 0.185118i | \(-0.940733\pi\) |
−0.185118 | − | 0.982716i | \(-0.559267\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.60241 | + | 2.60241i | −0.387945 | + | 0.387945i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.51027 | 0.366161 | 0.183081 | − | 0.983098i | \(-0.441393\pi\) | ||||
0.183081 | + | 0.983098i | \(0.441393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.3366 | −1.90522 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.66130 | + | 2.66130i | −0.372657 | + | 0.372657i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.50312 | + | 1.50312i | 0.206470 | + | 0.206470i | 0.802765 | − | 0.596295i | \(-0.203361\pi\) |
−0.596295 | + | 0.802765i | \(0.703361\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.32045i | − | 0.312889i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.79472i | 1.29734i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.31807 | + | 5.31807i | 0.692353 | + | 0.692353i | 0.962749 | − | 0.270396i | \(-0.0871546\pi\) |
−0.270396 | + | 0.962749i | \(0.587155\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.02169 | + | 1.02169i | −0.130815 | + | 0.130815i | −0.769483 | − | 0.638668i | \(-0.779486\pi\) |
0.638668 | + | 0.769483i | \(0.279486\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −16.5970 | −2.09103 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.14759 | −0.266375 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.22745 | + | 5.22745i | −0.638635 | + | 0.638635i | −0.950219 | − | 0.311584i | \(-0.899141\pi\) |
0.311584 | + | 0.950219i | \(0.399141\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.33918 | + | 4.33918i | 0.522376 | + | 0.522376i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.92097i | 0.227978i | 0.993482 | + | 0.113989i | \(0.0363628\pi\) | ||||
−0.993482 | + | 0.113989i | \(0.963637\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.39412i | − | 0.163169i | −0.996666 | − | 0.0815847i | \(-0.974002\pi\) | ||
0.996666 | − | 0.0815847i | \(-0.0259981\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.82762 | − | 1.82762i | −0.211035 | − | 0.211035i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.39938 | − | 7.39938i | 0.843237 | − | 0.843237i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.06317 | −0.569651 | −0.284825 | − | 0.958579i | \(-0.591936\pi\) | ||||
−0.284825 | + | 0.958579i | \(0.591936\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.49599 | 0.721777 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.44974 | − | 2.44974i | 0.268894 | − | 0.268894i | −0.559761 | − | 0.828654i | \(-0.689107\pi\) |
0.828654 | + | 0.559761i | \(0.189107\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.02966 | − | 1.02966i | −0.111682 | − | 0.111682i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.38097i | 0.362478i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.36007i | 0.992165i | 0.868275 | + | 0.496083i | \(0.165229\pi\) | ||||
−0.868275 | + | 0.496083i | \(0.834771\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.84817 | − | 6.84817i | −0.717883 | − | 0.717883i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.1668 | + | 13.1668i | −1.36533 | + | 1.36533i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.78959 | −0.388803 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.6313 | 1.89172 | 0.945859 | − | 0.324579i | \(-0.105223\pi\) | ||||
0.945859 | + | 0.324579i | \(0.105223\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.03876 | − | 6.03876i | 0.606918 | − | 0.606918i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.84108 | − | 4.84108i | −0.481705 | − | 0.481705i | 0.423971 | − | 0.905676i | \(-0.360636\pi\) |
−0.905676 | + | 0.423971i | \(0.860636\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.12540i | 0.899153i | 0.893242 | + | 0.449576i | \(0.148425\pi\) | ||||
−0.893242 | + | 0.449576i | \(0.851575\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 11.6557i | − | 1.13748i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.1505 | + | 10.1505i | 0.981290 | + | 0.981290i | 0.999828 | − | 0.0185385i | \(-0.00590132\pi\) |
−0.0185385 | + | 0.999828i | \(0.505901\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.35489 | − | 1.35489i | 0.129775 | − | 0.129775i | −0.639236 | − | 0.769011i | \(-0.720749\pi\) |
0.769011 | + | 0.639236i | \(0.220749\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 19.0483 | 1.80798 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.56039 | −0.240861 | −0.120431 | − | 0.992722i | \(-0.538428\pi\) | ||||
−0.120431 | + | 0.992722i | \(0.538428\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.67883 | + | 1.67883i | −0.156552 | + | 0.156552i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.58891 | − | 5.58891i | −0.516695 | − | 0.516695i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 6.56670i | − | 0.601969i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 5.61553i | − | 0.510503i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.7181 | + | 11.7181i | 1.05658 | + | 1.05658i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.707107 | − | 0.707107i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.7354 | −1.21882 | −0.609409 | − | 0.792856i | \(-0.708593\pi\) | ||||
−0.609409 | + | 0.792856i | \(0.708593\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 27.9918 | 2.46454 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.20726 | + | 5.20726i | −0.454960 | + | 0.454960i | −0.896997 | − | 0.442037i | \(-0.854256\pi\) |
0.442037 | + | 0.896997i | \(0.354256\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0841 | − | 12.0841i | −1.04783 | − | 1.04783i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1.75851i | − | 0.151348i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.7563i | 1.94420i | 0.234559 | + | 0.972102i | \(0.424635\pi\) | ||||
−0.234559 | + | 0.972102i | \(0.575365\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.28085 | − | 6.28085i | −0.532734 | − | 0.532734i | 0.388651 | − | 0.921385i | \(-0.372941\pi\) |
−0.921385 | + | 0.388651i | \(0.872941\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.58782 | + | 4.58782i | −0.386364 | + | 0.386364i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.98336 | 0.416729 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.30810 | −0.108632 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 24.3741 | − | 24.3741i | 2.01034 | − | 2.01034i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.9574 | − | 12.9574i | −1.06151 | − | 1.06151i | −0.997980 | − | 0.0635329i | \(-0.979763\pi\) |
−0.0635329 | − | 0.997980i | \(-0.520237\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.3417i | − | 1.16711i | −0.812073 | − | 0.583555i | \(-0.801661\pi\) | ||
0.812073 | − | 0.583555i | \(-0.198339\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 5.35920i | − | 0.433266i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.09425 | − | 5.09425i | −0.409180 | − | 0.409180i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.10564 | + | 2.10564i | −0.168049 | + | 0.168049i | −0.786121 | − | 0.618073i | \(-0.787914\pi\) |
0.618073 | + | 0.786121i | \(0.287914\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.49426 | −0.435723 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.7068 | −0.843817 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.34004 | − | 5.34004i | 0.418265 | − | 0.418265i | −0.466341 | − | 0.884605i | \(-0.654428\pi\) |
