Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(95,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.95");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.k (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.6567334422\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 287.9 | ||
Character | \(\chi\) | \(=\) | 384.287 |
Dual form | 384.4.k.a.95.9 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −1.96089 | − | 4.81196i | −0.377373 | − | 0.926061i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.30133 | + | 6.30133i | −0.563608 | + | 0.563608i | −0.930330 | − | 0.366723i | \(-0.880480\pi\) |
0.366723 | + | 0.930330i | \(0.380480\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.6728 | −1.33221 | −0.666104 | − | 0.745859i | \(-0.732039\pi\) | ||||
−0.666104 | + | 0.745859i | \(0.732039\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −19.3098 | + | 18.8714i | −0.715179 | + | 0.698941i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −40.4669 | − | 40.4669i | −1.10920 | − | 1.10920i | −0.993255 | − | 0.115946i | \(-0.963010\pi\) |
−0.115946 | − | 0.993255i | \(-0.536990\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 47.3131 | − | 47.3131i | 1.00941 | − | 1.00941i | 0.00945153 | − | 0.999955i | \(-0.496991\pi\) |
0.999955 | − | 0.00945153i | \(-0.00300856\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 42.6779 | + | 17.9655i | 0.734626 | + | 0.309245i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 41.7727i | 0.595963i | 0.954572 | + | 0.297982i | \(0.0963134\pi\) | ||||
−0.954572 | + | 0.297982i | \(0.903687\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.6193 | + | 10.6193i | 0.128223 | + | 0.128223i | 0.768306 | − | 0.640083i | \(-0.221100\pi\) |
−0.640083 | + | 0.768306i | \(0.721100\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 48.3807 | + | 118.725i | 0.502739 | + | 1.23371i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 53.4222i | 0.484317i | 0.970237 | + | 0.242158i | \(0.0778554\pi\) | ||||
−0.970237 | + | 0.242158i | \(0.922145\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 45.5866i | 0.364692i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 128.673 | + | 55.9134i | 0.917152 | + | 0.398538i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 105.268 | + | 105.268i | 0.674064 | + | 0.674064i | 0.958650 | − | 0.284586i | \(-0.0918562\pi\) |
−0.284586 | + | 0.958650i | \(0.591856\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.14755i | 0.0182361i | 0.999958 | + | 0.00911803i | \(0.00290240\pi\) | ||||
−0.999958 | + | 0.00911803i | \(0.997098\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −115.374 | + | 274.076i | −0.608606 | + | 1.44577i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 155.472 | − | 155.472i | 0.750843 | − | 0.750843i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −42.1756 | − | 42.1756i | −0.187395 | − | 0.187395i | 0.607174 | − | 0.794569i | \(-0.292303\pi\) |
−0.794569 | + | 0.607174i | \(0.792303\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −320.444 | − | 134.893i | −1.31570 | − | 0.553850i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 152.486 | 0.580836 | 0.290418 | − | 0.956900i | \(-0.406206\pi\) | ||||
0.290418 | + | 0.956900i | \(0.406206\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 221.247 | − | 221.247i | 0.784647 | − | 0.784647i | −0.195964 | − | 0.980611i | \(-0.562784\pi\) |
0.980611 | + | 0.195964i | \(0.0627836\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.76270 | − | 240.593i | 0.00915197 | − | 0.797009i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 381.086 | 1.18270 | 0.591352 | − | 0.806414i | \(-0.298594\pi\) | ||||
0.591352 | + | 0.806414i | \(0.298594\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 265.749 | 0.774779 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 201.008 | − | 81.9116i | 0.551898 | − | 0.224900i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −294.048 | + | 294.048i | −0.762088 | + | 0.762088i | −0.976699 | − | 0.214612i | \(-0.931151\pi\) |
0.214612 | + | 0.976699i | \(0.431151\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 509.990 | 1.25031 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 30.2765 | − | 71.9231i | 0.0703547 | − | 0.167131i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 445.445 | + | 445.445i | 0.982916 | + | 0.982916i | 0.999857 | − | 0.0169404i | \(-0.00539256\pi\) |
−0.0169404 | + | 0.999857i | \(0.505393\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −21.8473 | + | 21.8473i | −0.0458568 | + | 0.0458568i | −0.729663 | − | 0.683807i | \(-0.760323\pi\) |
0.683807 | + | 0.729663i | \(0.260323\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 476.429 | − | 465.611i | 0.952768 | − | 0.931135i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 596.270i | 1.13782i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −572.215 | − | 572.215i | −1.04339 | − | 1.04339i | −0.999015 | − | 0.0443759i | \(-0.985870\pi\) |
−0.0443759 | − | 0.999015i | \(-0.514130\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 257.065 | − | 104.755i | 0.448507 | − | 0.182768i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 612.406i | 1.02365i | 0.859089 | + | 0.511825i | \(0.171031\pi\) | ||||
−0.859089 | + | 0.511825i | \(0.828969\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 331.477i | − | 0.531458i | −0.964048 | − | 0.265729i | \(-0.914387\pi\) | ||
0.964048 | − | 0.265729i | \(-0.0856126\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 219.361 | − | 89.3901i | 0.337728 | − | 0.137625i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 998.433 | + | 998.433i | 1.47769 | + | 1.47769i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 427.462i | − | 0.608775i | −0.952548 | − | 0.304388i | \(-0.901548\pi\) | ||
0.952548 | − | 0.304388i | \(-0.0984518\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16.7398 | − | 728.808i | 0.0229628 | − | 0.999736i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −245.236 | + | 245.236i | −0.324314 | + | 0.324314i | −0.850420 | − | 0.526105i | \(-0.823652\pi\) |
0.526105 | + | 0.850420i | \(0.323652\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −263.224 | − | 263.224i | −0.335889 | − | 0.335889i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 300.128 | − | 712.967i | 0.369851 | − | 0.878599i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −188.997 | −0.225097 | −0.112548 | − | 0.993646i | \(-0.535901\pi\) | ||||
−0.112548 | + | 0.993646i | \(0.535901\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1167.35 | + | 1167.35i | −1.34474 | + | 1.34474i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.1459 | − | 6.17200i | 0.0168877 | − | 0.00688179i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −133.832 | −0.144535 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1474.45 | 1.54338 | 0.771689 | − | 0.636001i | \(-0.219412\pi\) | ||||
0.771689 | + | 0.636001i | \(0.219412\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1545.08 | + | 17.7419i | 1.56854 | + | 0.0180114i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −223.136 | + | 223.136i | −0.219830 | + | 0.219830i | −0.808427 | − | 0.588597i | \(-0.799681\pi\) |
0.588597 | + | 0.808427i | \(0.299681\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 217.914 | 0.208463 | 0.104232 | − | 0.994553i | \(-0.466762\pi\) | ||||
0.104232 | + | 0.994553i | \(0.466762\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1052.99 | − | 443.260i | −0.978675 | − | 0.411979i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −335.407 | − | 335.407i | −0.303038 | − | 0.303038i | 0.539163 | − | 0.842201i | \(-0.318740\pi\) |
−0.842201 | + | 0.539163i | \(0.818740\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1032.70 | + | 1032.70i | −0.907477 | + | 0.907477i | −0.996068 | − | 0.0885914i | \(-0.971763\pi\) |
