Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(2591,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.j (of order \(2\), degree \(1\), 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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.11007531417600000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.8 | ||
Root | \(-0.159959 + 0.596975i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.2591 |
Dual form | 4032.2.j.f.2591.5 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.51387 | −0.677022 | −0.338511 | − | 0.940962i | \(-0.609923\pi\) | ||||
−0.338511 | + | 0.940962i | \(0.609923\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 0.935622i | − 0.282101i | −0.990002 | − | 0.141050i | \(-0.954952\pi\) | ||||
0.990002 | − | 0.141050i | \(-0.0450479\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.14093i | 0.593788i | 0.954910 | + | 0.296894i | \(0.0959508\pi\) | ||||
−0.954910 | + | 0.296894i | \(0.904049\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 2.62210i | − 0.635952i | −0.948099 | − | 0.317976i | \(-0.896997\pi\) | ||||
0.948099 | − | 0.317976i | \(-0.103003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.46410 | 0.794719 | 0.397360 | − | 0.917663i | \(-0.369927\pi\) | ||||
0.397360 | + | 0.917663i | \(0.369927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.86474 | −1.43140 | −0.715698 | − | 0.698410i | \(-0.753891\pi\) | ||||
−0.715698 | + | 0.698410i | \(0.753891\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.70820 | −0.541641 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.44949 | 0.454859 | 0.227429 | − | 0.973795i | \(-0.426968\pi\) | ||||
0.227429 | + | 0.973795i | \(0.426968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 2.00000i | − 0.359211i | −0.983739 | − | 0.179605i | \(-0.942518\pi\) | ||||
0.983739 | − | 0.179605i | \(-0.0574821\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.51387i | − 0.255890i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.14093i | − 0.351967i | −0.984393 | − | 0.175984i | \(-0.943689\pi\) | ||||
0.984393 | − | 0.175984i | \(-0.0563106\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 2.62210i | − 0.409503i | −0.978814 | − | 0.204751i | \(-0.934361\pi\) | ||||
0.978814 | − | 0.204751i | \(-0.0656386\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.74597 | 1.18125 | 0.590624 | − | 0.806947i | \(-0.298881\pi\) | ||||
0.590624 | + | 0.806947i | \(0.298881\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3762 | 1.42528 | 0.712641 | − | 0.701529i | \(-0.247499\pi\) | ||||
0.712641 | + | 0.701529i | \(0.247499\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.41641i | 0.190988i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 9.79796i | − 1.27559i | −0.770208 | − | 0.637793i | \(-0.779848\pi\) | ||||
0.770208 | − | 0.637793i | \(-0.220152\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.2101i | 1.43530i | 0.696403 | + | 0.717651i | \(0.254783\pi\) | ||||
−0.696403 | + | 0.717651i | \(0.745217\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 3.24109i | − 0.402008i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.14093 | −0.261557 | −0.130778 | − | 0.991412i | \(-0.541748\pi\) | ||||
−0.130778 | + | 0.991412i | \(0.541748\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.62054 | −0.192323 | −0.0961616 | − | 0.995366i | \(-0.530657\pi\) | ||||
−0.0961616 | + | 0.995366i | \(0.530657\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.70820 | −0.668095 | −0.334047 | − | 0.942556i | \(-0.608415\pi\) | ||||
−0.334047 | + | 0.942556i | \(0.608415\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.935622 | 0.106624 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.70820i | 0.192188i | 0.995372 | + | 0.0960940i | \(0.0306349\pi\) | ||||
−0.995372 | + | 0.0960940i | \(0.969365\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1.87124i | − 0.205396i | −0.994713 | − | 0.102698i | \(-0.967253\pi\) | ||||
0.994713 | − | 0.102698i | \(-0.0327475\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.96951i | 0.430554i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.62210i | 0.277942i | 0.990296 | + | 0.138971i | \(0.0443794\pi\) | ||||
−0.990296 | + | 0.138971i | \(0.955621\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.14093 | −0.224431 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.24419 | −0.538043 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.7082 | 1.79800 | 0.898998 | − | 0.437953i | \(-0.144296\pi\) | ||||
0.898998 | + | 0.437953i | \(0.144296\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.38511 | 0.336831 | 0.168416 | − | 0.985716i | \(-0.446135\pi\) | ||||
0.168416 | + | 0.985716i | \(0.446135\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 9.41641i | − 0.927826i | −0.885881 | − | 0.463913i | \(-0.846445\pi\) | ||||
0.885881 | − | 0.463913i | \(-0.153555\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 8.86234i | − 0.856754i | −0.903600 | − | 0.428377i | \(-0.859085\pi\) | ||||
