Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(193,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bs (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: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 193.3 | ||
Root | \(-2.86589i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.193 |
Dual form | 1300.2.bs.d.357.3 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{7}{12}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −0.355132 | + | 1.32537i | −0.205036 | + | 0.765204i | 0.784403 | + | 0.620252i | \(0.212969\pi\) |
−0.989439 | + | 0.144952i | \(0.953697\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.40883 | + | 1.96809i | 1.28842 | + | 0.743868i | 0.978372 | − | 0.206854i | \(-0.0663226\pi\) |
0.310045 | + | 0.950722i | \(0.399656\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.967585 | + | 0.558635i | 0.322528 | + | 0.186212i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.83141 | − | 0.490724i | −0.552189 | − | 0.147959i | −0.0280738 | − | 0.999606i | \(-0.508937\pi\) |
−0.524116 | + | 0.851647i | \(0.675604\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.65910 | + | 2.43499i | −0.737502 | + | 0.675345i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.15223 | − | 0.844638i | 0.764528 | − | 0.204855i | 0.144575 | − | 0.989494i | \(-0.453818\pi\) |
0.619953 | + | 0.784639i | \(0.287152\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.920754 | + | 3.43630i | 0.211235 | + | 0.788341i | 0.987458 | + | 0.157882i | \(0.0504667\pi\) |
−0.776223 | + | 0.630459i | \(0.782867\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.81904 | + | 3.81904i | −0.833382 | + | 0.833382i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.88280 | − | 0.504494i | −0.392591 | − | 0.105194i | 0.0571230 | − | 0.998367i | \(-0.481807\pi\) |
−0.449714 | + | 0.893173i | \(0.648474\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.99474 | + | 3.99474i | −0.768788 | + | 0.768788i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.43876 | − | 4.29477i | 1.38134 | − | 0.797519i | 0.389025 | − | 0.921227i | \(-0.372812\pi\) |
0.992319 | + | 0.123709i | \(0.0394788\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.37363 | + | 2.37363i | 0.426317 | + | 0.426317i | 0.887372 | − | 0.461055i | \(-0.152529\pi\) |
−0.461055 | + | 0.887372i | \(0.652529\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.30078 | − | 2.25302i | 0.226437 | − | 0.392201i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.28885 | − | 0.744119i | 0.211886 | − | 0.122332i | −0.390302 | − | 0.920687i | \(-0.627629\pi\) |
0.602188 | + | 0.798355i | \(0.294296\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.28293 | − | 4.38904i | −0.365562 | − | 0.702809i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.45054 | + | 5.41349i | −0.226536 | + | 0.845445i | 0.755247 | + | 0.655441i | \(0.227517\pi\) |
−0.981783 | + | 0.190005i | \(0.939150\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.51311 | − | 5.64699i | −0.230747 | − | 0.861158i | −0.980020 | − | 0.198898i | \(-0.936264\pi\) |
0.749274 | − | 0.662261i | \(-0.230403\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.50747i | 0.511617i | 0.966727 | + | 0.255809i | \(0.0823417\pi\) | ||||
−0.966727 | + | 0.255809i | \(0.917658\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.24675 | + | 7.35558i | 0.606678 | + | 1.05080i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.47783i | 0.627022i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.97315 | − | 8.97315i | −1.23256 | − | 1.23256i | −0.962979 | − | 0.269578i | \(-0.913116\pi\) |
−0.269578 | − | 0.962979i | \(-0.586884\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.88136 | −0.646553 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.27489 | + | 1.14545i | −0.556543 | + | 0.149125i | −0.526118 | − | 0.850412i | \(-0.676353\pi\) |
−0.0304252 | + | 0.999537i | \(0.509686\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.33455 | + | 10.9718i | −0.811056 | + | 1.40479i | 0.101070 | + | 0.994879i | \(0.467774\pi\) |
−0.912126 | + | 0.409911i | \(0.865560\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.19889 | + | 3.80859i | 0.277034 | + | 0.479837i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.54852 | − | 4.41417i | −0.311352 | − | 0.539277i | 0.667303 | − | 0.744786i | \(-0.267448\pi\) |
−0.978655 | + | 0.205509i | \(0.934115\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.33729 | − | 2.31625i | 0.160990 | − | 0.278843i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.68768 | − | 1.52401i | 0.675003 | − | 0.180867i | 0.0949958 | − | 0.995478i | \(-0.469716\pi\) |
0.580008 | + | 0.814611i | \(0.303050\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.07919 | 0.828556 | 0.414278 | − | 0.910150i | \(-0.364034\pi\) | ||||
0.414278 | + | 0.910150i | \(0.364034\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.27716 | − | 5.27716i | −0.601388 | − | 0.601388i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.3886i | 1.61884i | 0.587230 | + | 0.809420i | \(0.300219\pi\) | ||||
−0.587230 | + | 0.809420i | \(0.699781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.19995 | − | 3.81042i | −0.244439 | − | 0.423380i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.5256i | 1.92368i | 0.273608 | + | 0.961841i | \(0.411783\pi\) | ||||
−0.273608 | + | 0.961841i | \(0.588217\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.05042 | + | 11.3843i | 0.327040 | + | 1.22053i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.12894 | − | 7.94530i | 0.225667 | − | 0.842200i | −0.756470 | − | 0.654029i | \(-0.773077\pi\) |
0.982136 | − | 0.188171i | \(-0.0602559\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.8567 | + | 3.06712i | −1.45258 | + | 0.321522i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.98890 | + | 2.30299i | −0.413629 | + | 0.238809i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.64859 | − | 2.85545i | 0.167389 | − | 0.289927i | −0.770112 | − | 0.637909i | \(-0.779800\pi\) |
0.937501 | + | 0.347982i | \(0.113133\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.49790 | − | 1.49790i | −0.150545 | − | 0.150545i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.78232 | − | 5.64782i | 0.973377 | − | 0.561979i | 0.0731129 | − | 0.997324i | \(-0.476707\pi\) |
0.900264 | + | 0.435344i | \(0.143373\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.51034 | + | 9.51034i | −0.937081 | + | 0.937081i | −0.998135 | − | 0.0610531i | \(-0.980554\pi\) |
0.0610531 | + | 0.998135i | \(0.480554\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.2044 | + | 3.00221i | 1.08317 | + | 0.290235i | 0.755894 | − | 0.654694i | \(-0.227203\pi\) |
0.327276 | + | 0.944929i | \(0.393869\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.0996 | + | 13.0996i | −1.25471 | + | 1.25471i | −0.301125 | + | 0.953585i | \(0.597362\pi\) |
