Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(841,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.841");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.q (of order \(3\), degree \(2\), 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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 3781.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.3781 |
Dual form | 4020.2.q.e.841.1 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | 0.755929 | − | 0.654654i | \(-0.227186\pi\) |
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | −0.788320 | − | 0.615265i | \(-0.789049\pi\) |
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.500000 | + | 0.866025i | −0.121268 | + | 0.210042i | −0.920268 | − | 0.391289i | \(-0.872029\pi\) |
0.799000 | + | 0.601331i | \(0.205363\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50000 | − | 4.33013i | 0.573539 | − | 0.993399i | −0.422659 | − | 0.906289i | \(-0.638903\pi\) |
0.996199 | − | 0.0871106i | \(-0.0277634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.500000 | − | 0.866025i | −0.109109 | − | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.500000 | + | 0.866025i | −0.104257 | + | 0.180579i | −0.913434 | − | 0.406986i | \(-0.866580\pi\) |
0.809177 | + | 0.587565i | \(0.199913\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.50000 | − | 4.33013i | −0.464238 | − | 0.804084i | 0.534928 | − | 0.844897i | \(-0.320339\pi\) |
−0.999167 | + | 0.0408130i | \(0.987005\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.50000 | + | 6.06218i | 0.628619 | + | 1.08880i | 0.987829 | + | 0.155543i | \(0.0497126\pi\) |
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.50000 | − | 2.59808i | −0.261116 | − | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.500000 | + | 0.866025i | 0.0845154 | + | 0.146385i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.50000 | + | 6.06218i | −0.575396 | + | 0.996616i | 0.420602 | + | 0.907245i | \(0.361819\pi\) |
−0.995998 | + | 0.0893706i | \(0.971514\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.500000 | − | 0.866025i | 0.0800641 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.50000 | − | 4.33013i | −0.390434 | − | 0.676252i | 0.602072 | − | 0.798441i | \(-0.294342\pi\) |
−0.992507 | + | 0.122189i | \(0.961009\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.500000 | + | 0.866025i | 0.0729325 | + | 0.126323i | 0.900185 | − | 0.435507i | \(-0.143431\pi\) |
−0.827253 | + | 0.561830i | \(0.810098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | − | 5.19615i | 0.428571 | − | 0.742307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.500000 | + | 0.866025i | −0.0700140 | + | 0.121268i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.50000 | + | 2.59808i | 0.202260 | + | 0.350325i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.50000 | − | 4.33013i | 0.331133 | − | 0.573539i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.0000 | −1.56227 | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.50000 | + | 2.59808i | −0.192055 | + | 0.332650i | −0.945931 | − | 0.324367i | \(-0.894849\pi\) |
0.753876 | + | 0.657017i | \(0.228182\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.500000 | − | 0.866025i | −0.0629941 | − | 0.109109i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.500000 | + | 0.866025i | −0.0620174 | + | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00000 | + | 1.73205i | −0.977356 | + | 0.211604i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.500000 | + | 0.866025i | −0.0601929 | + | 0.104257i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.50000 | − | 12.9904i | −0.890086 | − | 1.54167i | −0.839771 | − | 0.542941i | \(-0.817311\pi\) |
−0.0503155 | − | 0.998733i | \(-0.516023\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.50000 | + | 9.52628i | −0.643726 | + | 1.11497i | 0.340868 | + | 0.940111i | \(0.389279\pi\) |
−0.984594 | + | 0.174855i | \(0.944054\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.50000 | + | 2.59808i | −0.170941 | + | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.50000 | + | 2.59808i | 0.168763 | + | 0.292306i | 0.937985 | − | 0.346675i | \(-0.112689\pi\) |
−0.769222 | + | 0.638982i | \(0.779356\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.50000 | − | 6.06218i | 0.384175 | − | 0.665410i | −0.607479 | − | 0.794335i | \(-0.707819\pi\) |
0.991654 | + | 0.128925i | \(0.0411526\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.500000 | − | 0.866025i | 0.0542326 | − | 0.0939336i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.50000 | − | 4.33013i | −0.268028 | − | 0.464238i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.0000 | −1.48400 | −0.741999 | − | 0.670402i | \(-0.766122\pi\) | ||||
−0.741999 | + | 0.670402i | \(0.766122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.50000 | + | 6.06218i | 0.362933 | + | 0.628619i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.50000 | + | 4.33013i | −0.256495 | + | 0.444262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.50000 | − | 14.7224i | 0.863044 | − | 1.49484i | −0.00593185 | − | 0.999982i | \(-0.501888\pi\) |
0.868976 | − | 0.494854i | \(-0.164778\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.50000 | − | 2.59808i | −0.150756 | − | 0.261116i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.50000 | + | 2.59808i | 0.149256 | + | 0.258518i | 0.930953 | − | 0.365140i | \(-0.118979\pi\) |
−0.781697 | + | 0.623658i | \(0.785646\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.50000 | − | 11.2583i | −0.640464 | − | 1.10932i | −0.985329 | − | 0.170664i | \(-0.945409\pi\) |
0.344865 | − | 0.938652i | \(-0.387925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.500000 | + | 0.866025i | 0.0487950 | + | 0.0845154i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.00000 | −0.773389 | −0.386695 | − | 0.922208i | \(-0.626383\pi\) | ||||
−0.386695 | + | 0.922208i | \(0.626383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.50000 | + | 6.06218i | −0.332205 | + | 0.575396i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.50000 | − | 7.79423i | −0.423324 | − | 0.733219i | 0.572938 | − | 0.819599i | \(-0.305804\pi\) |
−0.996262 | + | 0.0863794i | \(0.972470\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.500000 | − | 0.866025i | 0.0466252 | − | 0.0807573i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.500000 | − | 0.866025i | 0.0462250 | − | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.00000 | 0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.50000 | − | 4.33013i | −0.225417 | − | 0.390434i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.50000 | − | 11.2583i | −0.576782 | − | 0.999015i | −0.995846 | − | 0.0910585i | \(-0.970975\pi\) |
