Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,6,Mod(191,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.191");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.f (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: | \(61.5873868082\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 5192x^{16} + 8441320x^{12} + 4098006217x^{8} + 8949568544x^{4} + 8386816 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{87}\cdot 3^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.8 | ||
Root | \(4.77687 - 4.77687i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.191 |
Dual form | 384.6.f.e.191.7 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −6.91183 | + | 13.9723i | −0.443394 | + | 0.896327i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −56.7417 | −1.01503 | −0.507513 | − | 0.861644i | \(-0.669435\pi\) | ||||
−0.507513 | + | 0.861644i | \(0.669435\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 130.269i | − | 1.00484i | −0.864624 | − | 0.502420i | \(-0.832443\pi\) | ||
0.864624 | − | 0.502420i | \(-0.167557\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −147.453 | − | 193.149i | −0.606803 | − | 0.794852i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 484.591i | 1.20752i | 0.797167 | + | 0.603758i | \(0.206331\pi\) | ||||
−0.797167 | + | 0.603758i | \(0.793669\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 555.929i | − | 0.912348i | −0.889890 | − | 0.456174i | \(-0.849219\pi\) | ||
0.889890 | − | 0.456174i | \(-0.150781\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 392.189 | − | 792.815i | 0.450057 | − | 0.909795i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1110.46i | − | 0.931928i | −0.884804 | − | 0.465964i | \(-0.845708\pi\) | ||
0.884804 | − | 0.465964i | \(-0.154292\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −741.084 | −0.470959 | −0.235480 | − | 0.971879i | \(-0.575666\pi\) | ||||
−0.235480 | + | 0.971879i | \(0.575666\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1820.17 | + | 900.400i | 0.900665 | + | 0.445540i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −459.270 | −0.181029 | −0.0905145 | − | 0.995895i | \(-0.528851\pi\) | ||||
−0.0905145 | + | 0.995895i | \(0.528851\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 94.6178 | 0.0302777 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3717.92 | − | 725.251i | 0.981500 | − | 0.191460i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3061.20 | 0.675923 | 0.337962 | − | 0.941160i | \(-0.390263\pi\) | ||||
0.337962 | + | 0.941160i | \(0.390263\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5980.71i | − | 1.11776i | −0.829249 | − | 0.558880i | \(-0.811231\pi\) | ||
0.829249 | − | 0.558880i | \(-0.188769\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6770.87 | − | 3349.41i | −1.08233 | − | 0.535406i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7391.70i | 1.01994i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3466.31i | − | 0.416258i | −0.978101 | − | 0.208129i | \(-0.933263\pi\) | ||
0.978101 | − | 0.208129i | \(-0.0667374\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7767.63 | + | 3842.49i | 0.817762 | + | 0.404530i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14979.6i | 1.39168i | 0.718195 | + | 0.695842i | \(0.244969\pi\) | ||||
−0.718195 | + | 0.695842i | \(0.755031\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16818.5 | 1.38713 | 0.693563 | − | 0.720396i | \(-0.256040\pi\) | ||||
0.693563 | + | 0.720396i | \(0.256040\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8366.73 | + | 10959.6i | 0.615921 | + | 0.806796i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 19676.9 | 1.29931 | 0.649654 | − | 0.760230i | \(-0.274914\pi\) | ||||
0.649654 | + | 0.760230i | \(0.274914\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −163.085 | −0.00970341 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15515.8 | + | 7675.35i | 0.835312 | + | 0.413212i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −32218.4 | −1.57549 | −0.787743 | − | 0.616004i | \(-0.788751\pi\) | ||||
−0.787743 | + | 0.616004i | \(0.788751\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 27496.5i | − | 1.22566i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5122.25 | − | 10354.7i | 0.208821 | − | 0.422134i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 5250.05i | − | 0.196351i | −0.995169 | − | 0.0981756i | \(-0.968699\pi\) | ||
0.995169 | − | 0.0981756i | \(-0.0313007\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 53641.2i | 1.84575i | 0.385094 | + | 0.922877i | \(0.374169\pi\) | ||||