−0.953585 | + | 0.301125i | \(0.902638\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.528522 | + | 1.97247i | 0.0501651 | + | 0.187219i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.34358 | + | 0.895908i | −0.314537 | + | 0.0842800i | −0.412634 | − | 0.910897i | \(-0.635391\pi\) |
0.0980969 | + | 0.995177i | \(0.468724\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.93318 | + | 0.870592i | −0.363622 | + | 0.0804863i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.4077 | + | 3.32464i | 1.13742 | + | 0.304770i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.41304 | − | 3.70257i | −0.583004 | − | 0.336598i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.65976 | − | 3.84501i | −0.600490 | − | 0.346693i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.50527 | + | 5.61773i | −0.133571 | + | 0.498493i | −1.00000 | 0.000807685i | \(-0.999743\pi\) | |
0.866429 | + | 0.499300i | \(0.166410\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.02172 | 0.706273 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.68008 | −0.146789 | −0.0733946 | − | 0.997303i | \(-0.523383\pi\) | ||||
−0.0733946 | + | 0.997303i | \(0.523383\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.62425 | + | 13.5259i | −0.314262 | + | 1.17284i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.06410 | − | 1.19171i | −0.176348 | − | 0.101815i | 0.409228 | − | 0.912432i | \(-0.365798\pi\) |
−0.585576 | + | 0.810618i | \(0.699132\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.97525 | − | 4.60451i | −0.676452 | − | 0.390550i | 0.122065 | − | 0.992522i | \(-0.461048\pi\) |
−0.798517 | + | 0.601972i | \(0.794382\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.64870 | − | 1.24562i | −0.391491 | − | 0.104900i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.06480 | − | 3.15457i | 0.507164 | − | 0.263798i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.2570 | + | 3.01631i | −0.928465 | + | 0.248781i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.50931 | − | 20.5610i | −0.451340 | − | 1.68442i | −0.698630 | − | 0.715483i | \(-0.746207\pi\) |
0.247290 | − | 0.968941i | \(-0.420460\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1541 | − | 14.1541i | 1.15184 | − | 1.15184i | 0.165660 | − | 0.986183i | \(-0.447024\pi\) |
0.986183 | − | 0.165660i | \(-0.0529756\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.52189 | + | 0.943689i | 0.284728 | + | 0.0762927i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.43479 | − | 9.43479i | 0.752978 | − | 0.752978i | −0.222056 | − | 0.975034i | \(-0.571277\pi\) |
0.975034 | + | 0.222056i | \(0.0712767\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.0794 | − | 8.70610i | 1.19588 | − | 0.690439i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.42525 | − | 5.42525i | −0.427570 | − | 0.427570i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2839 | − | 19.5443i | 0.883824 | − | 1.53083i | 0.0367678 | − | 0.999324i | \(-0.488294\pi\) |
0.847056 | − | 0.531504i | \(-0.178373\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.4774 | − | 6.04914i | 0.810767 | − | 0.468097i | −0.0364550 | − | 0.999335i | \(-0.511607\pi\) |
0.847222 | + | 0.531239i | \(0.178273\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.14164 | − | 12.9498i | 0.0878186 | − | 0.996136i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.02873 | + | 3.83928i | −0.0786691 | + | 0.293597i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.42843 | − | 5.33097i | −0.108601 | − | 0.405306i | 0.890127 | − | 0.455712i | \(-0.150615\pi\) |
−0.998729 | + | 0.0504057i | \(0.983949\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 6.07260i | − | 0.456445i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.2279 | + | 19.4473i | 0.839214 | + | 1.45356i | 0.890553 | + | 0.454880i | \(0.150318\pi\) |
−0.0513388 | + | 0.998681i | \(0.516349\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13.2607i | − | 0.985659i | −0.870126 | − | 0.492829i | \(-0.835963\pi\) | ||
0.870126 | − | 0.492829i | \(-0.164037\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.2921 | − | 12.2921i | −0.908655 | − | 0.908655i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.18749 | −0.452474 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −21.4794 | + | 5.75538i | −1.56240 | + | 0.418643i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.68516 | − | 4.65083i | 0.194291 | − | 0.336522i | −0.752377 | − | 0.658733i | \(-0.771093\pi\) |
0.946668 | + | 0.322211i | \(0.104426\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.31236 | − | 2.27308i | −0.0944659 | − | 0.163620i | 0.814920 | − | 0.579574i | \(-0.196781\pi\) |
−0.909386 | + | 0.415954i | \(0.863448\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.25778 | + | 5.64263i | 0.232107 | + | 0.402021i | 0.958428 | − | 0.285335i | \(-0.0921047\pi\) |
−0.726321 | + | 0.687356i | \(0.758771\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.74150 | + | 4.74843i | −0.194340 | + | 0.336607i | −0.946684 | − | 0.322164i | \(-0.895590\pi\) |
0.752344 | + | 0.658771i | \(0.228923\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.75549 | − | 1.81013i | 0.476495 | − | 0.127677i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 33.8100 | 2.37299 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.53994 | − | 1.53994i | −0.107033 | − | 0.107033i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 6.74509i | − | 0.466568i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.16194 | + | 12.4048i | 0.493048 | + | 0.853984i | 0.999968 | − | 0.00800885i | \(-0.00254932\pi\) |
−0.506920 | + | 0.861993i | \(0.669216\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.07952i | 0.553599i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.41979 | + | 12.7628i | 0.232150 | + | 0.866397i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.51405 | + | 9.38256i | −0.169884 | + | 0.634014i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.32542 | + | 9.92163i | −0.425493 | + | 0.667401i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.01942 | − | 4.05266i | 0.470055 | − | 0.271386i | −0.246208 | − | 0.969217i | \(-0.579185\pi\) |
0.716263 | + | 0.697831i | \(0.245851\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.32655 | − | 5.76176i | 0.220791 | − | 0.382421i | −0.734257 | − | 0.678871i | \(-0.762469\pi\) |
0.955048 | + | 0.296450i | \(0.0958028\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.32634 | − | 6.32634i | −0.418056 | − | 0.418056i | 0.466477 | − | 0.884533i | \(-0.345523\pi\) |
−0.884533 | + | 0.466477i | \(0.845523\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.86829 | − | 5.12011i | 0.583491 | − | 0.336879i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.8923 | − | 12.8923i | 0.844601 | − | 0.844601i | −0.144852 | − | 0.989453i | \(-0.546271\pi\) |