0.903600 | − | 0.428377i | \(-0.140915\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.74597i | 0.741929i | 0.928647 | + | 0.370965i | \(0.120973\pi\) | ||||
−0.928647 | + | 0.370965i | \(0.879027\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 12.7279i | − 1.19734i | −0.800995 | − | 0.598671i | \(-0.795696\pi\) | ||||
0.800995 | − | 0.598671i | \(-0.204304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.3923 | 0.969087 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.62210 | 0.240367 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.1246 | 0.920419 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.6692 | 1.04373 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1.70820i | − 0.151579i | −0.997124 | − | 0.0757893i | \(-0.975852\pi\) | ||||
0.997124 | − | 0.0757893i | \(-0.0241476\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 12.8257i | − 1.12059i | −0.828294 | − | 0.560293i | \(-0.810689\pi\) | ||||
0.828294 | − | 0.560293i | \(-0.189311\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.46410i | 0.300376i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 4.24264i | − 0.362473i | −0.983440 | − | 0.181237i | \(-0.941990\pi\) | ||||
0.983440 | − | 0.181237i | \(-0.0580100\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.28187 | 0.363183 | 0.181592 | − | 0.983374i | \(-0.441875\pi\) | ||||
0.181592 | + | 0.983374i | \(0.441875\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00310 | 0.167508 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.70820 | −0.307950 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.50496 | 0.696754 | 0.348377 | − | 0.937355i | \(-0.386733\pi\) | ||||
0.348377 | + | 0.937355i | \(0.386733\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 11.4164i | − 0.929054i | −0.885559 | − | 0.464527i | \(-0.846224\pi\) | ||||
0.885559 | − | 0.464527i | \(-0.153776\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.02774i | 0.243194i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 6.86474i | − 0.541017i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.9973 | 1.25301 | 0.626504 | − | 0.779418i | \(-0.284485\pi\) | ||||
0.626504 | + | 0.779418i | \(0.284485\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.24419 | −0.405808 | −0.202904 | − | 0.979199i | \(-0.565038\pi\) | ||||
−0.202904 | + | 0.979199i | \(0.565038\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.41641 | 0.647416 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.3118 | 0.860022 | 0.430011 | − | 0.902824i | \(-0.358510\pi\) | ||||
0.430011 | + | 0.902824i | \(0.358510\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 2.70820i | − 0.204721i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3.96336i | − 0.296235i | −0.988970 | − | 0.148118i | \(-0.952679\pi\) | ||||
0.988970 | − | 0.148118i | \(-0.0473214\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.505406i | 0.0375665i | 0.999824 | + | 0.0187833i | \(0.00597925\pi\) | ||||
−0.999824 | + | 0.0187833i | \(0.994021\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.24109i | 0.238290i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.45329 | −0.179402 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.3500 | −1.11069 | −0.555344 | − | 0.831621i | \(-0.687413\pi\) | ||||
−0.555344 | + | 0.831621i | \(0.687413\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.2918 | 0.740820 | 0.370410 | − | 0.928868i | \(-0.379217\pi\) | ||||
0.370410 | + | 0.928868i | \(0.379217\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.2019 | 1.65307 | 0.826533 | − | 0.562888i | \(-0.190310\pi\) | ||||
0.826533 | + | 0.562888i | \(0.190310\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 15.4164i | − 1.09284i | −0.837511 | − | 0.546420i | \(-0.815990\pi\) | ||||
0.837511 | − | 0.546420i | \(-0.184010\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.44949i | 0.171920i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.96951i | 0.277242i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 3.24109i | − 0.224191i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0278 | −0.828030 | −0.414015 | − | 0.910270i | \(-0.635874\pi\) | ||||
−0.414015 | + | 0.910270i | \(0.635874\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.7264 | −0.799732 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.61373 | 0.377620 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 4.00000i | − 0.267860i | −0.990991 | − | 0.133930i | \(-0.957240\pi\) | ||||
0.990991 | − | 0.133930i | \(-0.0427597\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 28.6791i | − 1.90350i | −0.306874 | − | 0.951750i | \(-0.599283\pi\) | ||||
0.306874 | − | 0.951750i | \(-0.400717\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 9.06914i | − 0.599305i | −0.954048 | − | 0.299653i | \(-0.903129\pi\) | ||||
0.954048 | − | 0.299653i | \(-0.0968708\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.2163i | 1.52095i | 0.649367 | + | 0.760475i | \(0.275034\pi\) | ||||