−0.385094 | + | 0.922877i | \(0.625831\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −25161.4 | + | 19208.6i | −0.798699 | + | 0.609740i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 31544.3i | 0.926057i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −66623.4 | −1.81317 | −0.906587 | − | 0.422019i | \(-0.861322\pi\) | ||||
−0.906587 | + | 0.422019i | \(0.861322\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3174.40 | − | 6417.08i | 0.0802673 | − | 0.162261i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −33198.9 | −0.781588 | −0.390794 | − | 0.920478i | \(-0.627800\pi\) | ||||
−0.390794 | + | 0.920478i | \(0.627800\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −80330.2 | −1.76430 | −0.882149 | − | 0.470970i | \(-0.843904\pi\) | ||||
−0.882149 | + | 0.470970i | \(0.843904\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −653.983 | + | 1322.03i | −0.0134250 | + | 0.0271387i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 63127.3 | 1.21336 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 19463.9i | − | 0.350883i | −0.984490 | − | 0.175442i | \(-0.943865\pi\) | ||
0.984490 | − | 0.175442i | \(-0.0561353\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −15564.2 | + | 56960.9i | −0.263581 | + | 0.964637i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 22867.0i | − | 0.364345i | −0.983267 | − | 0.182173i | \(-0.941687\pi\) | ||
0.983267 | − | 0.182173i | \(-0.0583130\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 63009.6i | 0.945931i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −21158.5 | + | 42772.2i | −0.299701 | + | 0.605848i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 33539.4i | 0.448829i | 0.974494 | + | 0.224414i | \(0.0720469\pi\) | ||||
−0.974494 | + | 0.224414i | \(0.927953\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −72420.4 | −0.916764 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 83564.6 | + | 41337.7i | 1.00188 | + | 0.495608i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 42050.4 | 0.478036 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −146327. | −1.57905 | −0.789524 | − | 0.613719i | \(-0.789673\pi\) | ||||
−0.789524 | + | 0.613719i | \(0.789673\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 93598.2 | − | 71454.4i | 0.959798 | − | 0.732725i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 113137. | 1.10357 | 0.551786 | − | 0.833986i | \(-0.313947\pi\) | ||||
0.551786 | + | 0.833986i | \(0.313947\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 159779.i | 1.48398i | 0.670411 | + | 0.741990i | \(0.266118\pi\) | ||||
−0.670411 | + | 0.741990i | \(0.733882\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −103279. | − | 51090.2i | −0.914198 | − | 0.452235i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16948.9i | 0.143114i | 0.997437 | + | 0.0715571i | \(0.0227968\pi\) | ||||
−0.997437 | + | 0.0715571i | \(0.977203\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 152539.i | 1.22974i | 0.788627 | + | 0.614872i | \(0.210792\pi\) | ||||
−0.788627 | + | 0.614872i | \(0.789208\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 48432.4 | + | 23958.5i | 0.373103 | + | 0.184566i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 145492.i | − | 1.07188i | −0.844258 | − | 0.535938i | \(-0.819958\pi\) | ||
0.844258 | − | 0.535938i | \(-0.180042\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26059.7 | 0.183749 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −107377. | + | 81973.4i | −0.725182 | + | 0.553616i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −144659. | −0.936438 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −73777.0 | −0.458097 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −209300. | − | 103537.i | −1.24740 | − | 0.617065i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 171949. | 0.984293 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 90945.7i | − | 0.500349i | −0.968201 | − | 0.250175i | \(-0.919512\pi\) | ||
0.968201 | − | 0.250175i | \(-0.0804880\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −116247. | + | 234994.i | −0.615044 | + | 1.24332i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 40671.9i | 0.207070i | 0.994626 | + | 0.103535i | \(0.0330153\pi\) | ||||
−0.994626 | + | 0.103535i | \(0.966985\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 96540.5i | 0.473239i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −210961. | + | 41152.0i | −0.996248 | + | 0.194337i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 330626.i | 1.50499i | 0.658595 | + | 0.752497i | \(0.271151\pi\) | ||||
−0.658595 | + | 0.752497i | \(0.728849\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 176648. | 0.775484 | 0.387742 | − | 0.921768i | \(-0.373255\pi\) | ||||