0.989453 | + | 0.144852i | \(0.0462707\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.0702 | − | 5.10985i | −1.23874 | − | 0.331920i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.58614 | − | 6.58614i | 0.426022 | − | 0.426022i | −0.461249 | − | 0.887271i | \(-0.652598\pi\) |
0.887271 | + | 0.461249i | \(0.152598\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00770 | + | 14.9569i | 0.258158 | + | 0.963461i | 0.966306 | + | 0.257396i | \(0.0828645\pi\) |
−0.708148 | + | 0.706065i | \(0.750469\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.5392 | + | 2.82398i | −0.676093 | + | 0.181159i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.8157 | − | 6.89544i | −0.688189 | − | 0.438747i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23.2279 | − | 6.22390i | −1.47201 | − | 0.394424i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.46212 | − | 0.844158i | −0.0922885 | − | 0.0532828i | 0.453145 | − | 0.891437i | \(-0.350302\pi\) |
−0.545434 | + | 0.838154i | \(0.683635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.20060 | + | 1.84787i | 0.201220 | + | 0.116174i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.68207 | − | 10.0096i | 0.167303 | − | 0.624384i | −0.830432 | − | 0.557120i | \(-0.811906\pi\) |
0.997735 | − | 0.0672638i | \(-0.0214269\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.85797 | 0.363997 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.59684 | 0.594030 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.527501 | + | 1.96866i | −0.0325271 | + | 0.121393i | −0.980280 | − | 0.197611i | \(-0.936682\pi\) |
0.947753 | + | 0.319004i | \(0.103348\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.77442 | + | 5.64326i | 0.598185 | + | 0.345362i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.59298 | − | 1.49706i | −0.158097 | − | 0.0912773i | 0.418864 | − | 0.908049i | \(-0.362428\pi\) |
−0.576961 | + | 0.816772i | \(0.695762\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.2999 | + | 7.31498i | 1.65835 | + | 0.444353i | 0.961933 | − | 0.273285i | \(-0.0881103\pi\) |
0.696416 | + | 0.717639i | \(0.254777\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.855887 | − | 19.4545i | 0.0518006 | − | 1.17744i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.0241 | − | 6.97314i | 1.56364 | − | 0.418975i | 0.629824 | − | 0.776738i | \(-0.283127\pi\) |
0.933813 | + | 0.357762i | \(0.116460\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.970696 | + | 3.62268i | 0.0581140 | + | 0.216884i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.76202 | + | 1.76202i | −0.105113 | + | 0.105113i | −0.757707 | − | 0.652594i | \(-0.773681\pi\) |
0.652594 | + | 0.757707i | \(0.273681\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.28547 | + | 2.22009i | 0.492520 | + | 0.131970i | 0.496527 | − | 0.868022i | \(-0.334609\pi\) |
−0.00400621 | + | 0.999992i | \(0.501275\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.5989 | + | 15.5989i | −0.920773 | + | 0.920773i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.49929 | + | 3.17502i | −0.323488 | + | 0.186766i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.19906 | + | 3.19906i | 0.187532 | + | 0.187532i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.80103 | − | 8.31563i | 0.280479 | − | 0.485804i | −0.691024 | − | 0.722832i | \(-0.742840\pi\) |
0.971503 | + | 0.237028i | \(0.0761733\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.27630 | − | 5.35567i | 0.538265 | − | 0.310768i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.23499 | − | 3.24310i | 0.360579 | − | 0.187553i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.95586 | − | 22.2276i | 0.343290 | − | 1.28118i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.01145 | + | 14.9709i | 0.230452 | + | 0.860058i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.6845i | − | 0.952235i | −0.879382 | − | 0.476118i | \(-0.842044\pi\) | ||
0.879382 | − | 0.476118i | \(-0.157956\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.22731 | − | 15.9822i | −0.524923 | − | 0.909193i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 32.6023i | − | 1.84870i | −0.381540 | − | 0.924352i | \(-0.624606\pi\) | ||
0.381540 | − | 0.924352i | \(-0.375394\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.98087 | + | 4.98087i | 0.281535 | + | 0.281535i | 0.833721 | − | 0.552186i | \(-0.186206\pi\) |
−0.552186 | + | 0.833721i | \(0.686206\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.4470 | 1.26075 | 0.630375 | − | 0.776291i | \(-0.282901\pi\) | ||||
0.630375 | + | 0.776291i | \(0.282901\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.7309 | + | 4.21509i | −0.880763 | + | 0.236000i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.95809 | + | 13.7838i | −0.444177 | + | 0.769337i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.80486 | + | 10.0543i | 0.322991 | + | 0.559437i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.7097 | − | 22.0138i | −0.702848 | − | 1.21737i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.90301 | + | 11.9564i | −0.380575 | + | 0.659176i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.70050 | + | 2.59924i | −0.533188 | + | 0.142867i | −0.515360 | − | 0.856974i | \(-0.672342\pi\) |
−0.0178279 | + | 0.999841i | \(0.505675\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.66277 | 0.0911190 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.79849 | − | 6.79849i | −0.370337 | − | 0.370337i | 0.497263 | − | 0.867600i | \(-0.334338\pi\) |
−0.867600 | + | 0.497263i | \(0.834338\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 4.74965i | − | 0.257965i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.18228 | − | 5.51188i | −0.172330 | − | 0.298485i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.87867i | 0.317418i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.10140 | + | 4.11047i | 0.0591260 | + | 0.220661i | 0.989167 | − | 0.146794i | \(-0.0468956\pi\) |
−0.930041 | + | 0.367456i | \(0.880229\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.59334 | − | 5.94641i | 0.0852893 | − | 0.318304i | −0.910080 | − | 0.414434i | \(-0.863980\pi\) |
0.995369 | + | 0.0961297i | \(0.0306464\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.895264 | − | 20.3496i | 0.0477857 | − | 1.08618i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.343121 | − | 0.198101i | 0.0182625 | − | 0.0105439i | −0.490841 | − | 0.871249i | \(-0.663310\pi\) |
0.509103 | + | 0.860705i | \(0.329977\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.81278 | + | 15.2642i | −0.466422 | + | 0.807866i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.01878 | + | 1.01878i | 0.0537691 | + | 0.0537691i | 0.733480 | − | 0.679711i | \(-0.237895\pi\) |