−0.649367 | + | 0.760475i | \(0.724966\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.62054 | 0.104824 | 0.0524122 | − | 0.998626i | \(-0.483309\pi\) | ||||
0.0524122 | + | 0.998626i | \(0.483309\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.29180 | 0.405290 | 0.202645 | − | 0.979252i | \(-0.435046\pi\) | ||||
0.202645 | + | 0.979252i | \(0.435046\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.51387 | 0.0967175 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.41641i | 0.471895i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 13.9822i | − 0.882548i | −0.897372 | − | 0.441274i | \(-0.854527\pi\) | ||||
0.897372 | − | 0.441274i | \(-0.145473\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.42280i | 0.403798i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 24.8369i | − 1.54928i | −0.632402 | − | 0.774640i | \(-0.717931\pi\) | ||||
0.632402 | − | 0.774640i | \(-0.282069\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.14093 | 0.133031 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.3531 | 1.07004 | 0.535020 | − | 0.844840i | \(-0.320304\pi\) | ||||
0.535020 | + | 0.844840i | \(0.320304\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.7082 | −0.964947 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.0365 | −1.77039 | −0.885193 | − | 0.465223i | \(-0.845974\pi\) | ||||
−0.885193 | + | 0.465223i | \(0.845974\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.00000i | 0.121491i | 0.998153 | + | 0.0607457i | \(0.0193479\pi\) | ||||
−0.998153 | + | 0.0607457i | \(0.980652\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.53385i | 0.152797i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.1078i | 1.32833i | 0.747587 | + | 0.664164i | \(0.231212\pi\) | ||||
−0.747587 | + | 0.664164i | \(0.768788\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.48683i | 0.565937i | 0.959129 | + | 0.282969i | \(0.0913192\pi\) | ||||
−0.959129 | + | 0.282969i | \(0.908681\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.0386 | 0.775067 | 0.387533 | − | 0.921856i | \(-0.373327\pi\) | ||||
0.387533 | + | 0.921856i | \(0.373327\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.62210 | 0.154777 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.1246 | 0.595565 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.3396 | 0.837726 | 0.418863 | − | 0.908049i | \(-0.362429\pi\) | ||||
0.418863 | + | 0.908049i | \(0.362429\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.8328i | 0.863600i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 14.6969i | − 0.849946i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.74597i | 0.446470i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 16.9706i | − 0.971732i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.09963 | 0.291051 | 0.145526 | − | 0.989354i | \(-0.453513\pi\) | ||||
0.145526 | + | 0.989354i | \(0.453513\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.4589 | −1.55705 | −0.778527 | − | 0.627611i | \(-0.784033\pi\) | ||||
−0.778527 | + | 0.627611i | \(0.784033\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.41641 | −0.532247 | −0.266123 | − | 0.963939i | \(-0.585743\pi\) | ||||
−0.266123 | + | 0.963939i | \(0.585743\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.60598 | 0.202532 | 0.101266 | − | 0.994859i | \(-0.467711\pi\) | ||||
0.101266 | + | 0.994859i | \(0.467711\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 2.29180i | − 0.128316i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 9.08321i | − 0.505403i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 5.79808i | − 0.321620i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.1661 | 1.65808 | 0.829039 | − | 0.559190i | \(-0.188888\pi\) | ||||
0.829039 | + | 0.559190i | \(0.188888\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.24109 | 0.177080 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00000 | 0.435788 | 0.217894 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217894 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.87124 | −0.101334 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.7336i | 0.576209i | 0.957599 | + | 0.288104i | \(0.0930250\pi\) | ||||
−0.957599 | + | 0.288104i | \(0.906975\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.57454i | 0.512513i | 0.966609 | + | 0.256257i | \(0.0824892\pi\) | ||||
−0.966609 | + | 0.256257i | \(0.917511\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 5.86319i | − 0.312066i | −0.987752 | − | 0.156033i | \(-0.950129\pi\) | ||||
0.987752 | − | 0.156033i | \(-0.0498706\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.45329 | 0.130207 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.86163 | 0.256587 | 0.128294 | − | 0.991736i | \(-0.459050\pi\) | ||||