0.0885914 | + | 0.996068i | \(0.471763\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −120.245 | + | 285.649i | −0.102822 | + | 0.244257i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1010.24i | 0.841020i | 0.907288 | + | 0.420510i | \(0.138149\pi\) | ||||
−0.907288 | + | 0.420510i | \(0.861851\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −336.630 | − | 336.630i | −0.272965 | − | 0.272965i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −20.7435 | + | 1806.47i | −0.0163909 | + | 1.42742i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1030.65i | − | 0.793947i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1944.14i | 1.46066i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −299.008 | − | 733.755i | −0.219192 | − | 0.537890i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1074.92 | − | 1074.92i | −0.769151 | − | 0.769151i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1504.32i | 1.05108i | 0.850769 | + | 0.525540i | \(0.176137\pi\) | ||||
−0.850769 | + | 0.525540i | \(0.823863\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1498.47 | − | 630.790i | −1.02274 | − | 0.430527i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1515.05 | + | 1515.05i | −1.01046 | + | 1.01046i | −0.0105196 | + | 0.999945i | \(0.503349\pi\) |
−0.999945 | + | 0.0105196i | \(0.996651\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −262.009 | − | 262.009i | −0.170820 | − | 0.170820i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1163.14 | + | 458.481i | −0.741533 | + | 0.292294i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2462.36 | 1.53557 | 0.767787 | − | 0.640706i | \(-0.221358\pi\) | ||||
0.767787 | + | 0.640706i | \(0.221358\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 782.125 | − | 782.125i | 0.477259 | − | 0.477259i | −0.426995 | − | 0.904254i | \(-0.640428\pi\) |
0.904254 | + | 0.426995i | \(0.140428\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −747.266 | − | 1833.77i | −0.446320 | − | 1.09526i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3829.23 | −2.23927 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1326.66 | −0.759816 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −521.104 | − | 1278.77i | −0.292381 | − | 0.717493i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2532.54 | − | 2532.54i | 1.39244 | − | 1.39244i | 0.572616 | − | 0.819824i | \(-0.305929\pi\) |
0.819824 | − | 0.572616i | \(-0.194071\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −571.667 | −0.308090 | −0.154045 | − | 0.988064i | \(-0.549230\pi\) | ||||
−0.154045 | + | 0.988064i | \(0.549230\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −788.310 | − | 806.624i | −0.416543 | − | 0.426220i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.8338 | − | 19.8338i | −0.0102780 | − | 0.0102780i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1664.95 | − | 1664.95i | 0.846353 | − | 0.846353i | −0.143323 | − | 0.989676i | \(-0.545779\pi\) |
0.989676 | + | 0.143323i | \(0.0457788\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1991.54 | + | 838.352i | 0.993331 | + | 0.418149i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1318.08i | − | 0.645211i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1893.19 | + | 1893.19i | 0.909731 | + | 0.909731i | 0.996250 | − | 0.0865194i | \(-0.0275744\pi\) |
−0.0865194 | + | 0.996250i | \(0.527574\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1000.03 | − | 2454.05i | −0.471833 | − | 1.15786i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2441.42i | 1.13127i | 0.824655 | + | 0.565636i | \(0.191369\pi\) | ||||
−0.824655 | + | 0.565636i | \(0.808631\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2280.06i | − | 1.03780i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −405.460 | − | 4.65585i | −0.181323 | − | 0.00208212i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 856.168 | + | 856.168i | 0.376262 | + | 0.376262i | 0.869751 | − | 0.493490i | \(-0.164279\pi\) |
−0.493490 | + | 0.869751i | \(0.664279\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1124.75i | − | 0.485846i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1270.00 | − | 3016.93i | 0.539315 | − | 1.28117i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2706.69 | + | 2706.69i | −1.13021 | + | 1.13021i | −0.140068 | + | 0.990142i | \(0.544732\pi\) |
−0.990142 | + | 0.140068i | \(0.955268\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 155.849 | + | 155.849i | 0.0640008 | + | 0.0640008i | 0.738383 | − | 0.674382i | \(-0.235590\pi\) |
−0.674382 | + | 0.738383i | \(0.735590\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 147.969 | + | 62.2882i | 0.0597713 | + | 0.0251611i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 531.524 | 0.211235 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1690.41 | − | 1690.41i | 0.661043 | − | 0.661043i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3174.72 | − | 1379.54i | −1.22184 | − | 0.530936i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1193.27 | −0.452054 | −0.226027 | − | 0.974121i | \(-0.572574\pi\) | ||||
−0.226027 | + | 0.974121i | \(0.572574\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5048.50 | −1.88290 | −0.941448 | − | 0.337158i | \(-0.890534\pi\) | ||||
−0.941448 | + | 0.337158i | \(0.890534\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2869.23 | − | 1169.22i | 1.05369 | − | 0.429382i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −544.245 | + | 544.245i | −0.196832 | + | 0.196832i | −0.798640 | − | 0.601809i | \(-0.794447\pi\) |
0.601809 | + | 0.798640i | \(0.294447\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −609.004 | −0.216941 | −0.108470 | − | 0.994100i | \(-0.534595\pi\) | ||||
−0.108470 | + | 0.994100i | \(0.534595\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1631.42 | + | 3875.52i | −0.572496 | + | 1.35999i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2597.27 | − | 2597.27i | −0.897994 | − | 0.897994i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −960.863 | + | 960.863i | −0.327364 | + | 0.327364i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1008.15 | − | 1031.57i | −0.338509 | − | 0.346373i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 859.463i | − | 0.284451i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −407.803 | − | 407.803i | −0.133053 | − | 0.133053i | 0.637444 | − | 0.770497i | \(-0.279992\pi\) |
−0.770497 | + | 0.637444i | \(0.779992\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2946.87 | − | 1200.86i | 0.947964 | − | 0.386298i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2788.30i | 0.884466i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 77.6591i | − | 0.0242942i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1595.05 | + | 649.989i | −0.492163 | + | 0.200558i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1976.40 | + | 1976.40i | 0.601569 | + | 0.601569i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2957.32i | 0.888057i | 0.896013 | + | 0.444028i | \(0.146451\pi\) | ||||
−0.896013 | + | 0.444028i | \(0.853549\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −860.283 | − | 880.269i | −0.254899 | − | 0.260821i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 254.883 | − | 254.883i | 0.0745250 | − | 0.0745250i | −0.668862 | − | 0.743387i | \(-0.733218\pi\) |
0.743387 | + | 0.668862i | \(0.233218\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −349.739 | − | 349.739i | −0.100923 | − | 0.100923i | 0.654842 | − | 0.755765i | \(-0.272735\pi\) |
−0.755765 | + | 0.654842i | \(0.772735\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2846.60 | − | 6762.23i | 0.810790 | − | 1.92607i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1869.42 | −0.525621 | −0.262810 | − | 0.964847i | \(-0.584649\pi\) | ||||
−0.262810 | + | 0.964847i | \(0.584649\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2401.35 | + | 2401.35i | −0.666581 | + | 0.666581i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2056.93 | + | 838.205i | −0.563763 | + | 0.229735i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2120.63 | 0.573943 | 0.286972 | − | 0.957939i | \(-0.407351\pi\) | ||||