−0.679711 | + | 0.733480i | \(0.737895\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.49411 | − | 3.17203i | 0.289164 | − | 0.166949i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.18476 | − | 7.18476i | 0.377102 | − | 0.377102i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.538690 | + | 0.144342i | 0.0281194 | + | 0.00753457i | 0.272851 | − | 0.962056i | \(-0.412033\pi\) |
−0.244732 | + | 0.969591i | \(0.578700\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.42769 | + | 4.42769i | −0.230496 | + | 0.230496i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.9280 | − | 48.2479i | −0.671187 | − | 2.50491i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.3357 | + | 7.32458i | −1.41539 | + | 0.379253i | −0.883846 | − | 0.467778i | \(-0.845055\pi\) |
−0.531544 | + | 0.847031i | \(0.678388\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.32269 | + | 29.5335i | −0.480143 | + | 1.52105i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.8036 | + | 8.52176i | 1.63364 | + | 0.437733i | 0.954969 | − | 0.296707i | \(-0.0958883\pi\) |
0.678674 | + | 0.734440i | \(0.262555\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.91101 | − | 3.99007i | −0.354062 | − | 0.204418i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.5203 | + | 8.38333i | 0.741955 | + | 0.428368i | 0.822780 | − | 0.568360i | \(-0.192422\pi\) |
−0.0808246 | + | 0.996728i | \(0.525755\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.69055 | − | 6.30922i | 0.0859355 | − | 0.320716i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.29738 | 0.420694 | 0.210347 | − | 0.977627i | \(-0.432541\pi\) | ||||
0.210347 | + | 0.977627i | \(0.432541\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.36113 | −0.321696 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.596651 | − | 2.22673i | 0.0300970 | − | 0.112324i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.4794 | − | 16.4426i | −1.42934 | − | 0.825230i | −0.432272 | − | 0.901743i | \(-0.642288\pi\) |
−0.997069 | + | 0.0765132i | \(0.975621\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.6397 | − | 9.60696i | −0.833029 | − | 0.480950i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.40754 | − | 1.18100i | −0.220102 | − | 0.0589762i | 0.147083 | − | 0.989124i | \(-0.453012\pi\) |
−0.367185 | + | 0.930148i | \(0.619678\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0915 | − | 0.531957i | −0.602320 | − | 0.0264986i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.72557 | + | 0.730314i | −0.135101 | + | 0.0362003i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.97968 | − | 11.1203i | −0.147336 | − | 0.549865i | −0.999640 | − | 0.0268189i | \(-0.991462\pi\) |
0.852304 | − | 0.523046i | \(-0.175204\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.31249 | − | 2.31249i | 0.114067 | − | 0.114067i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.8267 | − | 4.50870i | −0.827988 | − | 0.221859i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.93496 | − | 8.93496i | 0.437547 | − | 0.437547i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.961220 | + | 0.554961i | −0.0469587 | + | 0.0271116i | −0.523296 | − | 0.852151i | \(-0.675298\pi\) |
0.476337 | + | 0.879263i | \(0.341964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.20503 | − | 8.20503i | −0.399888 | − | 0.399888i | 0.478305 | − | 0.878194i | \(-0.341251\pi\) |
−0.878194 | + | 0.478305i | \(0.841251\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.95940 | + | 3.39377i | −0.0952691 | + | 0.165011i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −43.1868 | + | 24.9339i | −2.08996 | + | 1.20664i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.02717 | + | 9.15840i | 0.0978728 | + | 0.442172i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.85441 | + | 6.92074i | −0.0893236 | + | 0.333360i | −0.996098 | − | 0.0882564i | \(-0.971871\pi\) |
0.906774 | + | 0.421617i | \(0.138537\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.74484 | + | 17.7080i | 0.228022 | + | 0.850991i | 0.981171 | + | 0.193140i | \(0.0618673\pi\) |
−0.753149 | + | 0.657850i | \(0.771466\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6.93438i | − | 0.331716i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.8096 | − | 30.8472i | −0.850008 | − | 1.47226i | −0.881200 | − | 0.472743i | \(-0.843264\pi\) |
0.0311922 | − | 0.999513i | \(-0.490070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.48953i | 0.451883i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.4503 | − | 24.4503i | −1.16167 | − | 1.16167i | −0.984110 | − | 0.177558i | \(-0.943180\pi\) |
−0.177558 | − | 0.984110i | \(-0.556820\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 29.2075 | 1.38147 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.2540 | − | 7.83860i | 1.38058 | − | 0.369926i | 0.509250 | − | 0.860618i | \(-0.329923\pi\) |
0.871333 | + | 0.490692i | \(0.163256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.31306 | − | 9.20248i | 0.250182 | − | 0.433328i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.7329 | + | 23.7860i | 0.645226 | + | 1.11756i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.85187 | + | 3.20754i | 0.0866270 | + | 0.150042i | 0.906083 | − | 0.423099i | \(-0.139058\pi\) |
−0.819456 | + | 0.573142i | \(0.805724\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.21823 | + | 15.9664i | −0.430270 | + | 0.745250i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.9827 | − | 7.49794i | 1.30328 | − | 0.349214i | 0.460593 | − | 0.887611i | \(-0.347637\pi\) |
0.842691 | + | 0.538398i | \(0.180970\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.9117 | 0.600056 | 0.300028 | − | 0.953930i | \(-0.403004\pi\) | ||||
0.300028 | + | 0.953930i | \(0.403004\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.85556 | − | 3.85556i | −0.178414 | − | 0.178414i | 0.612250 | − | 0.790664i | \(-0.290265\pi\) |
−0.790664 | + | 0.612250i | \(0.790265\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 20.0629i | − | 0.926418i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.15400 | + | 15.8552i | 0.421794 | + | 0.730569i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.0844i | 0.509664i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.66956 | − | 13.6950i | −0.168018 | − | 0.627051i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.71558 | + | 28.7949i | −0.352534 | + | 1.31567i | 0.531026 | + | 0.847356i | \(0.321807\pi\) |
−0.883560 | + | 0.468319i | \(0.844860\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.61527 | + | 5.11703i | −0.0736498 | + | 0.233317i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.11716 | − | 5.26379i | 0.414845 | − | 0.239511i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.523570 | − | 0.906849i | 0.0237252 | − | 0.0410933i | −0.853919 | − | 0.520406i | \(-0.825781\pi\) |