0.128294 | + | 0.991736i | \(0.459050\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.00000 | −0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.64147 | 0.452315 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 27.4164i | − 1.43112i | −0.698549 | − | 0.715562i | \(-0.746170\pi\) | ||||
0.698549 | − | 0.715562i | \(-0.253830\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.3762i | 0.538706i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 13.8564i | − 0.717458i | −0.933442 | − | 0.358729i | \(-0.883210\pi\) | ||||
0.933442 | − | 0.358729i | \(-0.116790\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.24419i | 0.270090i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.11044 | −0.313872 | −0.156936 | − | 0.987609i | \(-0.550162\pi\) | ||||
−0.156936 | + | 0.987609i | \(0.550162\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.24419 | 0.267966 | 0.133983 | − | 0.990984i | \(-0.457223\pi\) | ||||
0.133983 | + | 0.990984i | \(0.457223\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.41641 | −0.0721868 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.578246 | −0.0293182 | −0.0146591 | − | 0.999893i | \(-0.504666\pi\) | ||||
−0.0146591 | + | 0.999893i | \(0.504666\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000i | 0.910299i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 2.58600i | − 0.130116i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 15.4919i | − 0.777518i | −0.921340 | − | 0.388759i | \(-0.872904\pi\) | ||||
0.921340 | − | 0.388759i | \(-0.127096\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 6.24574i | − 0.311898i | −0.987765 | − | 0.155949i | \(-0.950157\pi\) | ||||
0.987765 | − | 0.155949i | \(-0.0498435\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.28187 | 0.213295 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.00310 | −0.0992901 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.7082 | −1.46898 | −0.734488 | − | 0.678622i | \(-0.762578\pi\) | ||||
−0.734488 | + | 0.678622i | \(0.762578\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.79796 | 0.482126 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.83282i | 0.139057i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.8634i | 1.60548i | 0.596329 | + | 0.802740i | \(0.296625\pi\) | ||||
−0.596329 | + | 0.802740i | \(0.703375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.6715i | 1.49484i | 0.664353 | + | 0.747419i | \(0.268707\pi\) | ||||
−0.664353 | + | 0.747419i | \(0.731293\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.10117i | 0.344457i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.2101 | −0.542493 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.86474 | −0.330663 | −0.165331 | − | 0.986238i | \(-0.552869\pi\) | ||||
−0.165331 | + | 0.986238i | \(0.552869\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.4164 | 0.836979 | 0.418490 | − | 0.908222i | \(-0.362560\pi\) | ||||
0.418490 | + | 0.908222i | \(0.362560\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.7801 | −1.13756 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 20.0000i | − 0.954548i | −0.878755 | − | 0.477274i | \(-0.841625\pi\) | ||||
0.878755 | − | 0.477274i | \(-0.158375\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 25.8723i | − 1.22923i | −0.788828 | − | 0.614614i | \(-0.789312\pi\) | ||||
0.788828 | − | 0.614614i | \(-0.210688\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 3.96951i | − 0.188173i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 21.2132i | − 1.00111i | −0.865704 | − | 0.500556i | \(-0.833129\pi\) | ||||
0.865704 | − | 0.500556i | \(-0.166871\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.45329 | −0.115521 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.24109 | 0.151945 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.4164 | −0.721149 | −0.360575 | − | 0.932730i | \(-0.617419\pi\) | ||||
−0.360575 | + | 0.932730i | \(0.617419\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.4683 | 0.580708 | 0.290354 | − | 0.956919i | \(-0.406227\pi\) | ||||
0.290354 | + | 0.956919i | \(0.406227\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7082i | 0.822970i | 0.911417 | + | 0.411485i | \(0.134990\pi\) | ||||
−0.911417 | + | 0.411485i | \(0.865010\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.92672i | 0.366805i | 0.983038 | + | 0.183402i | \(0.0587111\pi\) | ||||
−0.983038 | + | 0.183402i | \(0.941289\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 2.14093i | − 0.0988591i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 7.24730i | − 0.333231i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.38149 | −0.430452 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.4558 | −1.16311 | −0.581554 | − | 0.813508i | \(-0.697555\pi\) | ||||
−0.581554 | + | 0.813508i | \(0.697555\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.58359 | 0.208994 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.8079 | −1.21728 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.0000i | 1.45006i | 0.688718 | + | 0.725029i | \(0.258174\pi\) | ||||