0.286972 | + | 0.957939i | \(0.407351\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3096.26 | 0.827584 | 0.413792 | − | 0.910372i | \(-0.364204\pi\) | ||||
0.413792 | + | 0.910372i | \(0.364204\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3539.82 | + | 1348.56i | −0.934483 | + | 0.356009i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1674.57 | + | 1674.57i | −0.436671 | + | 0.436671i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1004.87 | 0.258859 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1660.94 | + | 699.183i | 0.422723 | + | 0.177948i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2393.97 | + | 2393.97i | 0.602017 | + | 0.602017i | 0.940847 | − | 0.338830i | \(-0.110031\pi\) |
−0.338830 | + | 0.940847i | \(0.610031\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2161.83 | − | 2161.83i | 0.537205 | − | 0.537205i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −750.468 | + | 1782.77i | −0.184299 | + | 0.437810i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3582.50i | 0.869535i | 0.900543 | + | 0.434768i | \(0.143169\pi\) | ||||
−0.900543 | + | 0.434768i | \(0.856831\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1040.59 | + | 1040.59i | 0.249649 | + | 0.249649i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4019.28 | − | 46.1530i | −0.953208 | − | 0.0109456i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2196.24i | 0.514928i | 0.966288 | + | 0.257464i | \(0.0828869\pi\) | ||||
−0.966288 | + | 0.257464i | \(0.917113\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3705.79i | − | 0.859037i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 370.601 | + | 909.443i | 0.0849454 | + | 0.208453i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 64.1764 | + | 64.1764i | 0.0145461 | + | 0.0145461i | 0.714342 | − | 0.699796i | \(-0.246726\pi\) |
−0.699796 | + | 0.714342i | \(0.746726\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3627.40i | − | 0.813095i | −0.913630 | − | 0.406548i | \(-0.866732\pi\) | ||
0.913630 | − | 0.406548i | \(-0.133268\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7906.27 | + | 3328.19i | 1.75278 | + | 0.737843i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1844.75 | − | 1844.75i | 0.404518 | − | 0.404518i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3476.10 | + | 3476.10i | 0.754001 | + | 0.754001i | 0.975223 | − | 0.221222i | \(-0.0710046\pi\) |
−0.221222 | + | 0.975223i | \(0.571005\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −59.3988 | − | 60.7788i | −0.0127459 | − | 0.0130420i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5597.90 | 1.18841 | 0.594204 | − | 0.804314i | \(-0.297467\pi\) | ||||
0.594204 | + | 0.804314i | \(0.297467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 236.800 | − | 236.800i | 0.0497395 | − | 0.0497395i | −0.681800 | − | 0.731539i | \(-0.738802\pi\) |
0.731539 | + | 0.681800i | \(0.238802\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 262.429 | + | 643.993i | 0.0545437 | + | 0.133849i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3762.26 | −0.773795 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3168.04 | 0.644828 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2891.23 | − | 7094.98i | −0.582429 | − | 1.42926i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3077.11 | + | 3077.11i | −0.613537 | + | 0.613537i | −0.943866 | − | 0.330329i | \(-0.892840\pi\) |
0.330329 | + | 0.943866i | \(0.392840\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5613.79 | −1.10796 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2944.35 | − | 7469.63i | −0.575247 | − | 1.45937i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2527.57 | + | 2527.57i | 0.488873 | + | 0.488873i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5458.79 | + | 5458.79i | −1.04531 | + | 1.04531i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1511.26 | + | 636.175i | 0.286534 | + | 0.120618i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 275.334i | − | 0.0516905i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1749.92 | + | 1749.92i | 0.325321 | + | 0.325321i | 0.850804 | − | 0.525483i | \(-0.176115\pi\) |
−0.525483 | + | 0.850804i | \(0.676115\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −427.305 | − | 1048.59i | −0.0786685 | − | 0.193050i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 7073.49i | − | 1.28971i | −0.764304 | − | 0.644856i | \(-0.776917\pi\) | ||
0.764304 | − | 0.644856i | \(-0.223083\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9046.73i | 1.63371i | 0.576843 | + | 0.816855i | \(0.304284\pi\) | ||||
−0.576843 | + | 0.816855i | \(0.695716\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −68.1636 | + | 5936.10i | −0.0121923 | + | 1.06178i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4477.40 | + | 4477.40i | 0.793300 | + | 0.793300i | 0.982029 | − | 0.188729i | \(-0.0604369\pi\) |
−0.188729 | + | 0.982029i | \(0.560437\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8519.77i | − | 1.49535i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −956.269 | + | 2271.66i | −0.166273 | + | 0.394990i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −443.599 | + | 443.599i | −0.0764164 | + | 0.0764164i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2156.84 | + | 2156.84i | 0.368123 | + | 0.368123i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6994.33 | + | 2944.31i | 1.18284 | + | 0.497922i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9402.47 | −1.57561 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1060.84 | − | 1060.84i | 0.176160 | − | 0.176160i | −0.613519 | − | 0.789680i | \(-0.710247\pi\) |
0.789680 | + | 0.613519i | \(0.210247\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1610.32 | + | 18.4911i | 0.264999 | + | 0.00304296i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7211.43 | 1.17613 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −127.151 | −0.0205529 | −0.0102765 | − | 0.999947i | \(-0.503271\pi\) | ||||
−0.0102765 | + | 0.999947i | \(0.503271\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4861.22 | − | 1980.96i | 0.778836 | − | 0.317378i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 127.372 | − | 127.372i | 0.0202275 | − | 0.0202275i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1906.00 | 0.300041 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −959.756 | + | 2279.95i | −0.149773 | + | 0.355792i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2671.89 | − | 2671.89i | −0.413357 | − | 0.413357i | 0.469549 | − | 0.882906i | \(-0.344416\pi\) |
−0.882906 | + | 0.469549i | \(0.844416\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7144.55 | − | 7144.55i | 1.09581 | − | 1.09581i | 0.100920 | − | 0.994895i | \(-0.467821\pi\) |
0.994895 | − | 0.100920i | \(-0.0321785\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8733.34 | − | 3442.47i | 1.32807 | − | 0.523492i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4391.32i | 0.662114i | 0.943611 | + | 0.331057i | \(0.107405\pi\) | ||||
−0.943611 | + | 0.331057i | \(0.892595\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3858.97 | − | 3858.97i | −0.576938 | − | 0.576938i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4959.45 | + | 2020.99i | −0.735244 | + | 0.299614i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 750.165i | 0.110285i | 0.998479 | + | 0.0551423i | \(0.0175613\pi\) | ||||
−0.998479 | + | 0.0551423i | \(0.982439\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 6633.46i | − | 0.967118i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9355.09 | − | 3812.23i | 1.35266 | − | 0.551213i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2088.74 | + | 2088.74i | 0.299534 | + | 0.299534i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8873.45i | 1.26210i | 0.775743 | + | 0.631049i | \(0.217375\pi\) | ||||