0.884605 | + | 0.466341i | \(0.154428\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.24089 | + | 4.24089i | 0.330153 | + | 0.330153i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.0686i | 1.24343i | 0.783245 | + | 0.621714i | \(0.213563\pi\) | ||||
−0.783245 | + | 0.621714i | \(0.786437\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.38787i | 0.645221i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.86207 | − | 9.86207i | −0.754171 | − | 0.754171i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.1133 | − | 17.1133i | 1.30110 | − | 1.30110i | 0.373453 | − | 0.927649i | \(-0.378174\pi\) |
0.927649 | − | 0.373453i | \(-0.121826\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.50961 | 0.340894 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.4388 | −1.46111 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.04482 | + | 1.04482i | −0.0780933 | + | 0.0780933i | −0.745075 | − | 0.666981i | \(-0.767586\pi\) |
0.666981 | + | 0.745075i | \(0.267586\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.9886 | + | 11.9886i | 0.891104 | + | 0.891104i | 0.994627 | − | 0.103523i | \(-0.0330115\pi\) |
−0.103523 | + | 0.994627i | \(0.533012\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.73453i | − | 0.276065i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.36979i | 0.541838i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.38927 | + | 2.38927i | 0.174721 | + | 0.174721i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.60748 | − | 5.60748i | 0.407884 | − | 0.407884i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.0667471 | −0.00482965 | −0.00241483 | − | 0.999997i | \(-0.500769\pi\) | ||||
−0.00241483 | + | 0.999997i | \(0.500769\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.09895 | −0.0791039 | −0.0395520 | − | 0.999218i | \(-0.512593\pi\) | ||||
−0.0395520 | + | 0.999218i | \(0.512593\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.92497 | − | 3.92497i | 0.281073 | − | 0.281073i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.9289 | + | 11.9289i | 0.849899 | + | 0.849899i | 0.990120 | − | 0.140222i | \(-0.0447815\pi\) |
−0.140222 | + | 0.990120i | \(0.544782\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.0397i | 0.782584i | 0.920267 | + | 0.391292i | \(0.127972\pi\) | ||||
−0.920267 | + | 0.391292i | \(0.872028\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 19.1076i | − | 1.34774i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.17123 | − | 4.17123i | −0.292763 | − | 0.292763i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.53373 | + | 4.53373i | −0.316649 | + | 0.316649i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.73803 | −0.607335 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.79353 | 0.608261 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.59737 | − | 8.59737i | 0.591868 | − | 0.591868i | −0.346268 | − | 0.938136i | \(-0.612551\pi\) |
0.938136 | + | 0.346268i | \(0.112551\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.51080 | − | 3.51080i | −0.240556 | − | 0.240556i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.8301i | 0.738603i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 32.4888i | − | 2.20548i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.54792 | + | 2.54792i | 0.172172 | + | 0.172172i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.21128 | − | 2.21128i | 0.148747 | − | 0.148747i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.4238 | 1.43465 | 0.717323 | − | 0.696741i | \(-0.245367\pi\) | ||||
0.717323 | + | 0.696741i | \(0.245367\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.68037 | 0.245358 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.06331 | − | 8.06331i | 0.535181 | − | 0.535181i | −0.386929 | − | 0.922110i | \(-0.626464\pi\) |
0.922110 | + | 0.386929i | \(0.126464\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.63169 | + | 4.63169i | 0.306071 | + | 0.306071i | 0.843383 | − | 0.537313i | \(-0.180560\pi\) |
−0.537313 | + | 0.843383i | \(0.680560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 27.0465i | 1.77953i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26.0672i | 1.70772i | 0.520502 | + | 0.853860i | \(0.325745\pi\) | ||||
−0.520502 | + | 0.853860i | \(0.674255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.77503 | − | 1.77503i | −0.115790 | − | 0.115790i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.25353 | − | 9.25353i | 0.601081 | − | 0.601081i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.12209 | −0.331320 | −0.165660 | − | 0.986183i | \(-0.552975\pi\) | ||||
−0.165660 | + | 0.986183i | \(0.552975\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.4987 | 0.740695 | 0.370347 | − | 0.928893i | \(-0.379239\pi\) | ||||
0.370347 | + | 0.928893i | \(0.379239\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.6025 | + | 15.6025i | −1.00090 | + | 1.00090i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.43037 | + | 9.43037i | 0.602484 | + | 0.602484i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.13847i | − | 0.517838i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.95437i | 0.567460i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.8270 | + | 19.8270i | 1.25147 | + | 1.25147i | 0.955061 | + | 0.296408i | \(0.0957889\pi\) |
0.296408 | + | 0.955061i | \(0.404211\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.89564 | − | 3.89564i | 0.244917 | − | 0.244917i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.76365 | 0.235689 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.2494 | −1.51264 | −0.756319 | − | 0.654203i | \(-0.773004\pi\) | ||||
−0.756319 | + | 0.654203i | \(0.773004\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.5006 | + | 23.5006i | −1.46026 | + | 1.46026i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.40422 | − | 3.40422i | −0.210716 | − | 0.210716i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 22.5680i | − | 1.39160i | −0.718234 | − | 0.695802i | \(-0.755049\pi\) | ||
0.718234 | − | 0.695802i | \(-0.244951\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.12574i | − | 0.130583i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.1066 | − | 17.1066i | −1.04691 | − | 1.04691i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.10558 | + | 5.10558i | −0.311293 | + | 0.311293i | −0.845410 | − | 0.534117i | \(-0.820644\pi\) |
0.534117 | + | 0.845410i | \(0.320644\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.67920 | −0.405733 | −0.202866 | − | 0.979206i | \(-0.565026\pi\) | ||||
−0.202866 | + | 0.979206i | \(0.565026\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.0317 | 1.51498 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.64080 | + | 1.64080i | −0.0989441 | + | 0.0989441i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.8524 | − | 11.8524i | −0.712141 | − | 0.712141i | 0.254842 | − | 0.966983i | \(-0.417977\pi\) |
−0.966983 | + | 0.254842i | \(0.917977\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 26.5147i | − | 1.58739i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.477460i | 0.0284829i | 0.999899 | + | 0.0142414i | \(0.00453334\pi\) | ||||