0.419064 | − | 0.907957i | \(-0.362358\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.00000 | −0.433555 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | 0.170872 | 0.0854358 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.0000 | −1.69638 | −0.848189 | − | 0.529694i | \(-0.822307\pi\) | ||||
−0.848189 | + | 0.529694i | \(0.822307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.500000 | + | 0.866025i | 0.0421076 | + | 0.0729325i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.00000 | −0.250873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.50000 | + | 4.33013i | 0.207614 | + | 0.359597i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.00000 | − | 5.19615i | 0.247436 | − | 0.428571i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.50000 | − | 14.7224i | 0.691720 | − | 1.19809i | −0.279554 | − | 0.960130i | \(-0.590186\pi\) |
0.971274 | − | 0.237964i | \(-0.0764802\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.500000 | + | 0.866025i | −0.0404226 | + | 0.0700140i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.50000 | − | 6.06218i | −0.281127 | − | 0.486926i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.50000 | + | 6.06218i | −0.279330 | + | 0.483814i | −0.971219 | − | 0.238190i | \(-0.923446\pi\) |
0.691888 | + | 0.722005i | \(0.256779\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.00000 | 0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.5000 | + | 19.9186i | 0.900750 | + | 1.56014i | 0.826523 | + | 0.562902i | \(0.190315\pi\) |
0.0742262 | + | 0.997241i | \(0.476351\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.50000 | + | 2.59808i | 0.116775 | + | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.50000 | − | 2.59808i | −0.116073 | − | 0.201045i | 0.802135 | − | 0.597143i | \(-0.203697\pi\) |
−0.918208 | + | 0.396098i | \(0.870364\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.50000 | − | 4.33013i | 0.191180 | − | 0.331133i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.50000 | + | 11.2583i | −0.494186 | + | 0.855955i | −0.999978 | − | 0.00670064i | \(-0.997867\pi\) |
0.505792 | + | 0.862656i | \(0.331200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.500000 | − | 0.866025i | −0.0377964 | − | 0.0654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.0000 | −0.901975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.0000 | −1.19590 | −0.597948 | − | 0.801535i | \(-0.704017\pi\) | ||||
−0.597948 | + | 0.801535i | \(0.704017\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.50000 | − | 6.06218i | −0.260153 | − | 0.450598i | 0.706129 | − | 0.708083i | \(-0.250440\pi\) |
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.50000 | + | 2.59808i | −0.110883 | + | 0.192055i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.50000 | − | 6.06218i | 0.257325 | − | 0.445700i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.00000 | 0.219382 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.500000 | − | 0.866025i | −0.0363696 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.50000 | − | 2.59808i | 0.108536 | − | 0.187990i | −0.806641 | − | 0.591041i | \(-0.798717\pi\) |
0.915177 | + | 0.403051i | \(0.132050\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.500000 | + | 0.866025i | −0.0358057 | + | 0.0620174i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.5000 | − | 18.1865i | −0.748094 | − | 1.29574i | −0.948735 | − | 0.316072i | \(-0.897636\pi\) |
0.200641 | − | 0.979665i | \(-0.435697\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.50000 | − | 11.2583i | 0.460773 | − | 0.798082i | −0.538227 | − | 0.842800i | \(-0.680906\pi\) |
0.999000 | + | 0.0447181i | \(0.0142390\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.00000 | + | 1.73205i | −0.564276 | + | 0.122169i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.50000 | + | 4.33013i | −0.175466 | + | 0.303915i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.50000 | + | 4.33013i | 0.174608 | + | 0.302429i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.500000 | + | 0.866025i | −0.0347524 | + | 0.0601929i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.0000 | −1.03757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.50000 | − | 4.33013i | 0.172107 | − | 0.298098i | −0.767049 | − | 0.641588i | \(-0.778276\pi\) |
0.939156 | + | 0.343490i | \(0.111609\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.50000 | − | 12.9904i | −0.513892 | − | 0.890086i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.50000 | − | 6.06218i | 0.237595 | − | 0.411527i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.50000 | + | 9.52628i | −0.371656 | + | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.500000 | + | 0.866025i | 0.0336336 | + | 0.0582552i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0000 | 1.60716 | 0.803579 | − | 0.595198i | \(-0.202926\pi\) | ||||
0.803579 | + | 0.595198i | \(0.202926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.50000 | + | 7.79423i | 0.298675 | + | 0.517321i | 0.975833 | − | 0.218517i | \(-0.0701218\pi\) |
−0.677158 | + | 0.735838i | \(0.736789\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.50000 | − | 7.79423i | 0.297368 | − | 0.515057i | −0.678165 | − | 0.734910i | \(-0.737224\pi\) |
0.975533 | + | 0.219853i | \(0.0705577\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.50000 | + | 2.59808i | −0.0986928 | + | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.50000 | − | 14.7224i | −0.556854 | − | 0.964499i | −0.997757 | − | 0.0669439i | \(-0.978675\pi\) |
0.440903 | − | 0.897555i | \(-0.354658\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.500000 | − | 0.866025i | −0.0326164 | − | 0.0564933i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.50000 | + | 2.59808i | 0.0974355 | + | 0.168763i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.50000 | − | 12.9904i | −0.485135 | − | 0.840278i | 0.514719 | − | 0.857359i | \(-0.327896\pi\) |
−0.999854 | + | 0.0170808i | \(0.994563\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.0000 | −1.67481 | −0.837404 | − | 0.546585i | \(-0.815928\pi\) | ||||
−0.837404 | + | 0.546585i | \(0.815928\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00000 | + | 5.19615i | −0.191663 | + | 0.331970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.50000 | − | 4.33013i | −0.159071 | − | 0.275519i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.50000 | − | 6.06218i | 0.221803 | − | 0.384175i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.5000 | + | 18.1865i | −0.662754 | + | 1.14792i | 0.317135 | + | 0.948380i | \(0.397279\pi\) |
−0.979889 | + | 0.199543i | \(0.936054\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.00000 | 0.188608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.500000 | − | 0.866025i | 0.0313112 | − | 0.0542326i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.5000 | − | 18.1865i | −0.654972 | − | 1.13444i | −0.981901 | − | 0.189396i | \(-0.939347\pi\) |