−0.775743 | + | 0.631049i | \(0.782625\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2944.48 | + | 2877.62i | −0.415402 | + | 0.405970i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7255.01 | − | 7255.01i | 1.01526 | − | 1.01526i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −257.833 | − | 257.833i | −0.0357911 | − | 0.0357911i | 0.688985 | − | 0.724776i | \(-0.258057\pi\) |
−0.724776 | + | 0.688985i | \(0.758057\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3064.68 | + | 7280.28i | −0.422024 | + | 1.00254i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9961.15 | 1.36081 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3719.90 | − | 3719.90i | 0.504164 | − | 0.504164i | −0.408565 | − | 0.912729i | \(-0.633971\pi\) |
0.912729 | + | 0.408565i | \(0.133971\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7238.74 | − | 2949.81i | 0.973364 | − | 0.396649i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9336.03 | 1.24556 | 0.622779 | − | 0.782398i | \(-0.286004\pi\) | ||||
0.622779 | + | 0.782398i | \(0.286004\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12582.9 | −1.66567 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −97.0015 | + | 8447.48i | −0.0127412 | + | 1.10959i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5797.69 | − | 5797.69i | 0.755667 | − | 0.755667i | −0.219864 | − | 0.975531i | \(-0.570561\pi\) |
0.975531 | + | 0.219864i | \(0.0705613\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2231.59 | −0.288635 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10261.2 | + | 4319.52i | 1.31707 | + | 0.554430i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2693.58 | + | 2693.58i | 0.343110 | + | 0.343110i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 584.046 | − | 584.046i | 0.0738348 | − | 0.0738348i | −0.669225 | − | 0.743060i | \(-0.733374\pi\) |
0.743060 | + | 0.669225i | \(0.233374\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −747.007 | + | 1774.55i | −0.0937271 | + | 0.222653i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1656.54i | − | 0.206293i | −0.994666 | − | 0.103147i | \(-0.967109\pi\) | ||
0.994666 | − | 0.103147i | \(-0.0328911\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 148.921 | + | 148.921i | 0.0184076 | + | 0.0184076i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4486.97 | + | 4697.94i | 0.550517 | + | 0.576401i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3413.43i | 0.415718i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2543.09i | 0.307451i | 0.988114 | + | 0.153726i | \(0.0491272\pi\) | ||||
−0.988114 | + | 0.153726i | \(0.950873\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4828.41 | − | 11848.8i | −0.579484 | − | 1.42204i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10990.4 | − | 10990.4i | −1.30945 | − | 1.30945i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 3090.62i | − | 0.365572i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5297.21 | − | 2229.89i | −0.622076 | − | 0.261866i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3614.52 | + | 3614.52i | −0.421434 | + | 0.421434i | −0.885697 | − | 0.464263i | \(-0.846319\pi\) |
0.464263 | + | 0.885697i | \(0.346319\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10063.8 | − | 10063.8i | −1.16504 | − | 1.16504i | −0.983357 | − | 0.181683i | \(-0.941845\pi\) |
−0.181683 | − | 0.983357i | \(-0.558155\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7358.71 | + | 7191.63i | −0.845845 | + | 0.826640i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1904.27 | −0.217343 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 539.036 | − | 539.036i | 0.0610908 | − | 0.0610908i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7508.68 | + | 18426.1i | 0.845041 | + | 2.07370i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3495.35 | 0.390639 | 0.195319 | − | 0.980740i | \(-0.437426\pi\) | ||||
0.195319 | + | 0.980740i | \(0.437426\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16071.3 | 1.78369 | 0.891843 | − | 0.452345i | \(-0.149413\pi\) | ||||
0.891843 | + | 0.452345i | \(0.149413\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2601.44 | + | 6383.84i | 0.286734 | + | 0.703636i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −567.308 | + | 567.308i | −0.0621007 | + | 0.0621007i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2550.46 | 0.277282 | 0.138641 | − | 0.990343i | \(-0.455727\pi\) | ||||
0.138641 | + | 0.990343i | \(0.455727\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5131.57 | + | 5015.06i | −0.554106 | + | 0.541525i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6114.74 | + | 6114.74i | 0.655801 | + | 0.655801i | 0.954384 | − | 0.298582i | \(-0.0965138\pi\) |
−0.298582 | + | 0.954384i | \(0.596514\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1190.93 | − | 1190.93i | 0.126866 | − | 0.126866i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17152.5 | − | 7220.44i | −1.81495 | − | 0.764016i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7434.00i | 0.781364i | 0.920526 | + | 0.390682i | \(0.127761\pi\) | ||||
−0.920526 | + | 0.390682i | \(0.872239\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6170.62 | − | 6170.62i | −0.644265 | − | 0.644265i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1120.97 | + | 2750.84i | 0.116265 | + | 0.285310i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 14711.7i | − | 1.51581i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1301.43i | − | 0.133213i | −0.997779 | − | 0.0666063i | \(-0.978783\pi\) | ||
0.997779 | − | 0.0666063i | \(-0.0212172\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2335.65 | + | 5375.01i | −0.237514 | + | 0.546589i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11243.0 | − | 11243.0i | −1.13587 | − | 1.13587i | −0.989183 | − | 0.146689i | \(-0.953138\pi\) |
−0.146689 | − | 0.989183i | \(-0.546862\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7824.20i | 0.785359i | 0.919675 | + | 0.392679i | \(0.128452\pi\) | ||||
−0.919675 | + | 0.392679i | \(0.871548\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −56.5474 | + | 134.331i | −0.00563941 | + | 0.0133967i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7493.61 | − | 7493.61i | 0.742533 | − | 0.742533i | −0.230532 | − | 0.973065i | \(-0.574047\pi\) |
0.973065 | + | 0.230532i | \(0.0740465\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14118.2 | + | 14118.2i | 1.39001 | + | 1.39001i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11276.4 | − | 4746.88i | −1.10317 | − | 0.464384i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17906.3 | −1.74066 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −484.099 | + | 484.099i | −0.0467621 | + | 0.0467621i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 128.920 | − | 11227.1i | 0.0123749 | − | 1.07768i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13051.7 | −1.24499 | −0.622493 | − | 0.782626i | \(-0.713880\pi\) | ||||
−0.622493 | + | 0.782626i | \(0.713880\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3990.91 | −0.378316 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6342.53 | + | 2584.60i | −0.597505 | + | 0.243485i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9290.98 | + | 9290.98i | −0.869859 | + | 0.869859i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7486.49 | 0.696602 | 0.348301 | − | 0.937383i | \(-0.386759\pi\) | ||||
0.348301 | + | 0.937383i | \(0.386759\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5397.62 | − | 12822.3i | 0.499159 | − | 1.18577i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6345.55 | − | 6345.55i | −0.583239 | − | 0.583239i | 0.352553 | − | 0.935792i | \(-0.385314\pi\) |