−0.688718 | + | 0.725029i | \(0.741826\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.6425i | 1.47313i | 0.676364 | + | 0.736567i | \(0.263555\pi\) | ||||
−0.676364 | + | 0.736567i | \(0.736445\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 6.42280i | − 0.289268i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 1.62054i | − 0.0726914i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.0386 | −0.583690 | −0.291845 | − | 0.956466i | \(-0.594269\pi\) | ||||
−0.291845 | + | 0.956466i | \(0.594269\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.24109 | −0.144513 | −0.0722565 | − | 0.997386i | \(-0.523020\pi\) | ||||
−0.0722565 | + | 0.997386i | \(0.523020\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.12461 | −0.228042 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.1930 | −1.33828 | −0.669140 | − | 0.743136i | \(-0.733338\pi\) | ||||
−0.669140 | + | 0.743136i | \(0.733338\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 5.70820i | − 0.252516i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.2552i | 0.628159i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.5632i | 1.60186i | 0.598755 | + | 0.800932i | \(0.295662\pi\) | ||||
−0.598755 | + | 0.800932i | \(0.704338\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.28187 | 0.187233 | 0.0936164 | − | 0.995608i | \(-0.470157\pi\) | ||||
0.0936164 | + | 0.995608i | \(0.470157\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.24419 | −0.228441 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.1246 | 1.04890 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.61373 | 0.243158 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.4164i | 0.580042i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.935622i | 0.0403001i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 23.7433i | − 1.02080i | −0.859936 | − | 0.510402i | \(-0.829497\pi\) | ||||
0.859936 | − | 0.510402i | \(-0.170503\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 11.7264i | − 0.502303i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.6329 | −0.753927 | −0.376963 | − | 0.926228i | \(-0.623032\pi\) | ||||
−0.376963 | + | 0.926228i | \(0.623032\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.48528 | 0.361485 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.70820 | −0.0726402 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.2574 | 1.23967 | 0.619837 | − | 0.784730i | \(-0.287199\pi\) | ||||
0.619837 | + | 0.784730i | \(0.287199\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.5836i | 0.701411i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 41.5048i | − 1.74922i | −0.484827 | − | 0.874610i | \(-0.661118\pi\) | ||||
0.484827 | − | 0.874610i | \(-0.338882\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.2684i | 0.810627i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.2132i | 0.889304i | 0.895703 | + | 0.444652i | \(0.146673\pi\) | ||||
−0.895703 | + | 0.444652i | \(0.853327\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.1356 | −1.42853 | −0.714265 | − | 0.699875i | \(-0.753239\pi\) | ||||
−0.714265 | + | 0.699875i | \(0.753239\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.5911 | 0.775303 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.4164 | −0.891577 | −0.445788 | − | 0.895138i | \(-0.647077\pi\) | ||||
−0.445788 | + | 0.895138i | \(0.647077\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.87124 | 0.0776323 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 9.70820i | − 0.402073i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.4216i | 1.33818i | 0.743180 | + | 0.669092i | \(0.233317\pi\) | ||||
−0.743180 | + | 0.669092i | \(0.766683\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 6.92820i | − 0.285472i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.1105i | 0.538383i | 0.963087 | + | 0.269191i | \(0.0867564\pi\) | ||||
−0.963087 | + | 0.269191i | \(0.913244\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.96951 | −0.162734 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.0795 | 1.18816 | 0.594078 | − | 0.804408i | \(-0.297517\pi\) | ||||
0.594078 | + | 0.804408i | \(0.297517\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.58359 | −0.105387 | −0.0526935 | − | 0.998611i | \(-0.516781\pi\) | ||||
−0.0526935 | + | 0.998611i | \(0.516781\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.3273 | −0.623144 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.00000i | 0.324710i | 0.986732 | + | 0.162355i | \(0.0519090\pi\) | ||||
−0.986732 | + | 0.162355i | \(0.948091\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.63553i | − 0.0660583i | −0.999454 | − | 0.0330292i | \(-0.989485\pi\) | ||||
0.999454 | − | 0.0330292i | \(-0.0105154\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.7279i | 0.512407i | 0.966623 | + | 0.256203i | \(0.0824717\pi\) | ||||
−0.966623 | + | 0.256203i | \(0.917528\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.3483 | 1.17961 | 0.589805 | − | 0.807546i | \(-0.299205\pi\) | ||||