0.326929 | − | 0.945049i | \(-0.393986\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.00000 | 0.434959 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.50000 | − | 4.33013i | −0.154746 | − | 0.268028i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.0000 | 0.986602 | 0.493301 | − | 0.869859i | \(-0.335790\pi\) | ||||
0.493301 | + | 0.869859i | \(0.335790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.0000 | −0.856786 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.00000 | −0.0605228 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.50000 | − | 2.59808i | −0.0904534 | − | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0000 | 1.32185 | 0.660926 | − | 0.750451i | \(-0.270164\pi\) | ||||
0.660926 | + | 0.750451i | \(0.270164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.50000 | + | 6.06218i | 0.209540 | + | 0.362933i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.50000 | + | 4.33013i | −0.149137 | + | 0.258314i | −0.930909 | − | 0.365251i | \(-0.880983\pi\) |
0.781771 | + | 0.623565i | \(0.214316\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.0000 | 0.951101 | 0.475551 | − | 0.879688i | \(-0.342249\pi\) | ||||
0.475551 | + | 0.879688i | \(0.342249\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.50000 | + | 4.33013i | −0.148087 | + | 0.256495i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.50000 | + | 4.33013i | −0.147570 | + | 0.255599i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | + | 13.8564i | 0.470588 | + | 0.815083i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.50000 | − | 14.7224i | 0.498279 | − | 0.863044i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.0000 | 1.51894 | 0.759468 | − | 0.650545i | \(-0.225459\pi\) | ||||
0.759468 | + | 0.650545i | \(0.225459\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0000 | 0.698667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.50000 | − | 2.59808i | −0.0870388 | − | 0.150756i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.500000 | + | 0.866025i | 0.0289157 | + | 0.0500835i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | + | 6.92820i | 0.230556 | + | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.50000 | + | 2.59808i | 0.0861727 | + | 0.149256i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.50000 | − | 2.59808i | 0.0858898 | − | 0.148765i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.5000 | + | 19.9186i | −0.656340 | + | 1.13681i | 0.325216 | + | 0.945640i | \(0.394563\pi\) |
−0.981556 | + | 0.191174i | \(0.938771\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.50000 | − | 11.2583i | −0.369772 | − | 0.640464i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | 0.339140 | 0.169570 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169570 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.500000 | + | 0.866025i | 0.0281718 | + | 0.0487950i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.50000 | − | 16.4545i | 0.533573 | − | 0.924176i | −0.465658 | − | 0.884965i | \(-0.654182\pi\) |
0.999231 | − | 0.0392110i | \(-0.0124844\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.50000 | + | 12.9904i | −0.419919 | + | 0.727322i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.00000 | −0.446516 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.50000 | + | 4.33013i | 0.139104 | + | 0.240935i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.500000 | − | 0.866025i | 0.0277350 | − | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.00000 | 0.110600 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.500000 | − | 0.866025i | 0.0275659 | − | 0.0477455i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.5000 | + | 23.3827i | 0.742027 | + | 1.28523i | 0.951571 | + | 0.307429i | \(0.0994688\pi\) |
−0.209544 | + | 0.977799i | \(0.567198\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.50000 | + | 6.06218i | −0.191799 | + | 0.332205i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.00000 | − | 1.73205i | 0.437087 | − | 0.0946320i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.5000 | + | 26.8468i | −0.844339 | + | 1.46244i | 0.0418554 | + | 0.999124i | \(0.486673\pi\) |
−0.886194 | + | 0.463314i | \(0.846660\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.50000 | − | 7.79423i | −0.244406 | − | 0.423324i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.5000 | − | 18.1865i | 0.568607 | − | 0.984856i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.500000 | − | 0.866025i | 0.0269191 | − | 0.0466252i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.5000 | − | 23.3827i | −0.724718 | − | 1.25525i | −0.959090 | − | 0.283101i | \(-0.908637\pi\) |
0.234372 | − | 0.972147i | \(-0.424697\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.00000 | −0.321173 | −0.160586 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160586 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.500000 | − | 0.866025i | 0.0266880 | − | 0.0462250i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.50000 | + | 7.79423i | −0.239511 | + | 0.414845i | −0.960574 | − | 0.278024i | \(-0.910320\pi\) |
0.721063 | + | 0.692869i | \(0.243654\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.50000 | + | 12.9904i | 0.398059 | + | 0.689458i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.00000 | 0.0529256 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.00000 | −0.422224 | −0.211112 | − | 0.977462i | \(-0.567708\pi\) | ||||
−0.211112 | + | 0.977462i | \(0.567708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | − | 1.73205i | 0.0524864 | − | 0.0909091i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.50000 | − | 9.52628i | 0.287883 | − | 0.498628i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.50000 | + | 2.59808i | 0.0782994 | + | 0.135618i | 0.902516 | − | 0.430656i | \(-0.141718\pi\) |
−0.824217 | + | 0.566274i | \(0.808384\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.50000 | − | 4.33013i | −0.130145 | − | 0.225417i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.00000 | − | 5.19615i | −0.155752 | − | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.50000 | + | 14.7224i | 0.440113 | + | 0.762299i | 0.997697 | − | 0.0678218i | \(-0.0216049\pi\) |
−0.557584 | + | 0.830120i | \(0.688272\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.00000 | −0.257513 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.5000 | − | 21.6506i | 0.642082 | − | 1.11212i | −0.342885 | − | 0.939377i | \(-0.611404\pi\) |
0.984967 | − | 0.172741i | \(-0.0552624\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.50000 | − | 11.2583i | −0.333005 | − | 0.576782i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.500000 | + | 0.866025i | −0.0255488 | + | 0.0442518i | −0.878517 | − | 0.477711i | \(-0.841467\pi\) |
0.852968 | + | 0.521963i | \(0.174800\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.50000 | − | 2.59808i | 0.0764471 | − | 0.132410i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.5000 | + | 28.5788i | −0.836583 | + | 1.44900i | 0.0561516 | + | 0.998422i | \(0.482117\pi\) |