0.877644 | + | 0.479313i | \(0.159114\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.8962 | + | 21.8962i | 0.990180 | + | 0.990180i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.2673 | + | 21.5163i | −1.68185 | + | 0.971016i | −0.721418 | + | 0.692500i | \(0.756509\pi\) |
−0.960431 | + | 0.278517i | \(0.910157\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.8212 | − | 19.8212i | 0.892700 | − | 0.892700i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.3877 | + | 5.99877i | 1.00423 | + | 0.269082i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.9380 | + | 23.9380i | −1.07161 | + | 1.07161i | −0.0743807 | + | 0.997230i | \(0.523698\pi\) |
−0.997230 | + | 0.0743807i | \(0.976302\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.29649 | + | 16.0347i | 0.191953 | + | 0.716379i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.5893 | + | 4.44508i | −0.739678 | + | 0.198196i | −0.608935 | − | 0.793220i | \(-0.708403\pi\) |
−0.130743 | + | 0.991416i | \(0.541736\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.7578 | + | 6.11198i | 0.744241 | + | 0.271443i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.9359 | + | 8.55721i | 1.41554 | + | 0.379291i | 0.883898 | − | 0.467681i | \(-0.154910\pi\) |
0.531638 | + | 0.846972i | \(0.321577\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.1318 | + | 13.9325i | 1.06753 | + | 0.616336i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.4053 | − | 10.0490i | −0.768462 | − | 0.443672i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.72120 | − | 6.42360i | 0.0756982 | − | 0.282510i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.57280 | 0.332409 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.4907 | −1.33582 | −0.667910 | − | 0.744242i | \(-0.732811\pi\) | ||||
−0.667910 | + | 0.744242i | \(0.732811\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.10869 | − | 15.3338i | 0.179660 | − | 0.670502i | −0.816050 | − | 0.577981i | \(-0.803841\pi\) |
0.995711 | − | 0.0925209i | \(-0.0294925\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.48709 | + | 5.47738i | 0.413264 | + | 0.238598i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6282 | − | 9.60028i | −0.722964 | − | 0.417403i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.77621 | − | 1.27978i | −0.207270 | − | 0.0555377i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.32467 | − | 17.9271i | −0.403896 | − | 0.776508i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −29.7623 | + | 7.97479i | −1.28434 | + | 0.344138i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.16796 | − | 15.5550i | −0.179527 | − | 0.670003i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.14795 | − | 3.14795i | 0.135341 | − | 0.135341i | −0.636191 | − | 0.771532i | \(-0.719491\pi\) |
0.771532 | + | 0.636191i | \(0.219491\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.5753 | + | 4.70930i | 0.754230 | + | 0.202095i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.4832 | + | 16.4832i | −0.704771 | + | 0.704771i | −0.965431 | − | 0.260660i | \(-0.916060\pi\) |
0.260660 | + | 0.965431i | \(0.416060\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.2584 | + | 7.07741i | −0.523177 | + | 0.302056i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.6074 | + | 21.6074i | 0.920506 | + | 0.920506i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.3180 | + | 49.0482i | −1.20420 | + | 2.08574i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.2108 | − | 20.9063i | 1.53430 | − | 0.885828i | 0.535142 | − | 0.844762i | \(-0.320258\pi\) |
0.999156 | − | 0.0410659i | \(-0.0130754\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.7739 | + | 11.3315i | 0.751755 | + | 0.479272i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.19738 | − | 8.20073i | 0.0927734 | − | 0.346235i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.61558 | − | 9.76146i | −0.110233 | − | 0.411396i | 0.888653 | − | 0.458581i | \(-0.151642\pi\) |
−0.998886 | + | 0.0471841i | \(0.984975\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 17.3188i | − | 0.727320i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.12942 | − | 15.8126i | −0.382725 | − | 0.662899i | 0.608726 | − | 0.793381i | \(-0.291681\pi\) |
−0.991451 | + | 0.130482i | \(0.958348\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.0252i | 1.21467i | 0.794447 | + | 0.607334i | \(0.207761\pi\) | ||||
−0.794447 | + | 0.607334i | \(0.792239\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.21049 | + | 5.21049i | 0.217671 | + | 0.217671i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.27590 | 0.344530 | 0.172265 | − | 0.985051i | \(-0.444891\pi\) | ||||
0.172265 | + | 0.985051i | \(0.444891\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.47873 | − | 0.932124i | 0.144571 | − | 0.0387378i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −34.4919 | + | 59.7417i | −1.43097 | + | 2.47850i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0301 | + | 20.8368i | 0.498237 | + | 0.862972i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.8497 | + | 20.5242i | 0.489088 | + | 0.847125i | 0.999921 | − | 0.0125547i | \(-0.00399639\pi\) |
−0.510833 | + | 0.859680i | \(0.670663\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.97098 | + | 10.3420i | −0.246030 | + | 0.426136i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.63553 | + | 2.31388i | −0.355218 | + | 0.0951804i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.0364 | −1.11025 | −0.555125 | − | 0.831767i | \(-0.687330\pi\) | ||||
−0.555125 | + | 0.831767i | \(0.687330\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.31983 | − | 5.31983i | −0.217726 | − | 0.217726i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 35.7007i | − | 1.45869i | −0.684146 | − | 0.729345i | \(-0.739825\pi\) | ||
0.684146 | − | 0.729345i | \(-0.260175\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.8079 | + | 25.6480i | 0.604027 | + | 1.04620i | 0.992205 | + | 0.124620i | \(0.0397713\pi\) |
−0.388178 | + | 0.921584i | \(0.626895\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 5.69478i | − | 0.231910i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.84122 | + | 29.2638i | 0.318265 | + | 1.18778i | 0.920911 | + | 0.389773i | \(0.127446\pi\) |
−0.602646 | + | 0.798009i | \(0.705887\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.0070 | + | 44.8108i | −0.486549 | + | 1.81582i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.54066 | − | 9.32672i | −0.345518 | − | 0.377319i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.6003 | − | 11.8936i | 0.832036 | − | 0.480376i | −0.0225130 | − | 0.999747i | \(-0.507167\pi\) |
0.854549 | + | 0.519370i | \(0.173833\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.90280 | + | 8.49190i | −0.197379 | + | 0.341871i | −0.947678 | − | 0.319228i | \(-0.896576\pi\) |
0.750299 | + | 0.661099i | \(0.229910\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.211255 | − | 0.211255i | −0.00849105 | − | 0.00849105i | 0.702849 | − | 0.711340i | \(-0.251911\pi\) |