−0.935792 | + | 0.352553i | \(0.885314\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4397.35 | + | 4397.35i | −0.401717 | + | 0.401717i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9847.82 | + | 9624.23i | −0.894196 | + | 0.873893i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 15109.8i | − | 1.36372i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7412.65 | + | 7412.65i | 0.665001 | + | 0.665001i | 0.956555 | − | 0.291553i | \(-0.0941721\pi\) |
−0.291553 | + | 0.956555i | \(0.594172\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11748.0 | − | 4787.34i | 1.04763 | − | 0.426911i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 3879.66i | − | 0.343908i | −0.985105 | − | 0.171954i | \(-0.944992\pi\) | ||
0.985105 | − | 0.171954i | \(-0.0550080\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 2812.10i | − | 0.247796i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10971.5 | + | 4470.93i | −0.961071 | + | 0.391639i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4843.90 | − | 4843.90i | −0.421811 | − | 0.421811i | 0.464016 | − | 0.885827i | \(-0.346408\pi\) |
−0.885827 | + | 0.464016i | \(0.846408\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8178.48i | 0.708013i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 772.657 | + | 1960.18i | 0.0664983 | + | 0.168702i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1373.15 | + | 1373.15i | −0.117492 | + | 0.117492i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15421.3 | − | 15421.3i | −1.31186 | − | 1.31186i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2440.99 | − | 5798.69i | 0.206450 | − | 0.490432i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1803.41 | −0.151649 | −0.0758244 | − | 0.997121i | \(-0.524159\pi\) | ||||
−0.0758244 | + | 0.997121i | \(0.524159\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15074.6 | + | 15074.6i | −1.26036 | + | 1.26036i | −0.309440 | + | 0.950919i | \(0.600141\pi\) |
−0.950919 | + | 0.309440i | \(0.899859\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5412.25 | + | 2205.51i | −0.449924 | + | 0.183345i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −131.482 | −0.0108680 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9313.07 | 0.765437 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17007.7 | − | 195.297i | −1.38996 | − | 0.0159608i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7214.57 | − | 7214.57i | 0.586300 | − | 0.586300i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4227.02 | 0.341589 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18332.0 | + | 7716.96i | 1.47315 | + | 0.620133i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10754.0 | − | 10754.0i | −0.859386 | − | 0.859386i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13914.7 | + | 13914.7i | −1.10580 | + | 1.10580i | −0.112106 | + | 0.993696i | \(0.535760\pi\) |
−0.993696 | + | 0.112106i | \(0.964240\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 444.335 | − | 1055.54i | 0.0351165 | − | 0.0834208i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 13014.8i | − | 1.02292i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2457.00 | − | 2457.00i | −0.192054 | − | 0.192054i | 0.604529 | − | 0.796583i | \(-0.293361\pi\) |
−0.796583 | + | 0.604529i | \(0.793361\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.57855 | − | 834.158i | 0.000744631 | − | 0.0648470i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2235.76i | 0.172862i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10546.7i | 0.811015i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1042.26 | − | 2557.67i | −0.0797143 | − | 0.195616i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13996.0 | + | 13996.0i | 1.06468 | + | 1.06468i | 0.997758 | + | 0.0669265i | \(0.0213193\pi\) |
0.0669265 | + | 0.997758i | \(0.478681\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 20935.7i | − | 1.58406i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11448.9 | − | 4819.48i | −0.861627 | − | 0.362707i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10933.7 | + | 10933.7i | −0.818474 | + | 0.818474i | −0.985887 | − | 0.167413i | \(-0.946459\pi\) |
0.167413 | + | 0.985887i | \(0.446459\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6365.84 | − | 6365.84i | −0.474005 | − | 0.474005i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −413.020 | + | 17981.8i | −0.0305912 | + | 1.33186i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4515.04 | −0.332654 | −0.166327 | − | 0.986071i | \(-0.553191\pi\) | ||||
−0.166327 | + | 0.986071i | \(0.553191\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6425.75 | − | 6425.75i | 0.470945 | − | 0.470945i | −0.431276 | − | 0.902220i | \(-0.641936\pi\) |
0.902220 | + | 0.431276i | \(0.141936\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2339.88 | + | 5741.98i | 0.170593 | + | 0.418629i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2435.33 | −0.176627 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 962.109 | 0.0694161 | 0.0347081 | − | 0.999397i | \(-0.488950\pi\) | ||||
0.0347081 | + | 0.999397i | \(0.488950\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9899.54 | + | 24293.2i | 0.710554 | + | 1.74368i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6050.66 | − | 6050.66i | 0.432054 | − | 0.432054i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23798.4 | 1.69062 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11252.5 | − | 11513.9i | −0.795269 | − | 0.813745i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3139.23 | + | 3139.23i | 0.220732 | + | 0.220732i | 0.808807 | − | 0.588074i | \(-0.200114\pi\) |
−0.588074 | + | 0.808807i | \(0.700114\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.4250 | + | 33.4250i | −0.00233829 | + | 0.00233829i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3686.09 | + | 1551.68i | 0.256557 | + | 0.107999i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 28278.3i | − | 1.95827i | −0.203219 | − | 0.979133i | \(-0.565140\pi\) | ||
0.203219 | − | 0.979133i | \(-0.434860\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6494.47 | + | 6494.47i | 0.447475 | + | 0.447475i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1194.19 | + | 2930.50i | 0.0818675 | + | 0.200900i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10012.2i | 0.682950i | 0.939891 | + | 0.341475i | \(0.110927\pi\) | ||||
−0.939891 | + | 0.341475i | \(0.889073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10154.9i | 0.689229i | 0.938744 | + | 0.344614i | \(0.111990\pi\) | ||||
−0.938744 | + | 0.344614i | \(0.888010\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21847.9 | + | 250.877i | 1.47548 | + | 0.0169428i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12250.6 | − | 12250.6i | −0.823238 | − | 0.823238i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25322.5i | 1.69326i | 0.532183 | + | 0.846629i | \(0.321372\pi\) | ||||
−0.532183 | + | 0.846629i | \(0.678628\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7405.00 | + | 17590.9i | −0.492719 | + | 1.17048i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18030.3 | − | 18030.3i | 1.19383 | − | 1.19383i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13323.5 | − | 13323.5i | −0.877863 | − | 0.877863i | 0.115451 | − | 0.993313i | \(-0.463169\pi\) |
−0.993313 | + | 0.115451i | \(0.963169\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6507.77 | + | 2739.49i | 0.426697 | + | 0.179621i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2727.73 | 0.177981 | 0.0889906 | − | 0.996032i | \(-0.471636\pi\) | ||||
0.0889906 | + | 0.996032i | \(0.471636\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9506.19 | + | 9506.19i | −0.617263 | + | 0.617263i | −0.944829 | − | 0.327565i | \(-0.893772\pi\) |
0.327565 | + | 0.944829i | \(0.393772\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2987.01 | + | 6873.98i | −0.193019 | + | 0.444192i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4663.08 | 0.299876 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7848.55 | 0.502307 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4135.70 | + | 1685.31i | −0.263419 | + | 0.107344i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1761.79 | − | 1761.79i | 0.111681 | − | 0.111681i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6939.01 | −0.437778 | −0.218889 | − | 0.975750i | \(-0.570243\pi\) | ||||