−0.892735 | + | 0.450582i | \(0.851216\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.500000 | − | 0.866025i | −0.0252861 | − | 0.0437968i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000 | 0.605320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.50000 | − | 2.59808i | −0.0754732 | − | 0.130723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.0000 | −1.50566 | −0.752828 | − | 0.658217i | \(-0.771311\pi\) | ||||
−0.752828 | + | 0.658217i | \(0.771311\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.00000 | −0.250313 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.0000 | 0.499376 | 0.249688 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249688 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.00000 | 0.348695 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.0000 | 1.04093 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.5000 | + | 18.1865i | 0.519192 | + | 0.899266i | 0.999751 | + | 0.0223042i | \(0.00710022\pi\) |
−0.480560 | + | 0.876962i | \(0.659566\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.00000 | 0.0986527 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.00000 | + | 10.3923i | 0.295241 | + | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.50000 | + | 6.06218i | −0.171808 | + | 0.297581i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.0000 | −0.979404 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.5000 | − | 23.3827i | 0.659518 | − | 1.14232i | −0.321222 | − | 0.947004i | \(-0.604094\pi\) |
0.980741 | − | 0.195315i | \(-0.0625730\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.50000 | + | 2.59808i | −0.0731055 | + | 0.126622i | −0.900261 | − | 0.435351i | \(-0.856624\pi\) |
0.827155 | + | 0.561973i | \(0.189958\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.500000 | + | 0.866025i | 0.0243108 | + | 0.0421076i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.500000 | + | 0.866025i | −0.0242536 | + | 0.0420084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.00000 | 0.145180 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.00000 | −0.144841 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.50000 | − | 2.59808i | −0.0722525 | − | 0.125145i | 0.827636 | − | 0.561266i | \(-0.189685\pi\) |
−0.899888 | + | 0.436121i | \(0.856352\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.5000 | + | 25.1147i | 0.696826 | + | 1.20694i | 0.969561 | + | 0.244848i | \(0.0787382\pi\) |
−0.272736 | + | 0.962089i | \(0.587929\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.50000 | + | 4.33013i | 0.119866 | + | 0.207614i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.50000 | + | 4.33013i | 0.119591 | + | 0.207138i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.50000 | − | 14.7224i | 0.405683 | − | 0.702663i | −0.588718 | − | 0.808339i | \(-0.700367\pi\) |
0.994401 | + | 0.105675i | \(0.0337004\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | − | 5.19615i | 0.142857 | − | 0.247436i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.50000 | − | 2.59808i | −0.0712672 | − | 0.123438i | 0.828190 | − | 0.560448i | \(-0.189371\pi\) |
−0.899457 | + | 0.437009i | \(0.856038\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.0000 | 0.663664 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.5000 | + | 30.3109i | 0.825876 | + | 1.43046i | 0.901248 | + | 0.433304i | \(0.142652\pi\) |
−0.0753719 | + | 0.997155i | \(0.524014\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.50000 | + | 12.9904i | −0.353161 | + | 0.611693i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.50000 | − | 14.7224i | 0.399365 | − | 0.691720i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00000 | 0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.5000 | − | 19.9186i | −0.537947 | − | 0.931752i | −0.999014 | − | 0.0443868i | \(-0.985867\pi\) |
0.461067 | − | 0.887365i | \(-0.347467\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.500000 | + | 0.866025i | −0.0233380 | + | 0.0404226i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0000 | −0.465746 | −0.232873 | − | 0.972507i | \(-0.574813\pi\) | ||||
−0.232873 | + | 0.972507i | \(0.574813\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.5000 | − | 21.6506i | 0.580924 | − | 1.00619i | −0.414446 | − | 0.910074i | \(-0.636025\pi\) |
0.995370 | − | 0.0961164i | \(-0.0306421\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.50000 | − | 6.06218i | −0.162309 | − | 0.281127i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.5000 | + | 28.5788i | −0.763529 | + | 1.32247i | 0.177492 | + | 0.984122i | \(0.443202\pi\) |
−0.941021 | + | 0.338349i | \(0.890132\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.50000 | + | 6.06218i | 0.253966 | + | 0.279925i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.50000 | + | 6.06218i | −0.161271 | + | 0.279330i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.0000 | + | 20.7846i | 0.551761 | + | 0.955677i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.50000 | − | 4.33013i | 0.114708 | − | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.5000 | − | 33.7750i | 0.890978 | − | 1.54322i | 0.0522726 | − | 0.998633i | \(-0.483354\pi\) |
0.838705 | − | 0.544586i | \(-0.183313\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.50000 | + | 6.06218i | 0.159586 | + | 0.276412i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.50000 | + | 14.7224i | −0.385965 | + | 0.668511i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.5000 | − | 32.0429i | 0.838315 | − | 1.45200i | −0.0529875 | − | 0.998595i | \(-0.516874\pi\) |
0.891303 | − | 0.453409i | \(-0.149792\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.5000 | + | 19.9186i | 0.520048 | + | 0.900750i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.00000 | 0.225189 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.50000 | + | 2.59808i | 0.0674200 | + | 0.116775i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.50000 | + | 12.9904i | −0.336421 | + | 0.582698i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.50000 | − | 14.7224i | 0.380512 | − | 0.659067i | −0.610623 | − | 0.791921i | \(-0.709081\pi\) |
0.991136 | + | 0.132855i | \(0.0424144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.50000 | − | 2.59808i | −0.0670151 | − | 0.116073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.5000 | + | 25.1147i | 0.646523 | + | 1.11981i | 0.983948 | + | 0.178458i | \(0.0571109\pi\) |
−0.337424 | + | 0.941353i | \(0.609556\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.50000 | − | 2.59808i | −0.0667491 | − | 0.115613i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | + | 10.3923i | 0.266469 | + | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −42.0000 | −1.86162 | −0.930809 | − | 0.365507i | \(-0.880896\pi\) | ||||