0.589805 | + | 0.807546i | \(0.299205\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.62210 | −0.105052 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.12461 | −0.164984 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.61373 | −0.223834 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 28.5410i | − 1.13620i | −0.822960 | − | 0.568100i | \(-0.807679\pi\) | ||||
0.822960 | − | 0.568100i | \(-0.192321\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.58600i | 0.102622i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2.14093i | − 0.0848268i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 34.9427i | − 1.38015i | −0.723737 | − | 0.690076i | \(-0.757577\pi\) | ||||
0.723737 | − | 0.690076i | \(-0.242423\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.74597 | −0.305471 | −0.152736 | − | 0.988267i | \(-0.548808\pi\) | ||||
−0.152736 | + | 0.988267i | \(0.548808\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.7031 | 1.28569 | 0.642847 | − | 0.765995i | \(-0.277753\pi\) | ||||
0.642847 | + | 0.765995i | \(0.277753\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.16718 | −0.359843 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.9899 | −0.625735 | −0.312867 | − | 0.949797i | \(-0.601290\pi\) | ||||
−0.312867 | + | 0.949797i | \(0.601290\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.4164i | 0.758662i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.1275i | 1.56314i | 0.623815 | + | 0.781572i | \(0.285582\pi\) | ||||
−0.623815 | + | 0.781572i | \(0.714418\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 48.4974i | − 1.88633i | −0.332323 | − | 0.943166i | \(-0.607832\pi\) | ||||
0.332323 | − | 0.943166i | \(-0.392168\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 5.24419i | − 0.203361i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.8151 | −0.651083 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.4884 | 0.404900 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.7082 | 1.45354 | 0.726772 | − | 0.686879i | \(-0.241020\pi\) | ||||
0.726772 | + | 0.686879i | \(0.241020\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.4228 | −0.900210 | −0.450105 | − | 0.892976i | \(-0.648613\pi\) | ||||
−0.450105 | + | 0.892976i | \(0.648613\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.7082i | 0.679578i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.8723i | 0.989975i | 0.868900 | + | 0.494987i | \(0.164827\pi\) | ||||
−0.868900 | + | 0.494987i | \(0.835173\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.42280i | 0.245402i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.2148i | 0.846315i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.9229 | 1.48070 | 0.740348 | − | 0.672224i | \(-0.234661\pi\) | ||||
0.740348 | + | 0.672224i | \(0.234661\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.48218 | −0.245883 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.87539 | −0.260424 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.3762 | 0.391904 | 0.195952 | − | 0.980614i | \(-0.437220\pi\) | ||||
0.195952 | + | 0.980614i | \(0.437220\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 7.41641i | − 0.279715i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.38511i | 0.127310i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 19.9668i | − 0.749871i | −0.927051 | − | 0.374935i | \(-0.877665\pi\) | ||||
0.927051 | − | 0.374935i | \(-0.122335\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.7295i | 0.514173i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.03243 | −0.113407 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.6969 | 1.07022 | 0.535108 | − | 0.844784i | \(-0.320271\pi\) | ||||
0.535108 | + | 0.844784i | \(0.320271\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.41641 | 0.350685 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.63372 | −0.246370 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 24.8328i | − 0.920998i | −0.887660 | − | 0.460499i | \(-0.847670\pi\) | ||||
0.887660 | − | 0.460499i | \(-0.152330\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 20.3107i | − 0.751217i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 9.06914i | − 0.334976i | −0.985874 | − | 0.167488i | \(-0.946434\pi\) | ||||
0.985874 | − | 0.167488i | \(-0.0535656\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.00310i | 0.0737853i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.6993 | −1.57072 | −0.785360 | − | 0.619039i | \(-0.787522\pi\) | ||||
−0.785360 | + | 0.619039i | \(0.787522\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.3500 | 0.563138 | 0.281569 | − | 0.959541i | \(-0.409145\pi\) | ||||
0.281569 | + | 0.959541i | \(0.409145\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.8754 | −0.471718 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.86234 | 0.323823 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 15.4164i | − 0.562553i | −0.959627 | − | 0.281276i | \(-0.909242\pi\) | ||||