−0.999899 | + | 0.0142414i | \(0.995467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.482914 | + | 0.482914i | 0.0287063 | + | 0.0287063i | 0.721314 | − | 0.692608i | \(-0.243538\pi\) |
−0.692608 | + | 0.721314i | \(0.743538\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.92591 | − | 6.92591i | 0.410256 | − | 0.410256i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.9141 | −1.70674 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8796 | −0.875271 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −34.0508 | + | 34.0508i | −1.99609 | + | 1.99609i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.46638 | + | 7.46638i | 0.436190 | + | 0.436190i | 0.890728 | − | 0.454537i | \(-0.150195\pi\) |
−0.454537 | + | 0.890728i | \(0.650195\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 7.52088i | − | 0.437883i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.08052i | 0.236776i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.60544 | − | 3.60544i | −0.208508 | − | 0.208508i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −34.5346 | + | 34.5346i | −1.99054 | + | 1.99054i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.6953 | 1.01657 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.44489 | 0.0827344 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.39349 | + | 2.39349i | −0.136604 | + | 0.136604i | −0.772102 | − | 0.635498i | \(-0.780795\pi\) |
0.635498 | + | 0.772102i | \(0.280795\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.6777 | − | 16.6777i | −0.948764 | − | 0.948764i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 20.4404i | − | 1.15907i | −0.814948 | − | 0.579534i | \(-0.803235\pi\) | ||
0.814948 | − | 0.579534i | \(-0.196765\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.46975i | − | 0.139598i | −0.997561 | − | 0.0697992i | \(-0.977764\pi\) | ||
0.997561 | − | 0.0697992i | \(-0.0222359\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.7359 | + | 11.7359i | 0.661241 | + | 0.661241i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.2241 | + | 16.2241i | −0.911234 | + | 0.911234i | −0.996369 | − | 0.0851350i | \(-0.972868\pi\) |
0.0851350 | + | 0.996369i | \(0.472868\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.03537 | 0.169948 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −37.1026 | −2.07086 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.90198 | − | 3.90198i | 0.217112 | − | 0.217112i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.51857 | + | 1.51857i | 0.0842353 | + | 0.0842353i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.95246i | 0.273871i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 11.3204i | − | 0.624111i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.42340 | − | 3.42340i | −0.188167 | − | 0.188167i | 0.606736 | − | 0.794903i | \(-0.292479\pi\) |
−0.794903 | + | 0.606736i | \(0.792479\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −19.1792 | + | 19.1792i | −1.05102 | + | 1.05102i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.39273 | 0.403908 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.40017 | −0.294166 | −0.147083 | − | 0.989124i | \(-0.546988\pi\) | ||||
−0.147083 | + | 0.989124i | \(0.546988\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.67941 | − | 4.67941i | 0.254151 | − | 0.254151i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.8209 | + | 11.8209i | 0.640139 | + | 0.640139i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 28.5754i | 1.54292i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 6.13653i | − | 0.330379i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.07531 | + | 4.07531i | 0.218774 | + | 0.218774i | 0.807982 | − | 0.589208i | \(-0.200560\pi\) |
−0.589208 | + | 0.807982i | \(0.700560\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.55681 | − | 1.55681i | 0.0833339 | − | 0.0833339i | −0.664211 | − | 0.747545i | \(-0.731232\pi\) |
0.747545 | + | 0.664211i | \(0.231232\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.77655 | 0.201577 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.34919 | 0.0718103 | 0.0359052 | − | 0.999355i | \(-0.488569\pi\) | ||||
0.0359052 | + | 0.999355i | \(0.488569\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.35833 | − | 1.35833i | 0.0720929 | − | 0.0720929i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.0014 | + | 12.0014i | 0.635182 | + | 0.635182i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 23.2192i | − | 1.22546i | −0.790291 | − | 0.612732i | \(-0.790071\pi\) | ||
0.790291 | − | 0.612732i | \(-0.209929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.63903i | 0.244159i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.2630 | + | 10.2630i | 0.538670 | + | 0.538670i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.985792 | + | 0.985792i | −0.0515987 | + | 0.0515987i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.16452 | 0.269586 | 0.134793 | − | 0.990874i | \(-0.456963\pi\) | ||||
0.134793 | + | 0.990874i | \(0.456963\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23.5973 | −1.22843 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.77849 | − | 6.77849i | 0.351922 | − | 0.351922i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.5056 | + | 18.5056i | 0.958185 | + | 0.958185i | 0.999160 | − | 0.0409750i | \(-0.0130464\pi\) |
−0.0409750 | + | 0.999160i | \(0.513046\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.58464i | 0.133470i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.80926i | − | 0.144684i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.5254 | + | 13.5254i | 0.694754 | + | 0.694754i | 0.963274 | − | 0.268520i | \(-0.0865346\pi\) |
−0.268520 | + | 0.963274i | \(0.586535\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 25.1030 | − | 25.1030i | 1.28607 | − | 1.28607i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.9051 | −1.11930 | −0.559650 | − | 0.828729i | \(-0.689064\pi\) | ||||
−0.559650 | + | 0.828729i | \(0.689064\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.4643 | −0.533310 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −28.1843 | + | 28.1843i | −1.43269 | + | 1.43269i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.48844 | + | 4.48844i | 0.227573 | + | 0.227573i | 0.811678 | − | 0.584105i | \(-0.198554\pi\) |
−0.584105 | + | 0.811678i | \(0.698554\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.45725i | − | 0.174841i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 19.0337i | − | 0.960126i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.58020 | + | 3.58020i | 0.180139 | + | 0.180139i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.7892 | − | 11.7892i | 0.591682 | − | 0.591682i | −0.346404 | − | 0.938086i | \(-0.612597\pi\) |
0.938086 | + | 0.346404i | \(0.112597\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 44.1703 | 2.21128 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.9259 | 1.24474 | 0.622371 | − | 0.782722i | \(-0.286170\pi\) | ||||
0.622371 | + | 0.782722i | \(0.286170\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.9403 | − | 10.9403i | 0.544977 | − | 0.544977i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.59336 | − | 4.59336i | −0.228246 | − | 0.228246i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 17.1012i | − | 0.847675i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 21.5355i | − | 1.06486i | −0.846474 | − | 0.532430i | \(-0.821279\pi\) | ||