−0.711340 | + | 0.702849i | \(0.751911\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.53661 | − | 5.50596i | 0.382691 | − | 0.220947i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.8942 | − | 22.8942i | 0.917238 | − | 0.917238i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.93976 | + | 2.39540i | 0.357019 | + | 0.0956631i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.43425 | − | 3.43425i | 0.136932 | − | 0.136932i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.19224 | + | 11.9136i | 0.127081 | + | 0.474273i | 0.999905 | − | 0.0137616i | \(-0.00438059\pi\) |
−0.872824 | + | 0.488035i | \(0.837714\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.9845 | + | 5.08687i | −0.754564 | + | 0.202185i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.2033 | − | 9.21845i | −1.15708 | − | 0.365248i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.35468 | + | 1.70273i | 0.251387 | + | 0.0673590i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.13416 | + | 4.69626i | 0.321280 | + | 0.185491i | 0.651963 | − | 0.758251i | \(-0.273946\pi\) |
−0.330683 | + | 0.943742i | \(0.607279\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.0818 | − | 18.5225i | −1.26518 | − | 0.730454i | −0.291111 | − | 0.956689i | \(-0.594025\pi\) |
−0.974073 | + | 0.226235i | \(0.927358\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.71989 | − | 21.3469i | 0.224872 | − | 0.839234i | −0.757584 | − | 0.652738i | \(-0.773620\pi\) |
0.982456 | − | 0.186496i | \(-0.0597131\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.39115 | 0.329381 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.1300 | −0.710569 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.48243 | − | 20.4607i | 0.214544 | − | 0.800689i | −0.771783 | − | 0.635886i | \(-0.780635\pi\) |
0.986327 | − | 0.164803i | \(-0.0526987\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.84972 | + | 3.95469i | 0.267233 | + | 0.154287i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.59430 | + | 1.49782i | 0.101060 | + | 0.0583468i | 0.549678 | − | 0.835377i | \(-0.314750\pi\) |
−0.448618 | + | 0.893723i | \(0.648084\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.0257 | + | 3.22227i | 0.467744 | + | 0.125332i | 0.484990 | − | 0.874520i | \(-0.338823\pi\) |
−0.0172459 | + | 0.999851i | \(0.505490\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.9035 | − | 11.9070i | −0.423456 | − | 0.462430i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.1724 | + | 4.33337i | −0.626197 | + | 0.167789i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.87846 | + | 10.7426i | 0.111288 | + | 0.415332i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.9852 | − | 16.9852i | 0.655708 | − | 0.655708i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.5724 | + | 3.10082i | 0.446084 | + | 0.119528i | 0.474867 | − | 0.880058i | \(-0.342496\pi\) |
−0.0287825 | + | 0.999586i | \(0.509163\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.8173 | + | 20.8173i | −0.800072 | + | 0.800072i | −0.983107 | − | 0.183034i | \(-0.941408\pi\) |
0.183034 | + | 0.983107i | \(0.441408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.2395 | − | 6.48916i | 0.431334 | − | 0.249031i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.45510 | + | 6.45510i | 0.247360 | + | 0.247360i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.1132 | + | 22.7128i | −0.501764 | + | 0.869080i | 0.498234 | + | 0.867042i | \(0.333982\pi\) |
−0.999998 | + | 0.00203769i | \(0.999351\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.6314 | − | 6.13807i | 0.405615 | − | 0.234182i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 45.7100 | + | 2.01098i | 1.74141 | + | 0.0766122i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.868516 | + | 3.24135i | −0.0330399 | + | 0.123307i | −0.980476 | − | 0.196638i | \(-0.936998\pi\) |
0.947436 | + | 0.319945i | \(0.103664\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.15809 | − | 8.05411i | −0.0819791 | − | 0.305950i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.2898i | 0.692774i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.5086 | + | 21.6655i | 0.473118 | + | 0.819465i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 12.3175i | − | 0.465226i | −0.972569 | − | 0.232613i | \(-0.925272\pi\) | ||
0.972569 | − | 0.232613i | \(-0.0747276\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.74373 | + | 3.74373i | 0.141198 | + | 0.141198i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 44.4617 | 1.67215 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.1347 | − | 8.07458i | 1.13173 | − | 0.303247i | 0.356111 | − | 0.934444i | \(-0.384103\pi\) |
0.775623 | + | 0.631197i | \(0.217436\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.03796 | + | 13.9222i | −0.301447 | + | 0.522122i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.27159 | − | 5.66655i | −0.122522 | − | 0.212214i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.39013 | + | 11.0680i | 0.238644 | + | 0.413343i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.3069 | − | 35.1725i | 0.757318 | − | 1.31171i | −0.186895 | − | 0.982380i | \(-0.559843\pi\) |
0.944214 | − | 0.329334i | \(-0.106824\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −51.1363 | + | 13.7019i | −1.90442 | + | 0.510287i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.2468 | −0.790175 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.4875 | + | 17.4875i | 0.648577 | + | 0.648577i | 0.952649 | − | 0.304072i | \(-0.0983464\pi\) |
−0.304072 | + | 0.952649i | \(0.598346\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 28.1710i | − | 1.04337i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.53933 | − | 16.5226i | −0.352825 | − | 0.611110i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.8347i | 1.17584i | 0.808918 | + | 0.587921i | \(0.200053\pi\) | ||||
−0.808918 | + | 0.587921i | \(0.799947\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.50124 | + | 9.33476i | 0.0921344 | + | 0.343850i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.90923 | − | 7.12535i | 0.0702322 | − | 0.262110i | −0.921878 | − | 0.387481i | \(-0.873345\pi\) |
0.992110 | + | 0.125371i | \(0.0400120\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.9800 | − | 11.8861i | 0.476834 | − | 0.436646i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.0656 | − | 21.9772i | 1.39649 | − | 0.806265i | 0.402469 | − | 0.915434i | \(-0.368152\pi\) |
0.994023 | + | 0.109169i | \(0.0348189\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.79041 | + | 16.9575i | −0.358212 | + | 0.620442i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32.2853 | + | 32.2853i | 1.17968 | + | 1.17968i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.4235 | + | 22.7612i | −1.43858 | + | 0.830567i | −0.997751 | − | 0.0670229i | \(-0.978650\pi\) |