0.387742 | + | 0.921768i | \(0.373255\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −136004. | + | 274933.i | −0.576106 | + | 1.16460i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 269398. | 1.10168 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −173698. | −0.686079 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1127.22 | − | 2278.68i | 0.00430244 | − | 0.00869742i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 56218.4 | 0.207450 | 0.103725 | − | 0.994606i | \(-0.466924\pi\) | ||||
0.103725 | + | 0.994606i | \(0.466924\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 175958.i | − | 0.628010i | −0.949421 | − | 0.314005i | \(-0.898329\pi\) | ||
0.949421 | − | 0.314005i | \(-0.101671\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −214485. | + | 163741.i | −0.740745 | + | 0.565496i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 339355.i | 1.13456i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 78738.0i | 0.254938i | 0.991843 | + | 0.127469i | \(0.0406854\pi\) | ||||
−0.991843 | + | 0.127469i | \(0.959315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 222688. | − | 450167.i | 0.698562 | − | 1.41215i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 59828.7i | 0.181905i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 127815. | 0.376800 | 0.188400 | − | 0.982092i | \(-0.439670\pi\) | ||||
0.188400 | + | 0.982092i | \(0.439670\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 384190. | + | 190051.i | 1.09859 | + | 0.543451i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 307401. | 0.852933 | 0.426466 | − | 0.904503i | \(-0.359758\pi\) | ||||
0.426466 | + | 0.904503i | \(0.359758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 62236.2 | 0.167620 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 109275. | + | 143140.i | 0.285780 | + | 0.374343i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −283267. | −0.719582 | −0.359791 | − | 0.933033i | \(-0.617152\pi\) | ||||
−0.359791 | + | 0.933033i | \(0.617152\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 12325.8i | − | 0.0304242i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 73355.6 | + | 36287.5i | 0.175995 | + | 0.0870611i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 376390.i | 0.878023i | 0.898481 | + | 0.439012i | \(0.144671\pi\) | ||||
−0.898481 | + | 0.439012i | \(0.855329\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 698692.i | 1.58522i | 0.609730 | + | 0.792609i | \(0.291278\pi\) | ||||
−0.609730 | + | 0.792609i | \(0.708722\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −749494. | − | 370759.i | −1.65440 | − | 0.818397i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 196684.i | 0.422513i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 538120. | 1.12532 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −94477.9 | − | 484331.i | −0.192387 | − | 0.986251i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 874587. | 1.73468 | 0.867340 | − | 0.497716i | \(-0.165828\pi\) | ||||
0.867340 | + | 0.497716i | \(0.165828\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −182483. | −0.352637 | −0.176319 | − | 0.984333i | \(-0.556419\pi\) | ||||
−0.176319 | + | 0.984333i | \(0.556419\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −440748. | − | 218029.i | −0.830050 | − | 0.410609i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 288691. | 0.529991 | 0.264995 | − | 0.964250i | \(-0.414630\pi\) | ||||
0.264995 | + | 0.964250i | \(0.414630\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 961761.i | 1.72161i | 0.508935 | + | 0.860805i | \(0.330039\pi\) | ||||
−0.508935 | + | 0.860805i | \(0.669961\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 460490. | − | 930885.i | 0.803951 | − | 1.62520i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 398781.i | − | 0.679195i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 849968.i | − | 1.41260i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 67720.7 | + | 88707.6i | 0.109849 | + | 0.143891i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 359122.i | − | 0.568692i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 191585. | 0.296248 | 0.148124 | − | 0.988969i | \(-0.452677\pi\) | ||||
0.148124 | + | 0.988969i | \(0.452677\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 229465. | − | 463867.i | 0.346552 | − | 0.700558i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −954309. | −1.40797 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −779103. | −1.12317 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 555229. | − | 1.12240e6i | 0.782280 | − | 1.58139i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −617339. | −0.850243 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 449203.i | − | 0.604896i | −0.953166 | − | 0.302448i | \(-0.902196\pi\) | ||