−0.218889 | + | 0.975750i | \(0.570243\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1162.67 | + | 2761.98i | −0.0730049 | + | 0.173426i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9479.23 | − | 9479.23i | −0.592397 | − | 0.592397i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12573.4 | − | 12573.4i | 0.782067 | − | 0.782067i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11557.0 | − | 11825.5i | −0.715472 | − | 0.732094i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 25374.4i | − | 1.56354i | −0.623567 | − | 0.781770i | \(-0.714317\pi\) | ||
0.623567 | − | 0.781770i | \(-0.285683\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17483.4 | − | 17483.4i | −1.07228 | − | 1.07228i | −0.997175 | − | 0.0751092i | \(-0.976069\pi\) |
−0.0751092 | − | 0.997175i | \(-0.523931\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13417.2 | − | 5467.54i | 0.819070 | − | 0.333774i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 23409.6i | − | 1.42245i | −0.702964 | − | 0.711225i | \(-0.748141\pi\) | ||
0.702964 | − | 0.711225i | \(-0.251859\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 36051.6i | − | 2.18050i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −373.692 | + | 152.281i | −0.0224979 | + | 0.00916798i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9012.83 | − | 9012.83i | −0.540122 | − | 0.540122i | 0.383443 | − | 0.923565i | \(-0.374738\pi\) |
−0.923565 | + | 0.383443i | \(0.874738\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 19093.7i | − | 1.13901i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6255.44 | + | 6400.76i | 0.371458 | + | 0.380088i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −358.576 | + | 358.576i | −0.0211960 | + | 0.0211960i | −0.717625 | − | 0.696429i | \(-0.754771\pi\) |
0.696429 | + | 0.717625i | \(0.254771\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14598.1 | + | 14598.1i | 0.859004 | + | 0.859004i | 0.991221 | − | 0.132217i | \(-0.0422095\pi\) |
−0.132217 | + | 0.991221i | \(0.542210\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5634.84 | − | 13385.8i | 0.330074 | − | 0.784106i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3302.01 | 0.192551 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5623.67 | + | 5623.67i | −0.326461 | + | 0.326461i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14230.5 | − | 5798.97i | 0.822395 | − | 0.335129i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1768.19 | 0.101729 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26625.5 | −1.52502 | −0.762509 | − | 0.646978i | \(-0.776033\pi\) | ||||
−0.762509 | + | 0.646978i | \(0.776033\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2548.90 | + | 5865.75i | −0.145344 | + | 0.334478i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5301.22 | − | 5301.22i | 0.300949 | − | 0.300949i | −0.540436 | − | 0.841385i | \(-0.681741\pi\) |
0.841385 | + | 0.540436i | \(0.181741\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36378.8 | −2.05610 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1726.28 | − | 726.688i | −0.0971384 | − | 0.0408910i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4314.17 | + | 4314.17i | 0.241694 | + | 0.241694i | 0.817551 | − | 0.575857i | \(-0.195331\pi\) |
−0.575857 | + | 0.817551i | \(0.695331\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15516.1 | + | 15516.1i | −0.865461 | + | 0.865461i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −997.129 | + | 2368.73i | −0.0553753 | + | 0.131547i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27824.7i | 1.53851i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8509.21 | − | 8509.21i | −0.468460 | − | 0.468460i | 0.432955 | − | 0.901415i | \(-0.357471\pi\) |
−0.901415 | + | 0.432955i | \(0.857471\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −38121.4 | − | 437.744i | −2.08963 | − | 0.0239950i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9856.85i | 0.537974i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6369.75i | 0.346157i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3665.72 | + | 8995.56i | 0.198355 | + | 0.486757i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2086.28 | − | 2086.28i | −0.112408 | − | 0.112408i | 0.648666 | − | 0.761073i | \(-0.275327\pi\) |
−0.761073 | + | 0.648666i | \(0.775327\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 895.754i | − | 0.0480569i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16263.9 | + | 6846.40i | 0.868845 | + | 0.365745i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5505.39 | − | 5505.39i | 0.292859 | − | 0.292859i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19902.7 | + | 19902.7i | 1.05425 | + | 1.05425i | 0.998442 | + | 0.0558039i | \(0.0177722\pi\) |
0.0558039 | + | 0.998442i | \(0.482228\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8066.81 | + | 8254.22i | 0.425498 | + | 0.435383i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −168.149 | −0.00883203 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24129.2 | − | 24129.2i | 1.26207 | − | 1.26207i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4158.33 | − | 10204.4i | −0.216591 | − | 0.531507i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6725.66 | −0.348852 | −0.174426 | − | 0.984670i | \(-0.555807\pi\) | ||||
−0.174426 | + | 0.984670i | \(0.555807\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5376.57 | −0.277717 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6071.42 | − | 14899.1i | −0.312308 | − | 0.766393i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4798.83 | + | 4798.83i | −0.245826 | + | 0.245826i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14601.8 | −0.744911 | −0.372456 | − | 0.928050i | \(-0.621484\pi\) | ||||
−0.372456 | + | 0.928050i | \(0.621484\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13430.4 | + | 14389.1i | 0.682334 | + | 0.731040i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9242.08 | + | 9242.08i | 0.467621 | + | 0.467621i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16119.5 | − | 16119.5i | 0.812259 | − | 0.812259i | −0.172713 | − | 0.984972i | \(-0.555253\pi\) |
0.984972 | + | 0.172713i | \(0.0552533\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11341.6 | + | 4774.32i | 0.569173 | + | 0.239597i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 46311.5i | 2.31466i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26403.6 | + | 26403.6i | 1.31431 | + | 1.31431i | 0.918208 | + | 0.396099i | \(0.129636\pi\) |
0.396099 | + | 0.918208i | \(0.370364\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1970.43 | − | 4835.38i | −0.0976864 | − | 0.239719i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24491.2i | 1.20928i | 0.796499 | + | 0.604640i | \(0.206683\pi\) | ||||
−0.796499 | + | 0.604640i | \(0.793317\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31916.7i | 1.56958i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 107.519 | − | 9363.40i | 0.00526628 | − | 0.458620i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8275.45 | + | 8275.45i | 0.403709 | + | 0.403709i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15477.7i | 0.752050i | 0.926609 | + | 0.376025i | \(0.122709\pi\) | ||||
−0.926609 | + | 0.376025i | \(0.877291\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6825.38 | − | 16214.0i | 0.330320 | − | 0.784690i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3602.26 | − | 3602.26i | 0.173642 | − | 0.173642i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11191.6 | + | 11191.6i | 0.537340 | + | 0.537340i | 0.922747 | − | 0.385407i | \(-0.125939\pi\) |