0.959627 | − | 0.281276i | \(-0.0907578\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.2829i | 0.628990i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 12.0278i | − 0.437159i | −0.975819 | − | 0.218579i | \(-0.929858\pi\) | ||||
0.975819 | − | 0.218579i | \(-0.0701423\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 49.0547i | 1.77823i | 0.457682 | + | 0.889116i | \(0.348680\pi\) | ||||
−0.457682 | + | 0.889116i | \(0.651320\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.74597 | −0.280423 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.9768 | 0.757427 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.6324 | −1.74919 | −0.874593 | − | 0.484857i | \(-0.838872\pi\) | ||||
−0.874593 | + | 0.484857i | \(0.838872\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.41641i | 0.194563i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 9.08321i | − 0.325440i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.51622i | 0.0542545i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.2101 | 0.399596 | 0.199798 | − | 0.979837i | \(-0.435971\pi\) | ||||
0.199798 | + | 0.979837i | \(0.435971\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.7279 | 0.452553 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.0000 | −0.852265 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.28409 | −0.293438 | −0.146719 | − | 0.989178i | \(-0.546871\pi\) | ||||
−0.146719 | + | 0.989178i | \(0.546871\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.34072i | 0.188470i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.3923i | 0.366281i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.4342i | 1.66770i | 0.551994 | + | 0.833848i | \(0.313867\pi\) | ||||
−0.551994 | + | 0.833848i | \(0.686133\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −54.4148 | −1.91076 | −0.955381 | − | 0.295375i | \(-0.904555\pi\) | ||||
−0.955381 | + | 0.295375i | \(0.904555\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.2179 | −0.848315 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.8328 | 0.938761 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.0276 | −1.25737 | −0.628686 | − | 0.777659i | \(-0.716407\pi\) | ||||
−0.628686 | + | 0.777659i | \(0.716407\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1.70820i | − 0.0595442i | −0.999557 | − | 0.0297721i | \(-0.990522\pi\) | ||||
0.999557 | − | 0.0297721i | \(-0.00947816\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.4860i | 1.09488i | 0.836847 | + | 0.547438i | \(0.184397\pi\) | ||||
−0.836847 | + | 0.547438i | \(0.815603\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 53.9094i | − 1.87235i | −0.351533 | − | 0.936176i | \(-0.614339\pi\) | ||||
0.351533 | − | 0.936176i | \(-0.385661\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.62210i | 0.0908502i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.93901 | 0.274741 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.2117 | 0.697784 | 0.348892 | − | 0.937163i | \(-0.386558\pi\) | ||||
0.348892 | + | 0.937163i | \(0.386558\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.0000 | −0.793103 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.7413 | −0.438315 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.1246i | 0.347886i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.6969i | 0.503805i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.5584i | 1.38869i | 0.719641 | + | 0.694347i | \(0.244307\pi\) | ||||
−0.719641 | + | 0.694347i | \(0.755693\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.0485i | 1.53883i | 0.638751 | + | 0.769414i | \(0.279452\pi\) | ||||
−0.638751 | + | 0.769414i | \(0.720548\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.6580 | −1.55783 | −0.778916 | − | 0.627128i | \(-0.784230\pi\) | ||||
−0.778916 | + | 0.627128i | \(0.784230\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.3206 | −1.10021 | −0.550103 | − | 0.835097i | \(-0.685411\pi\) | ||||
−0.550103 | + | 0.835097i | \(0.685411\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.1246 | −0.582254 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.59823 | 0.0542163 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 4.58359i | − 0.155309i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.6692i | 0.394491i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 19.1491i | − 0.646619i | −0.946293 | − | 0.323309i | \(-0.895205\pi\) | ||||
0.946293 | − | 0.323309i | \(-0.104795\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 52.2958i | − 1.76189i | −0.473218 | − | 0.880945i | \(-0.656908\pi\) | ||||
0.473218 | − | 0.880945i | \(-0.343092\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.9399 | −1.68061 | −0.840306 | − | 0.542113i | \(-0.817625\pi\) | ||||
−0.840306 | + | 0.542113i | \(0.817625\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −56.1559 | −1.88553 | −0.942765 | − | 0.333458i | \(-0.891784\pi\) | ||||