0.953166 | − | 0.302448i | \(-0.0978038\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13951.7 | − | 18275.4i | −0.0183726 | − | 0.0240663i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 578361.i | 0.744962i | 0.928040 | + | 0.372481i | \(0.121493\pi\) | ||||
−0.928040 | + | 0.372481i | \(0.878507\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 342423.i | − | 0.431494i | −0.976449 | − | 0.215747i | \(-0.930781\pi\) | ||
0.976449 | − | 0.215747i | \(-0.0692186\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −436325. | + | 882036.i | −0.537998 | + | 1.08757i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 724022.i | − | 0.873699i | −0.899535 | − | 0.436849i | \(-0.856094\pi\) | ||
0.899535 | − | 0.436849i | \(-0.143906\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.11650e6 | −1.31883 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 271957. | + | 134531.i | 0.314506 | + | 0.155580i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.64343e6 | 1.86104 | 0.930521 | − | 0.366238i | \(-0.119355\pi\) | ||||
0.930521 | + | 0.366238i | \(0.119355\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.63037e6 | 1.80819 | 0.904095 | − | 0.427331i | \(-0.140546\pi\) | ||||
0.904095 | + | 0.427331i | \(0.140546\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −688300. | − | 611172.i | −0.747760 | − | 0.663969i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9253.73 | 0.00984921 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 411990.i | 0.429679i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 319505. | + | 158053.i | 0.326572 | + | 0.161549i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.50508e6i | 1.50791i | 0.656925 | + | 0.753956i | \(0.271857\pi\) | ||||
−0.656925 | + | 0.753956i | \(0.728143\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 222558.i | − | 0.218596i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −880392. | − | 435512.i | −0.847863 | − | 0.419420i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.20632e6i | 1.13927i | 0.821896 | + | 0.569637i | \(0.192916\pi\) | ||||
−0.821896 | + | 0.569637i | \(0.807084\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −451553. | −0.418273 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −451384. | − | 591269.i | −0.410152 | − | 0.537259i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.62597e6 | −1.44951 | −0.724757 | − | 0.689005i | \(-0.758048\pi\) | ||||
−0.724757 | + | 0.689005i | \(0.758048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.82813e6 | 1.59916 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −468625. | − | 231819.i | −0.402297 | − | 0.199008i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −137819. | −0.116126 | −0.0580630 | − | 0.998313i | \(-0.518492\pi\) | ||||
−0.0580630 | + | 0.998313i | \(0.518492\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.48417e6i | − | 1.22761i | −0.789457 | − | 0.613806i | \(-0.789638\pi\) | ||
0.789457 | − | 0.613806i | \(-0.210362\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 500558. | − | 1.01188e6i | 0.406488 | − | 0.821720i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 45850.9i | 0.0365608i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1.61429e6i | − | 1.26410i | −0.774927 | − | 0.632051i | \(-0.782214\pi\) | ||
0.774927 | − | 0.632051i | \(-0.217786\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.15517e6 | + | 881874.i | −0.888454 | + | 0.678260i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 110881.i | 0.0837704i | 0.999122 | + | 0.0418852i | \(0.0133364\pi\) | ||||
−0.999122 | + | 0.0418852i | \(0.986664\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.24585e6 | −0.924700 | −0.462350 | − | 0.886698i | \(-0.652994\pi\) | ||||
−0.462350 | + | 0.886698i | \(0.652994\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −290645. | + | 587542.i | −0.211959 | + | 0.428476i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.95138e6 | 1.39842 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 186726. | 0.131511 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.01139e6 | − | 2.04453e6i | 0.700141 | − | 1.41534i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.78388e6 | −1.89444 | −0.947222 | − | 0.320578i | \(-0.896123\pi\) | ||||
−0.947222 | + | 0.320578i | \(0.896123\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 297897.i | 0.199302i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 351450. | + | 1.80167e6i | 0.231192 | + | 1.18518i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 255321.i | 0.165162i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 2.19093e6i | − | 1.39384i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −781983. | + | 1.58079e6i | −0.489317 | + | 0.989161i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3.04369e6i | − | 1.87349i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 587991. | 0.356061 | 0.178031 | − | 0.984025i | \(-0.443027\pi\) | ||||