−0.930809 | + | 0.365507i | \(0.880896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.0000 | 0.486611 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.50000 | − | 4.33013i | 0.110378 | − | 0.191180i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.50000 | + | 11.2583i | 0.286424 | + | 0.496101i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.50000 | − | 2.59808i | 0.0659699 | − | 0.114263i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.50000 | + | 11.2583i | −0.285318 | + | 0.494186i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.50000 | − | 4.33013i | 0.109317 | − | 0.189343i | −0.806177 | − | 0.591675i | \(-0.798467\pi\) |
0.915494 | + | 0.402332i | \(0.131800\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.500000 | − | 0.866025i | −0.0218218 | − | 0.0377964i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.00000 | −0.304925 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | + | 19.0526i | 0.478261 | + | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.0000 | −0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.00000 | −0.216574 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.00000 | 0.345870 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.0000 | −0.690451 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.0000 | −0.775315 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.50000 | − | 6.06218i | −0.150199 | − | 0.260153i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.50000 | − | 11.2583i | −0.277920 | − | 0.481371i | 0.692948 | − | 0.720988i | \(-0.256312\pi\) |
−0.970868 | + | 0.239616i | \(0.922978\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.50000 | + | 2.59808i | −0.0640184 | + | 0.110883i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.0000 | −1.06504 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.50000 | − | 2.59808i | 0.0637865 | − | 0.110481i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.50000 | − | 6.06218i | 0.148567 | − | 0.257325i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.50000 | − | 7.79423i | −0.190671 | − | 0.330252i | 0.754802 | − | 0.655953i | \(-0.227733\pi\) |
−0.945473 | + | 0.325701i | \(0.894400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | + | 6.92820i | −0.169182 | + | 0.293032i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.00000 | 0.126660 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.50000 | + | 7.79423i | 0.189316 | + | 0.327906i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.500000 | − | 0.866025i | −0.0209980 | − | 0.0363696i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.5000 | − | 38.9711i | −0.943249 | − | 1.63376i | −0.759220 | − | 0.650835i | \(-0.774419\pi\) |
−0.184030 | − | 0.982921i | \(-0.558914\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.5000 | − | 18.1865i | −0.439411 | − | 0.761083i | 0.558233 | − | 0.829684i | \(-0.311480\pi\) |
−0.997644 | + | 0.0686016i | \(0.978146\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.50000 | − | 2.59808i | 0.0626634 | − | 0.108536i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.500000 | + | 0.866025i | −0.0208514 | + | 0.0361158i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.50000 | + | 14.7224i | 0.353860 | + | 0.612903i | 0.986922 | − | 0.161198i | \(-0.0515357\pi\) |
−0.633062 | + | 0.774101i | \(0.718202\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.00000 | −0.0831172 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.00000 | −0.290409 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.00000 | − | 15.5885i | −0.372742 | − | 0.645608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.500000 | + | 0.866025i | −0.0206725 | + | 0.0358057i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.50000 | + | 11.2583i | −0.268284 | + | 0.464681i | −0.968419 | − | 0.249329i | \(-0.919790\pi\) |
0.700135 | + | 0.714010i | \(0.253123\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.0000 | 1.44215 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.5000 | − | 18.1865i | −0.431912 | − | 0.748094i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.5000 | − | 33.7750i | 0.800769 | − | 1.38697i | −0.118342 | − | 0.992973i | \(-0.537758\pi\) |
0.919111 | − | 0.394000i | \(-0.128909\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.00000 | −0.0409960 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.50000 | − | 11.2583i | 0.266027 | − | 0.460773i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.50000 | − | 12.9904i | −0.306442 | − | 0.530773i | 0.671140 | − | 0.741331i | \(-0.265805\pi\) |
−0.977581 | + | 0.210558i | \(0.932472\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.50000 | + | 6.06218i | −0.142768 | + | 0.247281i | −0.928538 | − | 0.371237i | \(-0.878934\pi\) |
0.785770 | + | 0.618519i | \(0.212267\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.00000 | + | 1.73205i | −0.325785 | + | 0.0705346i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | + | 1.73205i | −0.0406558 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.5000 | + | 37.2391i | 0.872658 | + | 1.51149i | 0.859237 | + | 0.511578i | \(0.170939\pi\) |
0.0134214 | + | 0.999910i | \(0.495728\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.50000 | + | 4.33013i | −0.101305 | + | 0.175466i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.00000 | 0.0404557 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.5000 | + | 23.3827i | −0.545260 | + | 0.944418i | 0.453331 | + | 0.891342i | \(0.350236\pi\) |
−0.998591 | + | 0.0530754i | \(0.983098\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.50000 | + | 4.33013i | 0.100810 | + | 0.174608i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.0000 | −0.402585 | −0.201292 | − | 0.979531i | \(-0.564514\pi\) | ||||
−0.201292 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.5000 | − | 18.1865i | 0.422031 | − | 0.730978i | −0.574107 | − | 0.818780i | \(-0.694651\pi\) |
0.996138 | + | 0.0878015i | \(0.0279841\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.500000 | + | 0.866025i | −0.0200643 | + | 0.0347524i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.00000 | + | 12.1244i | 0.280449 | + | 0.485752i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.0000 | −0.599042 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.50000 | − | 6.06218i | −0.139554 | − | 0.241715i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.5000 | − | 18.1865i | 0.417998 | − | 0.723994i | −0.577740 | − | 0.816221i | \(-0.696065\pi\) |
0.995738 | + | 0.0922266i | \(0.0293984\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.50000 | − | 4.33013i | 0.0993661 | − | 0.172107i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.50000 | + | 11.2583i | 0.257945 | + | 0.446773i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.00000 | − | 5.19615i | −0.118864 | − | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.50000 | − | 12.9904i | −0.296695 | − | 0.513892i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.5000 | + | 30.3109i | 0.691208 | + | 1.19721i | 0.971442 | + | 0.237276i | \(0.0762547\pi\) |