0.846474 | − | 0.532430i | \(-0.178721\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −41.5898 | − | 41.5898i | −2.05148 | − | 2.05148i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23.9824 | − | 23.9824i | 1.18010 | − | 1.18010i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.46445 | −0.170063 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.9580 | 1.12426 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.2979 | − | 17.2979i | 0.845060 | − | 0.845060i | −0.144452 | − | 0.989512i | \(-0.546142\pi\) |
0.989512 | + | 0.144452i | \(0.0461419\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.4330 | − | 19.4330i | −0.947105 | − | 0.947105i | 0.0515648 | − | 0.998670i | \(-0.483579\pi\) |
−0.998670 | + | 0.0515648i | \(0.983579\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 9.23874i | − | 0.449203i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.45616i | 0.0706341i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.60744 | + | 4.60744i | 0.222970 | + | 0.222970i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.10767 | + | 9.10767i | −0.439723 | + | 0.439723i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.3769 | −1.36687 | −0.683433 | − | 0.730013i | \(-0.739514\pi\) | ||||
−0.683433 | + | 0.730013i | \(0.739514\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.04007 | 0.434438 | 0.217219 | − | 0.976123i | \(-0.430301\pi\) | ||||
0.217219 | + | 0.976123i | \(0.430301\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.39071 | − | 2.39071i | 0.114626 | − | 0.114626i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.36208 | − | 6.36208i | −0.304340 | − | 0.304340i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.2949i | 1.35044i | 0.737615 | + | 0.675221i | \(0.235952\pi\) | ||||
−0.737615 | + | 0.675221i | \(0.764048\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 49.0834i | 2.33731i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.1232 | + | 13.1232i | 0.623504 | + | 0.623504i | 0.946426 | − | 0.322922i | \(-0.104665\pi\) |
−0.322922 | + | 0.946426i | \(0.604665\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.61857 | − | 6.61857i | 0.313750 | − | 0.313750i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 47.3624 | 2.24016 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.3902 | −0.679116 | −0.339558 | − | 0.940585i | \(-0.610277\pi\) | ||||
−0.339558 | + | 0.940585i | \(0.610277\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.5203 | − | 10.5203i | 0.495380 | − | 0.495380i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26.2111 | + | 26.2111i | 1.23151 | + | 1.23151i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.68477i | 0.454029i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.54538i | 0.212624i | 0.994333 | + | 0.106312i | \(0.0339042\pi\) | ||||
−0.994333 | + | 0.106312i | \(0.966096\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.81066 | + | 1.81066i | 0.0845146 | + | 0.0845146i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.8046 | − | 19.8046i | 0.922393 | − | 0.922393i | −0.0748050 | − | 0.997198i | \(-0.523833\pi\) |
0.997198 | + | 0.0748050i | \(0.0238334\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.5997 | 0.678506 | 0.339253 | − | 0.940695i | \(-0.389826\pi\) | ||||
0.339253 | + | 0.940695i | \(0.389826\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.6207 | 0.863513 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.8105 | + | 19.8105i | −0.916722 | + | 0.916722i | −0.996789 | − | 0.0800671i | \(-0.974487\pi\) |
0.0800671 | + | 0.996789i | \(0.474487\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.5738 | + | 23.5738i | 1.08853 | + | 1.08853i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 7.69661i | − | 0.354641i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 25.1306i | − | 1.15550i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.67964 | + | 2.67964i | 0.122950 | + | 0.122950i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.53204 | − | 5.53204i | 0.253295 | − | 0.253295i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.0378 | −0.961243 | −0.480621 | − | 0.876928i | \(-0.659589\pi\) | ||||
−0.480621 | + | 0.876928i | \(0.659589\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.8273 | −0.721661 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 19.5680 | − | 19.5680i | 0.890375 | − | 0.890375i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.1743 | − | 13.1743i | −0.598214 | − | 0.598214i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.2724i | 0.465485i | 0.972538 | + | 0.232743i | \(0.0747699\pi\) | ||||
−0.972538 | + | 0.232743i | \(0.925230\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.5191i | 0.882685i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.95681 | + | 5.95681i | 0.268827 | + | 0.268827i | 0.828627 | − | 0.559801i | \(-0.189122\pi\) |
−0.559801 | + | 0.828627i | \(0.689122\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.34690 | − | 1.34690i | 0.0606612 | − | 0.0606612i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.54009 | −0.383849 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.66284 | 0.388581 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.81466 | − | 2.81466i | 0.126002 | − | 0.126002i | −0.641294 | − | 0.767295i | \(-0.721602\pi\) |
0.767295 | + | 0.641294i | \(0.221602\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.3673 | − | 29.3673i | −1.31203 | − | 1.31203i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 5.49759i | − | 0.245125i | −0.992461 | − | 0.122563i | \(-0.960889\pi\) | ||
0.992461 | − | 0.122563i | \(-0.0391113\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.84632i | 0.304657i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.3298 | − | 15.3298i | −0.680821 | − | 0.680821i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.37578 | + | 4.37578i | −0.193953 | + | 0.193953i | −0.797402 | − | 0.603449i | \(-0.793793\pi\) |
0.603449 | + | 0.797402i | \(0.293793\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.28693 | −0.278118 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.66402 | 0.294224 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.45263 | − | 6.45263i | 0.284337 | − | 0.284337i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.11887 | + | 4.11887i | 0.181148 | + | 0.181148i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 62.5532i | 2.74578i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 33.8729i | − | 1.48400i | −0.670401 | − | 0.741999i | \(-0.733878\pi\) | ||
0.670401 | − | 0.741999i | \(-0.266122\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.8060 | − | 27.8060i | −1.21587 | − | 1.21587i | −0.969065 | − | 0.246804i | \(-0.920620\pi\) |
−0.246804 | − | 0.969065i | \(-0.579380\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.24183 | + | 8.24183i | −0.359703 | + | 0.359703i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.4907 | 0.456981 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.3630 | 0.754915 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.5724 | − | 19.5724i | 0.849372 | − | 0.849372i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.73658 | − | 9.73658i | −0.421738 | − | 0.421738i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 14.3550i | − | 0.620622i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 3.81905i | − | 0.164804i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21.8827 | − | 21.8827i | −0.942553 | − | 0.942553i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.03066 | − | 3.03066i | 0.130298 | − | 0.130298i | −0.638950 | − | 0.769248i | \(-0.720631\pi\) |