0.178031 | + | 0.984025i | \(0.443027\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.23249e6 | − | 1.10437e6i | −1.33013 | − | 0.657988i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.26748e6 | 0.743086 | 0.371543 | − | 0.928416i | \(-0.378829\pi\) | ||||
0.371543 | + | 0.928416i | \(0.378829\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.70854e6 | 1.56270 | 0.781348 | − | 0.624096i | \(-0.214533\pi\) | ||||
0.781348 | + | 0.624096i | \(0.214533\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.42770e6 | − | 1.08993e6i | 0.810701 | − | 0.618902i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −264831. | −0.148020 | −0.0740100 | − | 0.997257i | \(-0.523580\pi\) | ||||
−0.0740100 | + | 0.997257i | \(0.523580\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.48343e6i | 0.816188i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −236816. | − | 117148.i | −0.128277 | − | 0.0634560i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 822947.i | 0.438900i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 52600.8i | − | 0.0276238i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.13133e6 | − | 1.05432e6i | −1.10225 | − | 0.545261i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.56330e6i | − | 1.30560i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −534781. | −0.268291 | −0.134145 | − | 0.990962i | \(-0.542829\pi\) | ||||
−0.134145 | + | 0.990962i | \(0.542829\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −669514. | + | 511117.i | −0.330864 | + | 0.252586i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.78032e6 | 1.84042 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.31960e6 | 0.632946 | 0.316473 | − | 0.948602i | \(-0.397501\pi\) | ||||
0.316473 | + | 0.948602i | \(0.397501\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.03287e6 | + | 1.00562e6i | 0.960750 | + | 0.475263i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.89819e6 | 1.34971 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.16819e6i | − | 0.995090i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −180121. | + | 364116.i | −0.0814734 | + | 0.164699i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.91141e6i | 1.29801i | 0.760783 | + | 0.649006i | \(0.224815\pi\) | ||||
−0.760783 | + | 0.649006i | \(0.775185\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.06388e6i | − | 0.467550i | −0.972291 | − | 0.233775i | \(-0.924892\pi\) | ||
0.972291 | − | 0.233775i | \(-0.0751080\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −403188. | − | 2.06690e6i | −0.174679 | − | 0.895470i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.38799e6i | 1.01999i | 0.860178 | + | 0.509995i | \(0.170353\pi\) | ||||
−0.860178 | + | 0.509995i | \(0.829647\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.88376e6 | 0.793332 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 999862. | − | 2.02123e6i | 0.415212 | − | 0.839355i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.68611e6 | 1.09999 | 0.549994 | − | 0.835169i | \(-0.314630\pi\) | ||||
0.549994 | + | 0.835169i | \(0.314630\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.92689e6 | −0.778197 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 509934. | − | 1.03084e6i | 0.203118 | − | 0.410604i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.55807e6 | 1.79081 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.87189e6i | − | 1.50058i | −0.661111 | − | 0.750288i | \(-0.729915\pi\) | ||
0.661111 | − | 0.750288i | \(-0.270085\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.89330e6 | − | 2.20879e6i | 1.10618 | − | 0.844478i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.19707e6i | 1.58311i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 206921.i | 0.0770074i | 0.999258 | + | 0.0385037i | \(0.0122591\pi\) | ||||
−0.999258 | + | 0.0385037i | \(0.987741\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.18848e6 | + | 2.40253e6i | −0.436430 | + | 0.882248i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.70181e6i | − | 0.616677i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.05927e6 | 0.736404 | 0.368202 | − | 0.929746i | \(-0.379973\pi\) | ||||
0.368202 | + | 0.929746i | \(0.379973\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.27073e6 | + | 628602.i | 0.448476 | + | 0.221852i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 545734. | 0.190101 | 0.0950504 | − | 0.995472i | \(-0.469699\pi\) | ||||