−0.280234 | + | 0.959932i | \(0.590412\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.0000 | −0.473234 | −0.236617 | − | 0.971603i | \(-0.576039\pi\) | ||||
−0.236617 | + | 0.971603i | \(0.576039\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.00000 | 0.315000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.5000 | − | 23.3827i | 0.530740 | − | 0.919268i | −0.468617 | − | 0.883402i | \(-0.655247\pi\) |
0.999357 | − | 0.0358667i | \(-0.0114192\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.0000 | + | 31.1769i | 0.706562 | + | 1.22380i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.50000 | − | 6.06218i | 0.137176 | − | 0.237595i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.5000 | + | 18.1865i | −0.410897 | + | 0.711694i | −0.994988 | − | 0.0999939i | \(-0.968118\pi\) |
0.584091 | + | 0.811688i | \(0.301451\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.0000 | −0.468879 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.50000 | + | 9.52628i | −0.214575 | + | 0.371656i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.5000 | + | 18.1865i | 0.409022 | + | 0.708447i | 0.994780 | − | 0.102039i | \(-0.0325366\pi\) |
−0.585758 | + | 0.810486i | \(0.699203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.0000 | −1.16686 | −0.583432 | − | 0.812162i | \(-0.698291\pi\) | ||||
−0.583432 | + | 0.812162i | \(0.698291\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.500000 | + | 0.866025i | 0.0194184 | + | 0.0336336i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.00000 | 0.193892 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.00000 | 0.193601 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.0000 | 0.927894 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.00000 | 0.347441 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.0000 | 1.77317 | 0.886585 | − | 0.462566i | \(-0.153071\pi\) | ||||
0.886585 | + | 0.462566i | \(0.153071\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.5000 | − | 32.0429i | −0.711013 | − | 1.23151i | −0.964477 | − | 0.264166i | \(-0.914903\pi\) |
0.253465 | − | 0.967345i | \(-0.418430\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.0000 | −0.652400 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.50000 | + | 7.79423i | 0.172440 | + | 0.298675i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.5000 | + | 18.1865i | −0.401771 | + | 0.695888i | −0.993940 | − | 0.109926i | \(-0.964939\pi\) |
0.592168 | + | 0.805814i | \(0.298272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.00000 | −0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.50000 | − | 7.79423i | 0.171686 | − | 0.297368i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.00000 | − | 5.19615i | 0.114291 | − | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.5000 | − | 28.5788i | −0.627690 | − | 1.08719i | −0.988014 | − | 0.154363i | \(-0.950667\pi\) |
0.360325 | − | 0.932827i | \(-0.382666\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.50000 | + | 2.59808i | −0.0569803 | + | 0.0986928i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.0000 | 0.758643 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.00000 | 0.189389 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.50000 | − | 14.7224i | −0.321500 | − | 0.556854i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.5000 | − | 32.0429i | −0.698735 | − | 1.21025i | −0.968905 | − | 0.247432i | \(-0.920413\pi\) |
0.270170 | − | 0.962813i | \(-0.412920\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.5000 | + | 30.3109i | 0.660025 | + | 1.14320i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.500000 | − | 0.866025i | −0.0188311 | − | 0.0326164i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.50000 | − | 2.59808i | 0.0564133 | − | 0.0977107i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.5000 | + | 26.8468i | −0.582115 | + | 1.00825i | 0.413114 | + | 0.910679i | \(0.364441\pi\) |
−0.995228 | + | 0.0975728i | \(0.968892\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.50000 | + | 2.59808i | 0.0562544 | + | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.00000 | −0.262152 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.00000 | 0.112194 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.50000 | − | 12.9904i | −0.280093 | − | 0.485135i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.5000 | − | 33.7750i | 0.727227 | − | 1.25959i | −0.230823 | − | 0.972996i | \(-0.574142\pi\) |
0.958051 | − | 0.286599i | \(-0.0925247\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.50000 | + | 11.2583i | −0.242073 | + | 0.419282i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.0000 | −0.966950 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.50000 | − | 4.33013i | −0.0928477 | − | 0.160817i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.500000 | − | 0.866025i | 0.0185440 | − | 0.0321191i | −0.856605 | − | 0.515974i | \(-0.827430\pi\) |
0.875148 | + | 0.483854i | \(0.160764\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.00000 | − | 6.92820i | 0.147945 | − | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.50000 | + | 4.33013i | 0.0923396 | + | 0.159937i | 0.908495 | − | 0.417895i | \(-0.137232\pi\) |
−0.816156 | + | 0.577832i | \(0.803899\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.00000 | + | 5.19615i | −0.110657 | + | 0.191663i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.5000 | + | 18.1865i | 0.607785 | + | 0.669910i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.50000 | − | 14.7224i | 0.312678 | − | 0.541573i | −0.666264 | − | 0.745716i | \(-0.732107\pi\) |
0.978941 | + | 0.204143i | \(0.0654407\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.50000 | − | 4.33013i | −0.0918398 | − | 0.159071i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.50000 | + | 14.7224i | −0.311835 | + | 0.540114i | −0.978760 | − | 0.205011i | \(-0.934277\pi\) |
0.666925 | + | 0.745125i | \(0.267610\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.00000 | −0.219823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.50000 | − | 6.06218i | 0.128058 | − | 0.221803i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.00000 | + | 6.92820i | 0.146157 | + | 0.253151i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.0000 | 1.89751 | 0.948753 | − | 0.316017i | \(-0.102346\pi\) | ||||
0.948753 | + | 0.316017i | \(0.102346\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.5000 | + | 18.1865i | −0.382641 | + | 0.662754i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.50000 | + | 14.7224i | −0.309347 | + | 0.535804i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.5000 | + | 18.1865i | 0.381629 | + | 0.661001i | 0.991295 | − | 0.131657i | \(-0.0420299\pi\) |