0.769248 | + | 0.638950i | \(0.220631\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −43.8211 | −1.88054 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.91611 | −0.0820771 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.4783 | − | 18.4783i | 0.790074 | − | 0.790074i | −0.191432 | − | 0.981506i | \(-0.561313\pi\) |
0.981506 | + | 0.191432i | \(0.0613131\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.76021 | + | 3.76021i | 0.160482 | + | 0.160482i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 4.95716i | − | 0.211182i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.8329i | 0.970953i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.4691 | − | 13.4691i | −0.571734 | − | 0.571734i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.2060 | + | 30.2060i | −1.27987 | + | 1.27987i | −0.339127 | + | 0.940741i | \(0.610132\pi\) |
−0.940741 | + | 0.339127i | \(0.889868\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.2585 | −0.983729 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.73334 | −0.368722 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.86747 | + | 2.86747i | −0.120850 | + | 0.120850i | −0.764945 | − | 0.644095i | \(-0.777234\pi\) |
0.644095 | + | 0.764945i | \(0.277234\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.81047 | + | 1.81047i | 0.0761670 | + | 0.0761670i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 29.2944i | − | 1.23025i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 35.8628i | − | 1.50345i | −0.659479 | − | 0.751723i | \(-0.729223\pi\) | ||
0.659479 | − | 0.751723i | \(-0.270777\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.6509 | + | 17.6509i | 0.738667 | + | 0.738667i | 0.972320 | − | 0.233653i | \(-0.0750679\pi\) |
−0.233653 | + | 0.972320i | \(0.575068\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.121988 | − | 0.121988i | 0.00509613 | − | 0.00509613i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.37423 | 0.0990122 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.1387 | 1.50448 | 0.752238 | − | 0.658892i | \(-0.228975\pi\) | ||||
0.752238 | + | 0.658892i | \(0.228975\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.00845 | − | 2.00845i | 0.0834685 | − | 0.0834685i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.0474 | − | 11.0474i | −0.458322 | − | 0.458322i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.93265i | 0.204290i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.90391i | 0.326786i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.4005 | + | 11.4005i | 0.470550 | + | 0.470550i | 0.902093 | − | 0.431542i | \(-0.142030\pi\) |
−0.431542 | + | 0.902093i | \(0.642030\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.3051 | − | 19.3051i | 0.795453 | − | 0.795453i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −43.6029 | −1.79358 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −35.0454 | −1.43914 | −0.719572 | − | 0.694418i | \(-0.755662\pi\) | ||||
−0.719572 | + | 0.694418i | \(0.755662\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.64336 | + | 4.64336i | −0.190359 | + | 0.190359i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.1764 | − | 20.1764i | −0.825764 | − | 0.825764i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.2753i | 0.746707i | 0.927689 | + | 0.373354i | \(0.121792\pi\) | ||||
−0.927689 | + | 0.373354i | \(0.878208\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.480142i | 0.0195854i | 0.999952 | + | 0.00979269i | \(0.00311716\pi\) | ||||
−0.999952 | + | 0.00979269i | \(0.996883\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.2389 | + | 19.2389i | 0.783470 | + | 0.783470i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.97078 | + | 3.97078i | −0.161435 | + | 0.161435i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.6107 | 1.56716 | 0.783581 | − | 0.621290i | \(-0.213391\pi\) | ||||
0.783581 | + | 0.621290i | \(0.213391\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.2468 | 0.617833 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.81204 | − | 3.81204i | 0.154218 | − | 0.154218i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.53592 | − | 5.53592i | −0.223594 | − | 0.223594i | 0.586416 | − | 0.810010i | \(-0.300538\pi\) |
−0.810010 | + | 0.586416i | \(0.800538\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 16.5718i | − | 0.668241i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.8836i | 1.28358i | 0.766879 | + | 0.641792i | \(0.221809\pi\) | ||||
−0.766879 | + | 0.641792i | \(0.778191\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.4054 | + | 29.4054i | 1.18190 | + | 1.18190i | 0.979251 | + | 0.202650i | \(0.0649553\pi\) |
0.202650 | + | 0.979251i | \(0.435045\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.95224 | − | 2.95224i | 0.118469 | − | 0.118469i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 42.2102 | 1.69112 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.0712 | + | 16.0712i | −0.641822 | + | 0.641822i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.58837 | − | 7.58837i | −0.302568 | − | 0.302568i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.7381i | 1.22367i | 0.790987 | + | 0.611833i | \(0.209568\pi\) | ||||
−0.790987 | + | 0.611833i | \(0.790432\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 31.4254i | 1.24905i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.71239 | + | 9.71239i | 0.385424 | + | 0.385424i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.2525 | + | 20.2525i | −0.802435 | + | 0.802435i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.06989 | 0.279681 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.6348 | 0.538540 | 0.269270 | − | 0.963065i | \(-0.413218\pi\) | ||||
0.269270 | + | 0.963065i | \(0.413218\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.9224 | + | 14.9224i | −0.588480 | + | 0.588480i | −0.937220 | − | 0.348740i | \(-0.886610\pi\) |
0.348740 | + | 0.937220i | \(0.386610\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.7932 | − | 19.7932i | −0.779356 | − | 0.779356i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.87972i | 0.191841i | 0.995389 | + | 0.0959207i | \(0.0305795\pi\) | ||||
−0.995389 | + | 0.0959207i | \(0.969420\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.4518i | 0.685043i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 59.3771 | + | 59.3771i | 2.32717 | + | 2.32717i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.2913 | + | 10.2913i | −0.402731 | + | 0.402731i | −0.879194 | − | 0.476463i | \(-0.841919\pi\) |
0.476463 | + | 0.879194i | \(0.341919\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.36417 | 0.287742 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.13088 | −0.200174 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.9025 | − | 21.9025i | 0.853201 | − | 0.853201i | −0.137325 | − | 0.990526i | \(-0.543851\pi\) |