0.0950504 | + | 0.995472i | \(0.469699\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.58195e6 | −1.23159 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.47994e6 | − | 3.24848e6i | −0.841712 | − | 1.10256i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.56814e6 | −1.53061 | −0.765307 | − | 0.643666i | \(-0.777413\pi\) | ||||
−0.765307 | + | 0.643666i | \(0.777413\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 510003.i | 0.168706i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −568282. | − | 281118.i | −0.185602 | − | 0.0918135i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.10442e6i | 0.356156i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.08838e6i | 0.665019i | 0.943100 | + | 0.332509i | \(0.107895\pi\) | ||||
−0.943100 | + | 0.332509i | \(0.892105\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.34890e6 | − | 667272.i | −0.424177 | − | 0.209831i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.03905e6i | 0.633237i | 0.948553 | + | 0.316619i | \(0.102548\pi\) | ||||
−0.948553 | + | 0.316619i | \(0.897452\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.32485e6 | −1.01979 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 883138. | − | 3.23206e6i | 0.267541 | − | 0.979132i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.67974e6 | 0.502638 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.09607e6 | −0.619580 | −0.309790 | − | 0.950805i | \(-0.600259\pi\) | ||||
−0.309790 | + | 0.950805i | \(0.600259\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.61962e6 | − | 2.28523e6i | −1.34897 | − | 0.667306i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −683921. | −0.197302 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.29751e6i | 0.369820i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.22096e6 | + | 2.46819e6i | −0.343845 | + | 0.695087i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 549636.i | 0.152947i | 0.997072 | + | 0.0764733i | \(0.0243660\pi\) | ||||
−0.997072 | + | 0.0764733i | \(0.975634\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.43018e6i | 1.21819i | 0.793096 | + | 0.609097i | \(0.208468\pi\) | ||||
−0.793096 | + | 0.609097i | \(0.791532\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.90142e6 | − | 3.80058e6i | −0.788424 | − | 1.03276i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 105070.i | − | 0.0282166i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.98780e6 | 1.85469 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.86203e6 | + | 3.76412e6i | −0.488477 | + | 0.987462i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.61758e6 | −1.19735 | −0.598675 | − | 0.800992i | \(-0.704306\pi\) | ||||
−0.598675 | + | 0.800992i | \(0.704306\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.59859e6 | 0.409747 | 0.204874 | − | 0.978788i | \(-0.434322\pi\) | ||||
0.204874 | + | 0.978788i | \(0.434322\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.20057e6 | − | 2.42697e6i | 0.304204 | − | 0.614951i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 340358. | 0.0852573 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.04081e6i | 1.24836i | 0.781281 | + | 0.624179i | \(0.214566\pi\) | ||||
−0.781281 | + | 0.624179i | \(0.785434\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 24047.4 | + | 31499.8i | 0.00588806 | + | 0.00771278i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 687693.i | 0.166489i | 0.996529 | + | 0.0832445i | \(0.0265282\pi\) | ||||
−0.996529 | + | 0.0832445i | \(0.973472\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 1.90308e6i | − | 0.455573i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −388572. | + | 785503.i | −0.0919820 | + | 0.185943i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.16418e6i | 0.506615i | 0.967386 | + | 0.253307i | \(0.0815184\pi\) | ||||
−0.967386 | + | 0.253307i | \(0.918482\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.25898e6 | −1.68048 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.45854e6 | + | 1.21619e6i | 0.562902 | + | 0.278456i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.10926e6 | 0.930539 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −128767. | −0.0288414 | −0.0144207 | − | 0.999896i | \(-0.504590\pi\) | ||||
−0.0144207 | + | 0.999896i | \(0.504590\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −805365. | − | 4.12862e6i | −0.178427 | − | 0.914687i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.38076e6 | −1.39836 | −0.699181 | − | 0.714944i | \(-0.746452\pi\) | ||||
−0.699181 | + | 0.714944i | \(0.746452\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.96689e6i | 1.29359i | 0.762666 | + | 0.646793i | \(0.223890\pi\) | ||||