−0.609666 | + | 0.792658i | \(0.708697\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.00000 | 0.108893 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.0000 | −0.797499 | −0.398750 | − | 0.917060i | \(-0.630556\pi\) | ||||
−0.398750 | + | 0.917060i | \(0.630556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.00000 | − | 1.73205i | −0.0362024 | − | 0.0627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.500000 | − | 0.866025i | 0.0180775 | − | 0.0313112i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.00000 | + | 10.3923i | −0.216647 | + | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.50000 | + | 4.33013i | 0.0901523 | + | 0.156148i | 0.907575 | − | 0.419890i | \(-0.137931\pi\) |
−0.817423 | + | 0.576038i | \(0.804598\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.5000 | − | 18.1865i | −0.378148 | − | 0.654972i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.5000 | + | 44.1673i | 0.917171 | + | 1.58859i | 0.803691 | + | 0.595047i | \(0.202867\pi\) |
0.113480 | + | 0.993540i | \(0.463800\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.50000 | + | 6.06218i | 0.125724 | + | 0.217760i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.00000 | 0.251124 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.0000 | −0.895718 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.5000 | + | 38.9711i | −0.805113 | + | 1.39450i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.50000 | − | 4.33013i | −0.0893427 | − | 0.154746i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.50000 | − | 6.06218i | 0.124920 | − | 0.216368i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.5000 | − | 35.5070i | 0.730746 | − | 1.26569i | −0.225819 | − | 0.974169i | \(-0.572506\pi\) |
0.956565 | − | 0.291520i | \(-0.0941610\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.0000 | 0.569615 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.50000 | + | 7.79423i | −0.160002 | + | 0.277131i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.50000 | + | 2.59808i | 0.0532666 | + | 0.0922604i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.00000 | −0.212798 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.5000 | + | 26.8468i | 0.549038 | + | 0.950962i | 0.998341 | + | 0.0575824i | \(0.0183392\pi\) |
−0.449303 | + | 0.893380i | \(0.648327\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.00000 | −0.0353775 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.0000 | −0.494666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33.0000 | 1.16454 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.00000 | −0.0352454 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.0000 | 0.492823 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.0000 | −1.47664 | −0.738321 | − | 0.674450i | \(-0.764381\pi\) | ||||
−0.738321 | + | 0.674450i | \(0.764381\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.5000 | − | 32.0429i | −0.649623 | − | 1.12518i | −0.983213 | − | 0.182462i | \(-0.941593\pi\) |
0.333590 | − | 0.942718i | \(-0.391740\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.5000 | − | 19.9186i | −0.402827 | − | 0.697718i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.0000 | + | 34.6410i | −0.699711 | + | 1.21194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.00000 | −0.0349428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.500000 | + | 0.866025i | −0.0174501 | + | 0.0302245i | −0.874619 | − | 0.484812i | \(-0.838888\pi\) |
0.857168 | + | 0.515036i | \(0.172221\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.5000 | + | 26.8468i | −0.540296 | + | 0.935820i | 0.458591 | + | 0.888648i | \(0.348354\pi\) |
−0.998887 | + | 0.0471726i | \(0.984979\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.50000 | − | 2.59808i | −0.0522233 | − | 0.0904534i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.50000 | − | 12.9904i | 0.260801 | − | 0.451720i | −0.705654 | − | 0.708556i | \(-0.749347\pi\) |
0.966455 | + | 0.256836i | \(0.0826802\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.0000 | −0.486240 | −0.243120 | − | 0.969996i | \(-0.578171\pi\) | ||||
−0.243120 | + | 0.969996i | \(0.578171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.0000 | 0.763172 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.00000 | + | 5.19615i | 0.103944 | + | 0.180036i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.50000 | + | 2.59808i | 0.0519096 | + | 0.0899101i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.50000 | + | 6.06218i | 0.120978 | + | 0.209540i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.50000 | + | 14.7224i | 0.293453 | + | 0.508275i | 0.974624 | − | 0.223849i | \(-0.0718624\pi\) |
−0.681171 | + | 0.732124i | \(0.738529\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00000 | − | 3.46410i | 0.0689655 | − | 0.119452i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.50000 | + | 4.33013i | −0.0861046 | + | 0.149137i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.00000 | − | 10.3923i | −0.206406 | − | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00000 | −0.0687208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.0000 | 0.549119 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.50000 | − | 6.06218i | −0.119978 | − | 0.207809i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.5000 | + | 19.9186i | −0.393753 | + | 0.681999i | −0.992941 | − | 0.118609i | \(-0.962157\pi\) |
0.599189 | + | 0.800608i | \(0.295490\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.50000 | + | 4.33013i | −0.0854982 | + | 0.148087i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.0000 | 0.341593 | 0.170797 | − | 0.985306i | \(-0.445366\pi\) | ||||
0.170797 | + | 0.985306i | \(0.445366\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.5000 | − | 25.1147i | −0.494734 | − | 0.856904i | 0.505248 | − | 0.862974i | \(-0.331401\pi\) |
−0.999982 | + | 0.00607046i | \(0.998068\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.50000 | + | 4.33013i | −0.0851998 | + | 0.147570i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.0000 | 1.63394 | 0.816970 | − | 0.576681i | \(-0.195652\pi\) | ||||
0.816970 | + | 0.576681i | \(0.195652\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.50000 | − | 11.2583i | 0.221007 | − | 0.382795i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.00000 | + | 13.8564i | 0.271694 | + | 0.470588i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.50000 | − | 7.79423i | 0.152652 | − | 0.264401i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.50000 | + | 7.79423i | −0.0847093 | + | 0.264097i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.50000 | − | 14.7224i | 0.287681 | − | 0.498279i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.500000 | + | 0.866025i | 0.0169031 | + | 0.0292770i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.50000 | − | 11.2583i | 0.219489 | − | 0.380167i | −0.735163 | − | 0.677891i | \(-0.762894\pi\) |