−0.385407 | + | 0.922747i | \(0.625939\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14641.7 | − | 6163.52i | −0.700212 | − | 0.294758i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10016.9 | 0.477153 | 0.238576 | − | 0.971124i | \(-0.423319\pi\) | ||||
0.238576 | + | 0.971124i | \(0.423319\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25479.7 | − | 25479.7i | 1.20895 | − | 1.20895i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10050.2 | + | 115.405i | 0.474988 | + | 0.00545424i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 42150.8 | 1.98432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1463.91 | 0.0686475 | 0.0343238 | − | 0.999411i | \(-0.489072\pi\) | ||||
0.0343238 | + | 0.999411i | \(0.489072\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17238.9 | − | 7024.89i | 0.805243 | − | 0.328139i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26695.6 | + | 26695.6i | −1.24214 | + | 1.24214i | −0.283030 | + | 0.959111i | \(0.591340\pi\) |
−0.959111 | + | 0.283030i | \(0.908660\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −143.486 | −0.00665055 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2966.80 | − | 7047.76i | 0.136980 | − | 0.325402i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1619.30 | + | 1619.30i | 0.0744768 | + | 0.0744768i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24782.2 | − | 24782.2i | 1.13544 | − | 1.13544i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7659.27 | + | 19431.1i | 0.349579 | + | 0.886860i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20982.8i | 0.954022i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14529.3 | + | 14529.3i | 0.658087 | + | 0.658087i | 0.954927 | − | 0.296840i | \(-0.0959328\pi\) |
−0.296840 | + | 0.954927i | \(0.595933\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10568.2 | − | 4306.58i | 0.476855 | − | 0.194320i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 24925.5i | − | 1.12041i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2067.33i | 0.0925763i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −17832.1 | + | 7266.64i | −0.795521 | + | 0.324177i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18417.2 | + | 18417.2i | 0.818532 | + | 0.818532i | 0.985895 | − | 0.167363i | \(-0.0535253\pi\) |
−0.167363 | + | 0.985895i | \(0.553525\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15919.0i | 0.704848i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3649.49 | − | 3566.63i | 0.160984 | − | 0.157329i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13413.8 | + | 13413.8i | −0.589494 | + | 0.589494i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8305.63 | + | 8305.63i | 0.363646 | + | 0.363646i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 182.971 | − | 434.657i | 0.00798128 | − | 0.0189599i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14088.2 | −0.612253 | −0.306127 | − | 0.951991i | \(-0.599033\pi\) | ||||
−0.306127 | + | 0.951991i | \(0.599033\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16384.8 | + | 16384.8i | −0.709429 | + | 0.709429i | −0.966415 | − | 0.256986i | \(-0.917271\pi\) |
0.256986 | + | 0.966415i | \(0.417271\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17454.9 | + | 7112.92i | −0.752976 | + | 0.306840i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23859.2 | −1.02546 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4698.99 | 0.201220 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 511.802 | − | 44570.8i | 0.0218361 | − | 1.90162i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1002.06 | + | 1002.06i | −0.0425968 | + | 0.0425968i | −0.728084 | − | 0.685488i | \(-0.759589\pi\) |
0.685488 | + | 0.728084i | \(0.259589\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36539.2 | 1.54760 | 0.773802 | − | 0.633428i | \(-0.218353\pi\) | ||||
0.773802 | + | 0.633428i | \(0.218353\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12494.2 | − | 5259.50i | −0.527262 | − | 0.221954i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1314.92 | − | 1314.92i | −0.0552892 | − | 0.0552892i | 0.678922 | − | 0.734211i | \(-0.262448\pi\) |
−0.734211 | + | 0.678922i | \(0.762448\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18101.1 | + | 18101.1i | −0.758357 | + | 0.758357i | −0.976023 | − | 0.217667i | \(-0.930155\pi\) |
0.217667 | + | 0.976023i | \(0.430155\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9910.59 | − | 23543.1i | 0.413712 | − | 0.982791i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11101.1i | 0.461740i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15384.2 | − | 15384.2i | −0.637594 | − | 0.637594i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −175.990 | + | 405.005i | −0.00726777 | + | 0.0167252i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11658.5i | 0.479734i | 0.970806 | + | 0.239867i | \(0.0771038\pi\) | ||||
−0.970806 | + | 0.239867i | \(0.922896\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 2226.09i | − | 0.0912745i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10976.8 | − | 26936.8i | −0.448473 | − | 1.10054i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14367.4 | + | 14367.4i | 0.584915 | + | 0.584915i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 47967.3i | − | 1.94590i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1603.81 | − | 675.133i | −0.0648322 | − | 0.0272915i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2253.11 | − | 2253.11i | 0.0907587 | − | 0.0907587i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8293.73 | − | 8293.73i | −0.332910 | − | 0.332910i | 0.520781 | − | 0.853690i | \(-0.325641\pi\) |
−0.853690 | + | 0.520781i | \(0.825641\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2584.27 | − | 2525.60i | 0.103369 | − | 0.101022i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5209.55 | 0.207649 | 0.103824 | − | 0.994596i | \(-0.466892\pi\) | ||||
0.103824 | + | 0.994596i | \(0.466892\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21529.9 | + | 21529.9i | −0.855168 | + | 0.855168i | −0.990764 | − | 0.135596i | \(-0.956705\pi\) |
0.135596 | + | 0.990764i | \(0.456705\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7377.37 | + | 18103.8i | 0.292009 | + | 0.716581i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31954.7 | 1.26043 | 0.630215 | − | 0.776420i | \(-0.282967\pi\) | ||||
0.630215 | + | 0.776420i | \(0.282967\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10790.0 | −0.424128 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6212.17 | − | 15244.5i | −0.243341 | − | 0.597150i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17298.0 | + | 17298.0i | −0.675254 | + | 0.675254i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −54146.5 | −2.10641 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −28471.4 | + | 27824.9i | −1.10379 | + | 1.07873i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26521.4 | + | 26521.4i | 1.02467 | + | 1.02467i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11937.5 | − | 11937.5i | 0.459636 | − | 0.459636i | −0.438900 | − | 0.898536i | \(-0.644632\pi\) |
0.898536 | + | 0.438900i | \(0.144632\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20840.8 | + | 8773.04i | 0.799706 | + | 0.336641i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30514.2i | 1.16691i | 0.812144 | + | 0.583457i | \(0.198300\pi\) | ||||
−0.812144 | + | 0.583457i | \(0.801700\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3179.05 | + | 3179.05i | 0.121159 | + | 0.121159i | 0.765087 | − | 0.643927i | \(-0.222696\pi\) |
−0.643927 | + | 0.765087i | \(0.722696\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11008.0 | + | 27013.3i | 0.418114 | + | 1.02604i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 24947.8i | − | 0.944380i | −0.881497 | − | 0.472190i | \(-0.843464\pi\) | ||