−0.762666 | + | 0.646793i | \(0.776110\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.74159e6 | − | 2.34557e6i | −1.01693 | − | 0.503055i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.67725e6i | 0.780245i | 0.920763 | + | 0.390122i | \(0.127567\pi\) | ||||
−0.920763 | + | 0.390122i | \(0.872433\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.67898e6i | 1.82195i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.10015e6 | − | 544224.i | −0.228508 | − | 0.113038i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.15008e6i | 1.67498i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −70119.8 | −0.0142596 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.75071e6 | + | 6.22296e6i | 0.956010 | + | 1.25228i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 408276. | 0.0813045 | 0.0406523 | − | 0.999173i | \(-0.487056\pi\) | ||||
0.0406523 | + | 0.999173i | \(0.487056\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.92702e6 | −0.379772 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −835948. | − | 413526.i | −0.163046 | − | 0.0806558i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.30285e6 | 1.60278 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 3.14606e6i | − | 0.601097i | −0.953767 | − | 0.300548i | \(-0.902830\pi\) | ||
0.953767 | − | 0.300548i | \(-0.0971697\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −883433. | + | 1.78587e6i | −0.167071 | + | 0.337736i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 566933.i | − | 0.106127i | −0.998591 | − | 0.0530637i | \(-0.983101\pi\) | ||
0.998591 | − | 0.0530637i | \(-0.0168986\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.39936e6i | − | 0.629912i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.31092e6 | + | 4.05444e6i | −0.974220 | + | 0.743734i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.32480e6i | 0.785371i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.53698e6 | 1.71459 | 0.857293 | − | 0.514829i | \(-0.172144\pi\) | ||||
0.857293 | + | 0.514829i | \(0.172144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.12471e6 | + | 4.29512e6i | −0.378186 | + | 0.764506i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.64354e6 | 1.69948 | 0.849741 | − | 0.527200i | \(-0.176758\pi\) | ||||
0.849741 | + | 0.527200i | \(0.176758\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.41957e6 | −1.12015 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −430167. | + | 869586.i | −0.0743219 | + | 0.150243i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.21318e6 | −0.549719 | −0.274860 | − | 0.961484i | \(-0.588631\pi\) | ||||
−0.274860 | + | 0.961484i | \(0.588631\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.04646e7i | 1.77284i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.75529e6 | + | 537472.i | −0.462247 | + | 0.0901701i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 9.06615e6i | − | 1.50628i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.53524e6i | 1.56894i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.95789e6 | − | 3.95790e6i | 0.319059 | − | 0.644981i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.10693e6i | 0.501461i | 0.968057 | + | 0.250730i | \(0.0806708\pi\) | ||||
−0.968057 | + | 0.250730i | \(0.919329\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.71972e6 | −1.39395 | −0.696976 | − | 0.717094i | \(-0.745472\pi\) | ||||
−0.696976 | + | 0.717094i | \(0.745472\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 172220. | + | 85193.9i | 0.0272701 | + | 0.0134899i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.64136e6 | −1.04167 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.22541e6 | −0.967228 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.01404e6 | + | 774137.i | −0.156070 | + | 0.119147i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.32760e6 | 1.26970 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 961710.i | − | 0.145265i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.25906e6 | − | 2.60155e6i | −0.786996 | − | 0.389311i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 79029.5i | − | 0.0117170i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 9.33788e6i | − | 1.37169i | −0.727749 | − | 0.685843i | \(-0.759433\pi\) | ||
0.727749 | − | 0.685843i | \(-0.240567\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.76236e6 | − | 4.82924e6i | −1.42087 | − | 0.702877i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 8.65532e6i | − | 1.24822i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.94115e6 | −0.420290 | −0.210145 | − | 0.977670i | \(-0.567394\pi\) | ||||