−0.440832 | + | 0.897590i | \(0.645317\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.63807 | − | 1.63807i | 0.0596946 | − | 0.0596946i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.5214 | − | 7.64229i | −1.03663 | − | 0.277764i | −0.299913 | − | 0.953967i | \(-0.596958\pi\) |
−0.736715 | + | 0.676203i | \(0.763624\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.58575 | + | 3.58575i | −0.130154 | + | 0.130154i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.80150 | − | 10.4553i | −0.101554 | − | 0.379006i | 0.896377 | − | 0.443292i | \(-0.146190\pi\) |
−0.997932 | + | 0.0642862i | \(0.979523\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −70.4352 | + | 18.8731i | −2.54993 | + | 0.683251i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.57819 | − | 13.4552i | 0.309741 | − | 0.485838i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.4310 | − | 5.74241i | −0.772820 | − | 0.207077i | −0.149203 | − | 0.988807i | \(-0.547671\pi\) |
−0.623617 | + | 0.781730i | \(0.714337\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.3140 | + | 7.10949i | 0.443478 | + | 0.256042i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.0395 | − | 8.68305i | −0.540933 | − | 0.312308i | 0.204524 | − | 0.978862i | \(-0.434435\pi\) |
−0.745457 | + | 0.666554i | \(0.767769\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.08036 | + | 7.76399i | −0.0746323 | + | 0.278532i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.9380 | −0.714352 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.1643 | −0.399491 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.5594 | + | 46.8724i | −0.448837 | + | 1.67508i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.3020 | + | 7.10259i | 0.438521 | + | 0.253180i | 0.702970 | − | 0.711220i | \(-0.251857\pi\) |
−0.264449 | + | 0.964400i | \(0.585190\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.42187 | − | 1.39827i | −0.0862210 | − | 0.0497797i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.1609 | − | 3.52645i | −0.467948 | − | 0.125386i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.87193 | − | 44.5996i | −0.350562 | − | 1.58378i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.5731 | − | 9.26384i | 1.22464 | − | 0.328142i | 0.412151 | − | 0.911115i | \(-0.364778\pi\) |
0.812491 | + | 0.582974i | \(0.198111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.96254 | + | 11.0564i | 0.104807 | + | 0.391146i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.49845 | − | 6.49845i | 0.229611 | − | 0.229611i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.9649 | − | 3.47392i | −0.457520 | − | 0.122592i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.90501 | − | 2.90501i | 0.102261 | − | 0.102261i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.6902 | + | 24.0699i | −1.46575 | + | 0.846251i | −0.999267 | − | 0.0382785i | \(-0.987813\pi\) |
−0.466483 | + | 0.884530i | \(0.654479\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.10824 | − | 5.10824i | −0.179375 | − | 0.179375i | 0.611709 | − | 0.791083i | \(-0.290483\pi\) |
−0.791083 | + | 0.611709i | \(0.790483\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.3901 | + | 33.5847i | −0.680041 | + | 1.17787i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.0116 | − | 10.3990i | 0.630145 | − | 0.363814i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.1209 | − | 4.77314i | −0.528368 | − | 0.166787i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.56803 | − | 24.5122i | 0.229226 | − | 0.855483i | −0.751441 | − | 0.659800i | \(-0.770641\pi\) |
0.980667 | − | 0.195683i | \(-0.0626923\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.47310 | + | 9.22975i | 0.0862070 | + | 0.321729i | 0.995540 | − | 0.0943402i | \(-0.0300741\pi\) |
−0.909333 | + | 0.416069i | \(0.863407\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 11.7291i | − | 0.407860i | −0.978985 | − | 0.203930i | \(-0.934629\pi\) | ||
0.978985 | − | 0.203930i | \(-0.0653715\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.8966 | + | 22.3376i | 0.447918 | + | 0.775817i | 0.998250 | − | 0.0591286i | \(-0.0188322\pi\) |
−0.550332 | + | 0.834946i | \(0.685499\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 36.9680i | 1.28241i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.5995 | + | 19.5995i | 0.679083 | + | 0.679083i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.9641 | −0.655494 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.07419 | − | 1.62757i | 0.209704 | − | 0.0561901i | −0.152437 | − | 0.988313i | \(-0.548712\pi\) |
0.362142 | + | 0.932123i | \(0.382046\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.3901 | − | 38.7808i | 0.772073 | − | 1.33727i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.70958 | − | 2.96108i | −0.0588810 | − | 0.101985i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.5740 | − | 25.2429i | −0.500768 | − | 0.867356i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.88488 | + | 10.1929i | −0.201969 | + | 0.349820i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.80205 | + | 0.750808i | −0.0960532 | + | 0.0257374i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.9142 | 1.67479 | 0.837394 | − | 0.546599i | \(-0.184078\pi\) | ||||
0.837394 | + | 0.546599i | \(0.184078\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.72229 | + | 5.72229i | 0.195470 | + | 0.195470i | 0.798055 | − | 0.602585i | \(-0.205863\pi\) |
−0.602585 | + | 0.798055i | \(0.705863\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 19.4601i | − | 0.663971i | −0.943284 | − | 0.331986i | \(-0.892281\pi\) | ||
0.943284 | − | 0.331986i | \(-0.107719\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.1346 | − | 26.2140i | −0.515787 | − | 0.893370i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.62230i | 0.327547i | 0.986498 | + | 0.163773i | \(0.0523666\pi\) | ||||
−0.986498 | + | 0.163773i | \(0.947633\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.25510 | − | 8.41615i | −0.0765873 | − | 0.285828i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.06081 | − | 26.3513i | 0.239522 | − | 0.893907i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.5253 | + | 5.53210i | 0.593821 | + | 0.187448i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.19031 | − | 1.84192i | 0.107976 | − | 0.0623397i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.8244 | + | 29.1407i | −0.568120 | + | 0.984013i | 0.428632 | + | 0.903479i | \(0.358996\pi\) |
−0.996752 | + | 0.0805336i | \(0.974338\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.31630 | + | 9.31630i | 0.314231 | + | 0.314231i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.0355 | − | 8.10341i | 0.472869 | − | 0.273011i | −0.244571 | − | 0.969631i | \(-0.578647\pi\) |