0.990526 | + | 0.137325i | \(0.0438505\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.40595 | + | 5.40595i | 0.210267 | + | 0.210267i | 0.804381 | − | 0.594114i | \(-0.202497\pi\) |
−0.594114 | + | 0.804381i | \(0.702497\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.08276i | 0.313908i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.0895i | 0.662704i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.19608 | − | 2.19608i | −0.0850326 | − | 0.0850326i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −39.1546 | + | 39.1546i | −1.51380 | + | 1.51380i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.35280 | −0.129433 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.3820 | 1.36388 | 0.681938 | − | 0.731410i | \(-0.261138\pi\) | ||||
0.681938 | + | 0.731410i | \(0.261138\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.24345 | + | 1.24345i | −0.0478605 | + | 0.0478605i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.17061 | + | 5.17061i | 0.198723 | + | 0.198723i | 0.799452 | − | 0.600730i | \(-0.205123\pi\) |
−0.600730 | + | 0.799452i | \(0.705123\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 84.0196i | − | 3.22438i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.4733i | 1.12942i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.5989 | − | 26.5989i | −1.01778 | − | 1.01778i | −0.999839 | − | 0.0179409i | \(-0.994289\pi\) |
−0.0179409 | − | 0.999839i | \(-0.505711\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.0912 | − | 16.0912i | 0.614811 | − | 0.614811i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.9299 | −0.645916 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.56520 | 0.173920 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.7989 | − | 21.7989i | 0.829270 | − | 0.829270i | −0.158146 | − | 0.987416i | \(-0.550552\pi\) |
0.987416 | + | 0.158146i | \(0.0505516\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −27.2324 | − | 27.2324i | −1.03447 | − | 1.03447i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.88246i | 0.336931i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 9.33640i | − | 0.353641i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −47.6409 | − | 47.6409i | −1.80194 | − | 1.80194i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.2175 | + | 15.2175i | −0.574756 | + | 0.574756i | −0.933454 | − | 0.358698i | \(-0.883221\pi\) |
0.358698 | + | 0.933454i | \(0.383221\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.9285 | −1.05334 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.48816 | 0.244358 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.8313 | + | 21.8313i | −0.821052 | + | 0.821052i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.87350 | + | 4.87350i | 0.183028 | + | 0.183028i | 0.792674 | − | 0.609646i | \(-0.208688\pi\) |
−0.609646 | + | 0.792674i | \(0.708688\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.6343i | 0.698842i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 17.1048i | − | 0.640579i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.52377 | − | 3.52377i | −0.131781 | − | 0.131781i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.36121 | − | 9.36121i | 0.349601 | − | 0.349601i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.27351 | −0.345843 | −0.172922 | − | 0.984936i | \(-0.555321\pi\) | ||||
−0.172922 | + | 0.984936i | \(0.555321\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.1520 | 1.53258 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.0152 | + | 21.0152i | −0.781563 | + | 0.781563i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.924966 | + | 0.924966i | 0.0343524 | + | 0.0343524i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.6056i | 0.393341i | 0.980470 | + | 0.196670i | \(0.0630129\pi\) | ||||
−0.980470 | + | 0.196670i | \(0.936987\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 37.5430i | − | 1.39048i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.1513 | − | 11.1513i | −0.412445 | − | 0.412445i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.6530 | + | 29.6530i | −1.09526 | + | 1.09526i | −0.100301 | + | 0.994957i | \(0.531981\pi\) |
−0.994957 | + | 0.100301i | \(0.968019\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −34.4702 | −1.27145 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.1544 | −0.631892 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.8751 | + | 30.8751i | −1.13576 | + | 1.13576i | −0.146559 | + | 0.989202i | \(0.546820\pi\) |
−0.989202 | + | 0.146559i | \(0.953180\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.8740 | + | 14.8740i | 0.546410 | + | 0.546410i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.3956i | 0.821617i | 0.911722 | + | 0.410808i | \(0.134753\pi\) | ||||
−0.911722 | + | 0.410808i | \(0.865247\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.3245i | 0.671360i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.01594 | − | 9.01594i | −0.329876 | − | 0.329876i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 45.7749 | − | 45.7749i | 1.67258 | − | 1.67258i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.6448 | −0.753341 | −0.376670 | − | 0.926347i | \(-0.622931\pi\) | ||||
−0.376670 | + | 0.926347i | \(0.622931\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −72.4724 | −2.64104 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.1411 | + | 10.1411i | −0.369073 | + | 0.369073i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.1323 | + | 24.1323i | 0.877104 | + | 0.877104i | 0.993234 | − | 0.116130i | \(-0.0370490\pi\) |
−0.116130 | + | 0.993234i | \(0.537049\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.2395i | 0.516860i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 50.1874i | 1.81929i | 0.415383 | + | 0.909647i | \(0.363648\pi\) | ||||
−0.415383 | + | 0.909647i | \(0.636352\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.11004 | − | 6.11004i | −0.221198 | − | 0.221198i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.78953 | + | 3.78953i | −0.137011 | + | 0.137011i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.1517 | 0.583206 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.6887 | −1.03454 | −0.517270 | − | 0.855822i | \(-0.673052\pi\) | ||||
−0.517270 | + | 0.855822i | \(0.673052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 44.3187 | − | 44.3187i | 1.59610 | − | 1.59610i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −37.5957 | − | 37.5957i | −1.35222 | − | 1.35222i | −0.883171 | − | 0.469052i | \(-0.844596\pi\) |
−0.469052 | − | 0.883171i | \(-0.655404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.20435i | 0.258788i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 85.9001i | − | 3.08165i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.1810 | − | 17.1810i | −0.615572 | − | 0.615572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.15194 | + | 3.15194i | −0.112785 | + | 0.112785i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.30030 | 0.0822061 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.97783 | 0.106283 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.13285 | − | 3.13285i | 0.111674 | − | 0.111674i | −0.649062 | − | 0.760736i | \(-0.724838\pi\) |