−0.942765 | + | 0.333458i | \(0.891784\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.70820 | 0.0572913 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.00000i | 0.200558i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 4.89898i | − 0.163390i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 27.2074i | − 0.906410i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 0.765117i | − 0.0254334i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.5198 | 0.913779 | 0.456889 | − | 0.889524i | \(-0.348964\pi\) | ||||
0.456889 | + | 0.889524i | \(0.348964\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.2942 | 1.69945 | 0.849727 | − | 0.527223i | \(-0.176767\pi\) | ||||
0.849727 | + | 0.527223i | \(0.176767\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.75078 | −0.0579422 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.8257 | 0.423542 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.583592i | 0.0192509i | 0.999954 | + | 0.00962546i | \(0.00306393\pi\) | ||||
−0.999954 | + | 0.00962546i | \(0.996936\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3.46948i | − 0.114199i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.79808i | 0.190640i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.86008i | 0.126645i | 0.997993 | + | 0.0633226i | \(0.0201697\pi\) | ||||
−0.997993 | + | 0.0633226i | \(0.979830\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.46410 | −0.113531 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.71396 | 0.121459 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.4164 | 0.960992 | 0.480496 | − | 0.876997i | \(-0.340457\pi\) | ||||
0.480496 | + | 0.876997i | \(0.340457\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.8899 | −1.46337 | −0.731685 | − | 0.681643i | \(-0.761266\pi\) | ||||
−0.731685 | + | 0.681643i | \(0.761266\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.0000i | 0.586161i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 3.96336i | − 0.128792i | −0.997924 | − | 0.0643959i | \(-0.979488\pi\) | ||||
0.997924 | − | 0.0643959i | \(-0.0205120\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 12.2209i | − 0.396707i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 28.4605i | − 0.921926i | −0.887419 | − | 0.460963i | \(-0.847504\pi\) | ||||
0.887419 | − | 0.460963i | \(-0.152496\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.2379 | 0.751961 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.24264 | 0.137002 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0000 | 0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.5804 | −0.501551 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.2918i | 1.36001i | 0.733206 | + | 0.680006i | \(0.238023\pi\) | ||||
−0.733206 | + | 0.680006i | \(0.761977\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 8.64147i | − 0.277318i | −0.990340 | − | 0.138659i | \(-0.955721\pi\) | ||||
0.990340 | − | 0.138659i | \(-0.0442792\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.28187i | 0.137270i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 7.48373i | − 0.239426i | −0.992809 | − | 0.119713i | \(-0.961803\pi\) | ||||
0.992809 | − | 0.119713i | \(-0.0381974\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.45329 | 0.0784075 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.4264 | −1.35319 | −0.676596 | − | 0.736354i | \(-0.736546\pi\) | ||||
−0.676596 | + | 0.736354i | \(0.736546\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35.1246 | −1.11916 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −53.1740 | −1.69084 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 10.8328i | − 0.344116i | −0.985087 | − | 0.172058i | \(-0.944958\pi\) | ||||
0.985087 | − | 0.172058i | \(-0.0550416\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.3384i | 0.739877i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 18.1383i | − 0.574445i | −0.957864 | − | 0.287222i | \(-0.907268\pi\) | ||||
0.957864 | − | 0.287222i | \(-0.0927319\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.2.j.f.2591.8 | yes | 16 | |
3.2 | odd | 2 | inner | 4032.2.j.f.2591.12 | yes | 16 | |
4.3 | odd | 2 | inner | 4032.2.j.f.2591.6 | yes | 16 | |
8.3 | odd | 2 | inner | 4032.2.j.f.2591.9 | yes | 16 | |
8.5 | even | 2 | inner | 4032.2.j.f.2591.11 | yes | 16 | |
12.11 | even | 2 | inner | 4032.2.j.f.2591.10 | yes | 16 | |
24.5 | odd | 2 | inner | 4032.2.j.f.2591.7 | yes | 16 | |
24.11 | even | 2 | inner | 4032.2.j.f.2591.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4032.2.j.f.2591.5 | ✓ | 16 | 24.11 | even | 2 | inner | |
4032.2.j.f.2591.6 | yes | 16 | 4.3 | odd | 2 | inner | |
4032.2.j.f.2591.7 | yes | 16 | 24.5 | odd | 2 | inner | |
4032.2.j.f.2591.8 | yes | 16 | 1.1 | even | 1 | trivial | |
4032.2.j.f.2591.9 | yes | 16 | 8.3 | odd | 2 | inner | |
4032.2.j.f.2591.10 | yes | 16 | 12.11 | even | 2 | inner | |
4032.2.j.f.2591.11 | yes | 16 | 8.5 | even | 2 | inner | |
4032.2.j.f.2591.12 | yes | 16 | 3.2 | odd | 2 | inner |