0.717440 | + | 0.696620i | \(0.245314\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.4033 | + | 11.4033i | −0.383751 | + | 0.383751i | −0.872451 | − | 0.488701i | \(-0.837471\pi\) |
0.488701 | + | 0.872451i | \(0.337471\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.4811 | − | 9.77507i | −1.22491 | − | 0.328215i | −0.412317 | − | 0.911041i | \(-0.635280\pi\) |
−0.812597 | + | 0.582826i | \(0.801947\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.1874 | + | 16.1874i | −0.542907 | + | 0.542907i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.15913 | + | 8.05799i | 0.0723336 | + | 0.269953i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.0527 | + | 3.22952i | −0.403329 | + | 0.108072i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.08406 | + | 9.41541i | 0.0695847 | + | 0.314371i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.8511 | + | 7.46267i | 0.928886 | + | 0.248894i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −35.8645 | − | 20.7064i | −1.19482 | − | 0.689829i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.3447 | + | 15.7875i | 0.909974 | + | 0.525374i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.90409 | + | 10.8382i | −0.0964288 | + | 0.359877i | −0.997232 | − | 0.0743499i | \(-0.976312\pi\) |
0.900803 | + | 0.434227i | \(0.142979\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.6203 | 0.418589 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.03630 | 0.100597 | 0.0502985 | − | 0.998734i | \(-0.483983\pi\) | ||||
0.0502985 | + | 0.998734i | \(0.483983\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.60022 | − | 32.0964i | 0.284626 | − | 1.06224i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.72711 | − | 3.30655i | −0.189126 | − | 0.109192i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.8704 | − | 17.8231i | −1.01832 | − | 0.587929i | −0.104705 | − | 0.994503i | \(-0.533390\pi\) |
−0.913617 | + | 0.406575i | \(0.866723\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.1132 | + | 5.92521i | 0.728654 | + | 0.195242i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.4132 | + | 17.9019i | −0.375669 | + | 0.589250i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.5149 | + | 3.88925i | −0.476731 | + | 0.127740i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.3000 | − | 42.1722i | −0.370741 | − | 1.38363i | −0.859469 | − | 0.511189i | \(-0.829205\pi\) |
0.488727 | − | 0.872437i | \(-0.337461\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.3658 | + | 21.3658i | −0.700235 | + | 0.700235i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 43.2101 | + | 11.5781i | 1.41464 | + | 0.379050i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.0726 | + | 10.0726i | −0.329059 | + | 0.329059i | −0.852228 | − | 0.523170i | \(-0.824749\pi\) |
0.523170 | + | 0.852228i | \(0.324749\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.37037 | + | 4.83263i | −0.273157 | + | 0.157707i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.2833 | + | 36.2833i | 1.18280 | + | 1.18280i | 0.979016 | + | 0.203784i | \(0.0653242\pi\) |
0.203784 | + | 0.979016i | \(0.434676\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.46215 | − | 9.46073i | 0.177872 | − | 0.308084i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.8529 | + | 9.73003i | −0.547646 | + | 0.316184i | −0.748172 | − | 0.663505i | \(-0.769068\pi\) |
0.200526 | + | 0.979688i | \(0.435735\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.8243 | + | 17.2378i | −0.611062 | + | 0.559561i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.97165 | + | 29.7506i | −0.258499 | + | 0.964730i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.98557 | + | 33.5346i | 0.291071 | + | 1.08629i | 0.944288 | + | 0.329121i | \(0.106752\pi\) |
−0.653217 | + | 0.757171i | \(0.726581\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 22.3462i | − | 0.722351i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.69078 | − | 8.12467i | −0.151473 | − | 0.262359i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 19.7317i | − | 0.636508i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.16407 | + | 9.16407i | 0.295308 | + | 0.295308i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.5727 | 0.950993 | 0.475497 | − | 0.879718i | \(-0.342268\pi\) | ||||
0.475497 | + | 0.879718i | \(0.342268\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.3872 | + | 4.12298i | −0.494308 | + | 0.132449i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.2631 | − | 26.4365i | 0.489817 | − | 0.848389i | −0.510114 | − | 0.860107i | \(-0.670397\pi\) |
0.999931 | + | 0.0117182i | \(0.00373011\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.1242 | − | 31.3920i | −0.581035 | − | 1.00638i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.0029 | − | 43.3063i | −0.799915 | − | 1.38549i | −0.919671 | − | 0.392689i | \(-0.871545\pi\) |
0.119757 | − | 0.992803i | \(-0.461789\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.79789 | + | 13.5063i | −0.249222 | + | 0.431664i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.9928 | + | 5.35705i | −0.638321 | + | 0.171038i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −57.3856 | −1.83032 | −0.915158 | − | 0.403096i | \(-0.867934\pi\) | ||||
−0.915158 | + | 0.403096i | \(0.867934\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.3952 | − | 13.3952i | −0.426372 | − | 0.426372i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.3955i | 0.362356i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.96166 | − | 10.3259i | −0.189378 | − | 0.328013i | 0.755665 | − | 0.654959i | \(-0.227314\pi\) |
−0.945043 | + | 0.326946i | \(0.893981\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 13.7798i | − | 0.437290i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.8526 | + | 44.2347i | 0.375377 | + | 1.40093i | 0.852793 | + | 0.522249i | \(0.174907\pi\) |
−0.477416 | + | 0.878677i | \(0.658427\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.17607 | + | 8.12119i | −0.0688477 | + | 0.256943i |
(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 | 1300.2.bs.d.193.3 | 20 | ||
5.2 | odd | 4 | 1300.2.bn.d.557.3 | 20 | |||
5.3 | odd | 4 | 260.2.bf.c.37.3 | ✓ | 20 | ||
5.4 | even | 2 | 260.2.bk.c.193.3 | yes | 20 | ||
13.6 | odd | 12 | 1300.2.bn.d.1293.3 | 20 | |||
65.19 | odd | 12 | 260.2.bf.c.253.3 | yes | 20 | ||
65.32 | even | 12 | inner | 1300.2.bs.d.357.3 | 20 | ||
65.58 | even | 12 | 260.2.bk.c.97.3 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bf.c.37.3 | ✓ | 20 | 5.3 | odd | 4 | ||
260.2.bf.c.253.3 | yes | 20 | 65.19 | odd | 12 | ||
260.2.bk.c.97.3 | yes | 20 | 65.58 | even | 12 | ||
260.2.bk.c.193.3 | yes | 20 | 5.4 | even | 2 | ||
1300.2.bn.d.557.3 | 20 | 5.2 | odd | 4 | |||
1300.2.bn.d.1293.3 | 20 | 13.6 | odd | 12 | |||
1300.2.bs.d.193.3 | 20 | 1.1 | even | 1 | trivial | ||
1300.2.bs.d.357.3 | 20 | 65.32 | even | 12 | inner |