0.760736 | + | 0.649062i | \(0.224838\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 41.2457 | + | 41.2457i | 1.46839 | + | 1.46839i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.5463i | 0.410541i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.10304i | 0.110192i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.88503 | + | 3.88503i | 0.137788 | + | 0.137788i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.0562195 | − | 0.0562195i | 0.00199140 | − | 0.00199140i | −0.706110 | − | 0.708102i | \(-0.749552\pi\) |
0.708102 | + | 0.706110i | \(0.249552\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.65536 | 0.129317 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 34.4485 | 1.21718 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.28748 | − | 2.28748i | 0.0807233 | − | 0.0807233i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.57088 | + | 7.57088i | 0.266838 | + | 0.266838i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 18.6621i | − | 0.656937i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 3.59856i | − | 0.126518i | −0.997997 | − | 0.0632592i | \(-0.979851\pi\) | ||
0.997997 | − | 0.0632592i | \(-0.0201495\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.36274 | + | 7.36274i | 0.258541 | + | 0.258541i | 0.824460 | − | 0.565920i | \(-0.191479\pi\) |
−0.565920 | + | 0.824460i | \(0.691479\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.2070 | − | 12.2070i | 0.428119 | − | 0.428119i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.55196 | −0.264534 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −41.0414 | −1.43586 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25.2038 | + | 25.2038i | −0.880691 | + | 0.880691i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.7799 | + | 14.7799i | 0.515824 | + | 0.515824i | 0.916305 | − | 0.400481i | \(-0.131157\pi\) |
−0.400481 | + | 0.916305i | \(0.631157\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.7544i | 1.83890i | 0.393203 | + | 0.919452i | \(0.371367\pi\) | ||||
−0.393203 | + | 0.919452i | \(0.628633\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 5.99752i | − | 0.208807i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.8883 | − | 16.8883i | −0.587265 | − | 0.587265i | 0.349625 | − | 0.936890i | \(-0.386309\pi\) |
−0.936890 | + | 0.349625i | \(0.886309\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.55974 | + | 8.55974i | −0.297292 | + | 0.297292i | −0.839952 | − | 0.542660i | \(-0.817417\pi\) |
0.542660 | + | 0.839952i | \(0.317417\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 43.3232 | 1.50287 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.4201 | −0.672868 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.3622 | − | 11.3622i | 0.393206 | − | 0.393206i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.95827 | + | 8.95827i | 0.309643 | + | 0.309643i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.5407i | 0.605572i | 0.953059 | + | 0.302786i | \(0.0979168\pi\) | ||||
−0.953059 | + | 0.302786i | \(0.902083\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.2889i | 0.940996i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.872614 | − | 0.872614i | −0.0300544 | − | 0.0300544i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.93112 | − | 5.93112i | 0.204037 | − | 0.204037i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.3238 | −0.870137 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.76516 | −0.0605803 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.3726 | + | 12.3726i | −0.424129 | + | 0.424129i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.3577 | − | 15.3577i | −0.525839 | − | 0.525839i | 0.393490 | − | 0.919329i | \(-0.371268\pi\) |
−0.919329 | + | 0.393490i | \(0.871268\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.9471i | 0.476980i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 17.9553i | − | 0.613341i | −0.951816 | − | 0.306671i | \(-0.900785\pi\) | ||
0.951816 | − | 0.306671i | \(-0.0992150\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.3048 | + | 33.3048i | 1.13634 | + | 1.13634i | 0.989100 | + | 0.147245i | \(0.0470405\pi\) |
0.147245 | + | 0.989100i | \(0.452960\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 52.8439 | − | 52.8439i | 1.80091 | − | 1.80091i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.3557 | 1.10140 | 0.550701 | − | 0.834703i | \(-0.314361\pi\) | ||||
0.550701 | + | 0.834703i | \(0.314361\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.2019 | −0.822889 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.1942 | − | 27.1942i | 0.923564 | − | 0.923564i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.30766 | − | 8.30766i | −0.281818 | − | 0.281818i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.8765i | 0.537956i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 68.5699i | − | 2.32074i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.18877 | − | 3.18877i | −0.107800 | − | 0.107800i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.2297 | − | 26.2297i | 0.885714 | − | 0.885714i | −0.108394 | − | 0.994108i | \(-0.534571\pi\) |
0.994108 | + | 0.108394i | \(0.0345707\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.2914 | −0.920515 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.3359 | −1.59479 | −0.797394 | − | 0.603459i | \(-0.793789\pi\) | ||||
−0.797394 | + | 0.603459i | \(0.793789\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.08371 | + | 8.08371i | −0.272039 | + | 0.272039i | −0.829920 | − | 0.557882i | \(-0.811614\pi\) |
0.557882 | + | 0.829920i | \(0.311614\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.7453 | + | 13.7453i | 0.462043 | + | 0.462043i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.9255i | 0.433994i | 0.976172 | + | 0.216997i | \(0.0696263\pi\) | ||||
−0.976172 | + | 0.216997i | \(0.930374\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 61.9412i | 2.07744i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.6586 | + | 10.6586i | 0.357078 | + | 0.357078i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.72664 | − | 6.72664i | 0.225098 | − | 0.225098i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.47760 | 0.0493906 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.1787 | 0.440025 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.66378 | − | 6.66378i | 0.222250 | − | 0.222250i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.18878 | + | 2.18878i | 0.0729190 | + | 0.0729190i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 126.232i | − | 4.20074i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 16.9544i | − | 0.563584i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.4991 | − | 16.4991i | −0.547844 | − | 0.547844i | 0.377973 | − | 0.925817i | \(-0.376621\pi\) |
−0.925817 | + | 0.377973i | \(0.876621\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.8169 | + | 17.8169i | −0.590951 | + | 0.590951i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.6745 | 0.883765 | 0.441883 | − | 0.897073i | \(-0.354311\pi\) | ||||
0.441883 | + | 0.897073i | \(0.354311\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.03908 | 0.266055 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.64071 | + | 2.64071i | −0.0872993 | + | 0.0872993i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.4827 | + | 23.4827i | 0.775467 | + | 0.775467i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 57.7425i | − | 1.90475i | −0.304932 | − | 0.952374i | \(-0.598634\pi\) | ||