0.954652 | + | 0.297724i | \(0.0962275\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.0000 | 0.876958 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.5000 | + | 18.1865i | −0.353754 | + | 0.612720i | −0.986904 | − | 0.161309i | \(-0.948428\pi\) |
0.633150 | + | 0.774029i | \(0.281762\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.5000 | + | 26.8468i | 0.521617 | + | 0.903466i | 0.999684 | + | 0.0251431i | \(0.00800415\pi\) |
−0.478067 | + | 0.878323i | \(0.658663\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.0000 | 0.403376 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.50000 | − | 16.4545i | 0.318979 | − | 0.552487i | −0.661296 | − | 0.750125i | \(-0.729993\pi\) |
0.980275 | + | 0.197637i | \(0.0633268\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.50000 | + | 11.2583i | −0.218003 | + | 0.377592i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50000 | − | 2.59808i | −0.0502519 | − | 0.0870388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.00000 | 0.167319 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.0000 | 0.534821 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.500000 | + | 0.866025i | 0.0166945 | + | 0.0289157i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.5000 | − | 30.3109i | 0.583658 | − | 1.01092i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.00000 | + | 5.19615i | −0.0999445 | + | 0.173109i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.00000 | + | 6.92820i | 0.133112 | + | 0.230556i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.50000 | + | 6.06218i | 0.116344 | + | 0.201514i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.50000 | + | 9.52628i | 0.182625 | + | 0.316315i | 0.942773 | − | 0.333434i | \(-0.108207\pi\) |
−0.760149 | + | 0.649749i | \(0.774874\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.50000 | + | 2.59808i | 0.0497519 | + | 0.0861727i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.0000 | −0.694999 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.50000 | − | 2.59808i | 0.0495885 | − | 0.0858898i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.00000 | − | 10.3923i | −0.198137 | − | 0.343184i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.50000 | + | 9.52628i | −0.181428 | + | 0.314243i | −0.942367 | − | 0.334581i | \(-0.891405\pi\) |
0.760939 | + | 0.648824i | \(0.224739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.5000 | + | 19.9186i | −0.378938 | + | 0.656340i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.0000 | −0.493731 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.50000 | + | 6.06218i | −0.115079 | + | 0.199323i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.50000 | − | 11.2583i | −0.213488 | − | 0.369772i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.00000 | −0.0656179 | −0.0328089 | − | 0.999462i | \(-0.510445\pi\) | ||||
−0.0328089 | + | 0.999462i | \(0.510445\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.0000 | − | 25.9808i | −0.491605 | − | 0.851485i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.0000 | −0.785725 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.00000 | −0.0981105 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.00000 | 0.195803 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.0000 | 0.456387 | 0.228193 | − | 0.973616i | \(-0.426718\pi\) | ||||
0.228193 | + | 0.973616i | \(0.426718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.00000 | 0.162822 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.500000 | + | 0.866025i | 0.0162650 | + | 0.0281718i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.50000 | + | 9.52628i | 0.178538 | + | 0.309236i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.50000 | − | 16.4545i | 0.308059 | − | 0.533573i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.0000 | 0.712650 | 0.356325 | − | 0.934362i | \(-0.384030\pi\) | ||||
0.356325 | + | 0.934362i | \(0.384030\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.50000 | + | 2.59808i | −0.0485389 | + | 0.0840718i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.50000 | + | 12.9904i | −0.242441 | + | 0.419919i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.00000 | − | 1.73205i | −0.0322917 | − | 0.0559308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | + | 15.5885i | −0.290323 | + | 0.502853i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.00000 | −0.257796 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.00000 | 0.0643823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.5000 | − | 18.1865i | −0.337657 | − | 0.584839i | 0.646334 | − | 0.763054i | \(-0.276301\pi\) |
−0.983992 | + | 0.178215i | \(0.942968\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.50000 | + | 4.33013i | 0.0803116 | + | 0.139104i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.5000 | + | 38.9711i | 0.722059 | + | 1.25064i | 0.960173 | + | 0.279406i | \(0.0901376\pi\) |
−0.238114 | + | 0.971237i | \(0.576529\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.0000 | + | 17.3205i | 0.320585 | + | 0.555270i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.500000 | − | 0.866025i | 0.0160128 | − | 0.0277350i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.5000 | − | 26.8468i | 0.495889 | − | 0.858905i | −0.504100 | − | 0.863645i | \(-0.668176\pi\) |
0.999989 | + | 0.00474056i | \(0.00150897\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.0000 | + | 36.3731i | 0.671163 | + | 1.16249i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.0000 | 1.27580 | 0.637901 | − | 0.770118i | \(-0.279803\pi\) | ||||
0.637901 | + | 0.770118i | \(0.279803\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.5000 | + | 18.1865i | 0.334558 | + | 0.579471i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.500000 | − | 0.866025i | 0.0159152 | − | 0.0275659i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.00000 | − | 6.92820i | 0.127193 | − | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.0000 | 1.01651 | 0.508257 | − | 0.861206i | \(-0.330290\pi\) | ||||
0.508257 | + | 0.861206i | \(0.330290\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.5000 | + | 23.3827i | 0.428410 | + | 0.742027i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.50000 | + | 11.2583i | −0.206064 | + | 0.356913i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.0000 | 1.33015 | 0.665077 | − | 0.746775i | \(-0.268399\pi\) | ||||
0.665077 | + | 0.746775i | \(0.268399\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.50000 | + | 6.06218i | −0.110735 | + | 0.191799i |
(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 | 4020.2.q.e.3781.1 | yes | 2 | |
67.37 | even | 3 | inner | 4020.2.q.e.841.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.q.e.841.1 | ✓ | 2 | 67.37 | even | 3 | inner | |
4020.2.q.e.3781.1 | yes | 2 | 1.1 | even | 1 | trivial |