0.881497 | − | 0.472190i | \(-0.156536\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 37115.9i | − | 1.40026i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −30170.0 | + | 28815.2i | −1.13438 | + | 1.08344i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4046.88 | + | 4046.88i | 0.151650 | + | 0.151650i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 34111.5i | − | 1.27399i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7206.27 | − | 17118.8i | 0.268239 | − | 0.637214i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −331.338 | + | 331.338i | −0.0122923 | + | 0.0122923i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12283.2 | − | 12283.2i | −0.454176 | − | 0.454176i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 36971.5 | + | 15563.4i | 1.36250 | + | 0.573551i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1964.11 | −0.0721427 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19465.8 | − | 19465.8i | 0.712626 | − | 0.712626i | −0.254458 | − | 0.967084i | \(-0.581897\pi\) |
0.967084 | + | 0.254458i | \(0.0818970\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 97.8296 | − | 8519.59i | 0.00356964 | − | 0.310866i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4256.52 | −0.154802 | −0.0774010 | − | 0.997000i | \(-0.524662\pi\) | ||||
−0.0774010 | + | 0.997000i | \(0.524662\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19847.8 | 0.719460 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1324.90 | + | 539.900i | −0.0478686 | + | 0.0195066i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 37380.7 | − | 37380.7i | 1.34615 | − | 1.34615i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37455.2 | 1.34443 | 0.672216 | − | 0.740355i | \(-0.265343\pi\) | ||||
0.672216 | + | 0.740355i | \(0.265343\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4989.16 | − | 11852.0i | 0.178500 | − | 0.424034i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28974.8 | + | 28974.8i | 1.03328 | + | 1.03328i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1922.64 | − | 1922.64i | 0.0683416 | − | 0.0683416i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4207.89 | + | 4112.35i | −0.149089 | + | 0.145704i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 51223.8i | − | 1.80904i | −0.426429 | − | 0.904521i | \(-0.640229\pi\) | ||
0.426429 | − | 0.904521i | \(-0.359771\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2822.08 | + | 2822.08i | 0.0993448 | + | 0.0993448i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −34037.3 | + | 13870.3i | −1.19435 | + | 0.486703i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21303.7i | 0.745138i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 30708.1i | − | 1.07064i | −0.844650 | − | 0.535320i | \(-0.820191\pi\) | ||
0.844650 | − | 0.535320i | \(-0.179809\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 43532.4 | − | 17739.6i | 1.51292 | − | 0.616518i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −817.247 | − | 817.247i | −0.0283119 | − | 0.0283119i | 0.692809 | − | 0.721121i | \(-0.256373\pi\) |
−0.721121 | + | 0.692809i | \(0.756373\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8146.12i | 0.281309i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 28697.9 | − | 11312.0i | 0.987877 | − | 0.389397i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18142.1 | + | 18142.1i | −0.622535 | + | 0.622535i | −0.946179 | − | 0.323644i | \(-0.895092\pi\) |
0.323644 | + | 0.946179i | \(0.395092\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15683.2 | − | 15683.2i | −0.536457 | − | 0.536457i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12765.4 | − | 30324.8i | 0.435274 | − | 1.03401i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8325.23 | 0.282981 | 0.141490 | − | 0.989940i | \(-0.454811\pi\) | ||||
0.141490 | + | 0.989940i | \(0.454811\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7519.21 | − | 7519.21i | 0.254781 | − | 0.254781i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −40996.8 | + | 16706.3i | −1.38478 | + | 0.564304i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −60753.4 | −2.04570 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29781.1 | 0.999667 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12806.3 | + | 147.053i | 0.428532 | + | 0.00492078i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31812.2 | − | 31812.2i | 1.06122 | − | 1.06122i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8911.71 | −0.296361 | −0.148181 | − | 0.988960i | \(-0.547342\pi\) | ||||
−0.148181 | + | 0.988960i | \(0.547342\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3004.42 | + | 1264.73i | 0.0996037 | + | 0.0419288i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24556.5 | − | 24556.5i | −0.811593 | − | 0.811593i | 0.173280 | − | 0.984873i | \(-0.444563\pi\) |
−0.984873 | + | 0.173280i | \(0.944563\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19297.2 | + | 19297.2i | −0.635808 | + | 0.635808i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6149.30 | − | 14607.9i | 0.201985 | − | 0.479824i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 501.936i | 0.0164364i | 0.999966 | + | 0.00821819i | \(0.00261596\pi\) | ||||
−0.999966 | + | 0.00821819i | \(0.997384\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7648.10 | + | 7648.10i | 0.249678 | + | 0.249678i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 452.769 | − | 39429.9i | 0.0147358 | − | 1.28328i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52008.6i | 1.68751i | 0.536732 | + | 0.843753i | \(0.319659\pi\) | ||||
−0.536732 | + | 0.843753i | \(0.680341\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 6858.94i | − | 0.221872i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18437.2 | + | 45244.3i | 0.594592 | + | 1.45911i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11819.5 | + | 11819.5i | 0.380018 | + | 0.380018i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27605.3i | 0.884876i | 0.896799 | + | 0.442438i | \(0.145886\pi\) | ||||
−0.896799 | + | 0.442438i | \(0.854114\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7184.91 | − | 3024.53i | −0.229613 | − | 0.0966571i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3837.54 | − | 3837.54i | 0.122269 | − | 0.122269i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3224.20 | + | 3224.20i | 0.102419 | + | 0.102419i | 0.756459 | − | 0.654041i | \(-0.226927\pi\) |
−0.654041 | + | 0.756459i | \(0.726927\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3068.67 | − | 7785.03i | −0.0971856 | − | 0.246554i |
(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 | 384.4.k.a.287.9 | 44 | ||
3.2 | odd | 2 | inner | 384.4.k.a.287.3 | 44 | ||
4.3 | odd | 2 | 384.4.k.b.287.14 | 44 | |||
8.3 | odd | 2 | 48.4.k.a.11.20 | yes | 44 | ||
8.5 | even | 2 | 192.4.k.a.143.14 | 44 | |||
12.11 | even | 2 | 384.4.k.b.287.20 | 44 | |||
16.3 | odd | 4 | inner | 384.4.k.a.95.3 | 44 | ||
16.5 | even | 4 | 48.4.k.a.35.3 | yes | 44 | ||
16.11 | odd | 4 | 192.4.k.a.47.20 | 44 | |||
16.13 | even | 4 | 384.4.k.b.95.20 | 44 | |||
24.5 | odd | 2 | 192.4.k.a.143.20 | 44 | |||
24.11 | even | 2 | 48.4.k.a.11.3 | ✓ | 44 | ||
48.5 | odd | 4 | 48.4.k.a.35.20 | yes | 44 | ||
48.11 | even | 4 | 192.4.k.a.47.14 | 44 | |||
48.29 | odd | 4 | 384.4.k.b.95.14 | 44 | |||
48.35 | even | 4 | inner | 384.4.k.a.95.9 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.4.k.a.11.3 | ✓ | 44 | 24.11 | even | 2 | ||
48.4.k.a.11.20 | yes | 44 | 8.3 | odd | 2 | ||
48.4.k.a.35.3 | yes | 44 | 16.5 | even | 4 | ||
48.4.k.a.35.20 | yes | 44 | 48.5 | odd | 4 | ||
192.4.k.a.47.14 | 44 | 48.11 | even | 4 | |||
192.4.k.a.47.20 | 44 | 16.11 | odd | 4 | |||
192.4.k.a.143.14 | 44 | 8.5 | even | 2 | |||
192.4.k.a.143.20 | 44 | 24.5 | odd | 2 | |||
384.4.k.a.95.3 | 44 | 16.3 | odd | 4 | inner | ||
384.4.k.a.95.9 | 44 | 48.35 | even | 4 | inner | ||
384.4.k.a.287.3 | 44 | 3.2 | odd | 2 | inner | ||
384.4.k.a.287.9 | 44 | 1.1 | even | 1 | trivial | ||
384.4.k.b.95.14 | 44 | 48.29 | odd | 4 | |||
384.4.k.b.95.20 | 44 | 16.13 | even | 4 | |||
384.4.k.b.287.14 | 44 | 4.3 | odd | 2 | |||
384.4.k.b.287.20 | 44 | 12.11 | even | 2 |