0.304932 | − | 0.952374i | \(-0.401366\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 8.74878i | − | 0.288282i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.91714 | + | 2.91714i | 0.0960188 | + | 0.0960188i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.21123 | − | 5.21123i | 0.171344 | − | 0.171344i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 33.5848 | 1.10307 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.5386 | 1.39565 | 0.697823 | − | 0.716270i | \(-0.254152\pi\) | ||||
0.697823 | + | 0.716270i | \(0.254152\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35.7372 | + | 35.7372i | −1.17124 | + | 1.17124i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 37.3572 | + | 37.3572i | 1.22302 | + | 1.22302i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 3.37894i | − | 0.110503i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 16.6795i | − | 0.544894i | −0.962171 | − | 0.272447i | \(-0.912167\pi\) | ||
0.962171 | − | 0.272447i | \(-0.0878330\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.51376 | + | 4.51376i | 0.147301 | + | 0.147301i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.63152 | − | 9.63152i | 0.313979 | − | 0.313979i | −0.532470 | − | 0.846449i | \(-0.678736\pi\) |
0.846449 | + | 0.532470i | \(0.178736\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.2227 | −0.495721 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.93018 | −0.257969 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.44034 | − | 3.44034i | 0.111796 | − | 0.111796i | −0.648996 | − | 0.760792i | \(-0.724811\pi\) |
0.760792 | + | 0.648996i | \(0.224811\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.11707 | − | 2.11707i | −0.0687231 | − | 0.0687231i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 59.3028i | − | 1.92302i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.6965i | 0.573247i | 0.958043 | + | 0.286623i | \(0.0925328\pi\) | ||||
−0.958043 | + | 0.286623i | \(0.907467\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.0471973 | + | 0.0471973i | 0.00152727 | + | 0.00152727i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.54750 | + | 5.54750i | −0.179325 | + | 0.179325i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 102.622 | 3.31384 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.9027 | 0.674281 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 37.3577 | − | 37.3577i | 1.20384 | − | 1.20384i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.777073 | + | 0.777073i | 0.0250149 | + | 0.0250149i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.0023i | 0.482442i | 0.970470 | + | 0.241221i | \(0.0775479\pi\) | ||||
−0.970470 | + | 0.241221i | \(0.922452\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.2627i | 0.458183i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.3135 | + | 14.3135i | 0.459340 | + | 0.459340i | 0.898439 | − | 0.439098i | \(-0.144702\pi\) |
−0.439098 | + | 0.898439i | \(0.644702\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.3241 | + | 28.3241i | −0.908030 | + | 0.908030i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.55074 | −0.177766 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.1433 | 1.54024 | 0.770120 | − | 0.637900i | \(-0.220196\pi\) | ||||
0.770120 | + | 0.637900i | \(0.220196\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.3580 | + | 15.3580i | −0.490845 | + | 0.490845i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.98651 | − | 4.98651i | −0.159207 | − | 0.159207i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 0.791292i | − | 0.0252383i | −0.999920 | − | 0.0126191i | \(-0.995983\pi\) | ||
0.999920 | − | 0.0126191i | \(-0.00401690\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 16.8700i | − | 0.537523i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.6893 | + | 20.6893i | 0.658547 | + | 0.658547i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.1818 | + | 18.1818i | −0.578149 | + | 0.578149i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60.2424 | 1.91366 | 0.956832 | − | 0.290643i | \(-0.0938690\pi\) | ||||
0.956832 | + | 0.290643i | \(0.0938690\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.5133 | 0.397099 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.80625 | − | 7.80625i | 0.247475 | − | 0.247475i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.15773 | + | 1.15773i | 0.0366655 | + | 0.0366655i | 0.725202 | − | 0.688536i | \(-0.241746\pi\) |
−0.688536 | + | 0.725202i | \(0.741746\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 12.9598i | − | 0.410031i |
(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 | 320.2.l.a.241.1 | 16 | ||
3.2 | odd | 2 | 2880.2.t.c.2161.5 | 16 | |||
4.3 | odd | 2 | 80.2.l.a.21.3 | ✓ | 16 | ||
5.2 | odd | 4 | 1600.2.q.h.49.8 | 16 | |||
5.3 | odd | 4 | 1600.2.q.g.49.1 | 16 | |||
5.4 | even | 2 | 1600.2.l.i.1201.8 | 16 | |||
8.3 | odd | 2 | 640.2.l.b.481.1 | 16 | |||
8.5 | even | 2 | 640.2.l.a.481.8 | 16 | |||
12.11 | even | 2 | 720.2.t.c.181.6 | 16 | |||
16.3 | odd | 4 | 80.2.l.a.61.3 | yes | 16 | ||
16.5 | even | 4 | 640.2.l.a.161.8 | 16 | |||
16.11 | odd | 4 | 640.2.l.b.161.1 | 16 | |||
16.13 | even | 4 | inner | 320.2.l.a.81.1 | 16 | ||
20.3 | even | 4 | 400.2.q.h.149.1 | 16 | |||
20.7 | even | 4 | 400.2.q.g.149.8 | 16 | |||
20.19 | odd | 2 | 400.2.l.h.101.6 | 16 | |||
32.3 | odd | 8 | 5120.2.a.v.1.7 | 8 | |||
32.13 | even | 8 | 5120.2.a.u.1.7 | 8 | |||
32.19 | odd | 8 | 5120.2.a.s.1.2 | 8 | |||
32.29 | even | 8 | 5120.2.a.t.1.2 | 8 | |||
48.29 | odd | 4 | 2880.2.t.c.721.8 | 16 | |||
48.35 | even | 4 | 720.2.t.c.541.6 | 16 | |||
80.3 | even | 4 | 400.2.q.g.349.8 | 16 | |||
80.13 | odd | 4 | 1600.2.q.h.849.8 | 16 | |||
80.19 | odd | 4 | 400.2.l.h.301.6 | 16 | |||
80.29 | even | 4 | 1600.2.l.i.401.8 | 16 | |||
80.67 | even | 4 | 400.2.q.h.349.1 | 16 | |||
80.77 | odd | 4 | 1600.2.q.g.849.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.l.a.21.3 | ✓ | 16 | 4.3 | odd | 2 | ||
80.2.l.a.61.3 | yes | 16 | 16.3 | odd | 4 | ||
320.2.l.a.81.1 | 16 | 16.13 | even | 4 | inner | ||
320.2.l.a.241.1 | 16 | 1.1 | even | 1 | trivial | ||
400.2.l.h.101.6 | 16 | 20.19 | odd | 2 | |||
400.2.l.h.301.6 | 16 | 80.19 | odd | 4 | |||
400.2.q.g.149.8 | 16 | 20.7 | even | 4 | |||
400.2.q.g.349.8 | 16 | 80.3 | even | 4 | |||
400.2.q.h.149.1 | 16 | 20.3 | even | 4 | |||
400.2.q.h.349.1 | 16 | 80.67 | even | 4 | |||
640.2.l.a.161.8 | 16 | 16.5 | even | 4 | |||
640.2.l.a.481.8 | 16 | 8.5 | even | 2 | |||
640.2.l.b.161.1 | 16 | 16.11 | odd | 4 | |||
640.2.l.b.481.1 | 16 | 8.3 | odd | 2 | |||
720.2.t.c.181.6 | 16 | 12.11 | even | 2 | |||
720.2.t.c.541.6 | 16 | 48.35 | even | 4 | |||
1600.2.l.i.401.8 | 16 | 80.29 | even | 4 | |||
1600.2.l.i.1201.8 | 16 | 5.4 | even | 2 | |||
1600.2.q.g.49.1 | 16 | 5.3 | odd | 4 | |||
1600.2.q.g.849.1 | 16 | 80.77 | odd | 4 | |||
1600.2.q.h.49.8 | 16 | 5.2 | odd | 4 | |||
1600.2.q.h.849.8 | 16 | 80.13 | odd | 4 | |||
2880.2.t.c.721.8 | 16 | 48.29 | odd | 4 | |||
2880.2.t.c.2161.5 | 16 | 3.2 | odd | 2 | |||
5120.2.a.s.1.2 | 8 | 32.19 | odd | 8 | |||
5120.2.a.t.1.2 | 8 | 32.29 | even | 8 | |||
5120.2.a.u.1.7 | 8 | 32.13 | even | 8 | |||
5120.2.a.v.1.7 | 8 | 32.3 | odd | 8 |