−0.210145 | + | 0.977670i | \(0.567394\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.03608e7 | − | 7.90956e6i | 1.46710 | − | 1.12001i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.26861e6 | −0.318332 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.53555e6 | −0.352581 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.74814e6 | − | 1.35945e6i | −0.378709 | − | 0.187340i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.13152e6 | 1.24711 | 0.623555 | − | 0.781779i | \(-0.285688\pi\) | ||||
0.623555 | + | 0.781779i | \(0.285688\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.34988e6i | − | 1.26554i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.71940e6 | + | 7.51881e6i | −0.498960 | + | 1.00865i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.23038e7i | 1.63595i | 0.575254 | + | 0.817975i | \(0.304903\pi\) | ||||
−0.575254 | + | 0.817975i | \(0.695097\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.25548e6i | 1.08798i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.42025e6 | + | 2.02753e6i | 0.969306 | + | 0.264856i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 482588.i | − | 0.0624879i | −0.999512 | − | 0.0312440i | \(-0.990053\pi\) | ||
0.999512 | − | 0.0312440i | \(-0.00994688\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −226475. | −0.0290689 | −0.0145345 | − | 0.999894i | \(-0.504627\pi\) | ||||
−0.0145345 | + | 0.999894i | \(0.504627\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.04500e6 | + | 1.22200e7i | −0.769148 | + | 1.55484i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −43455.1 | −0.00548114 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.54105e6 | 0.317741 | 0.158871 | − | 0.987299i | \(-0.449215\pi\) | ||||
0.158871 | + | 0.987299i | \(0.449215\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.26129e6 | − | 2.54971e6i | 0.156357 | − | 0.316078i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.97886e6 | −0.366109 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.56127e7i | − | 1.90243i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.09276e6 | − | 4.65131e6i | 0.736079 | − | 0.561934i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.14425e6i | 0.735993i | 0.929827 | + | 0.367997i | \(0.119956\pi\) | ||||
−0.929827 | + | 0.367997i | \(0.880044\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.43221e6i | 0.526420i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.99539e6 | + | 4.03370e6i | −0.234995 | + | 0.475045i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.36071e7i | − | 1.58901i | −0.607255 | − | 0.794507i | \(-0.707729\pi\) | ||
0.607255 | − | 0.794507i | \(-0.292271\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.20822e6 | 0.950509 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.34381e7 | − | 6.64754e6i | −1.54312 | − | 0.763352i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.20455e6 | 0.706551 | 0.353275 | − | 0.935519i | \(-0.385068\pi\) | ||||
0.353275 | + | 0.935519i | \(0.385068\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 228374. | 0.0257906 | 0.0128953 | − | 0.999917i | \(-0.495895\pi\) | ||||
0.0128953 | + | 0.999917i | \(0.495895\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.82382e6 | + | 1.28682e7i | 1.10024 | + | 1.44121i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.18623e6 | 0.464980 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.17119e6i | − | 0.129020i | −0.997917 | − | 0.0645101i | \(-0.979452\pi\) | ||
0.997917 | − | 0.0645101i | \(-0.0205485\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.57191e6 | + | 2.75631e6i | 0.608780 | + | 0.301151i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1.09390e7i | − | 1.18542i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 526490.i | − | 0.0565899i | −0.999600 | − | 0.0282950i | \(-0.990992\pi\) | ||
0.999600 | − | 0.0282950i | \(-0.00900777\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.18761e7 | + | 5.87484e6i | 1.26615 | + | 0.626337i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.34265e6i | 0.247739i | 0.992299 | + | 0.123869i | \(0.0395304\pi\) | ||||
−0.992299 | + | 0.123869i | \(0.960470\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −881741. | −0.0924942 | −0.0462471 | − | 0.998930i | \(-0.514726\pi\) | ||||
−0.0462471 | + | 0.998930i | \(0.514726\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.70753e6 | + | 333086.i | −0.177680 | + | 0.0346599i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.36916e6 | 0.451001 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00524e7 | −1.02936 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.01778e6 | + | 2.48219e6i | 0.509733 | + | 0.252155i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.84921e6 | −0.387922 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 6.37410e6i | − | 0.637302i | −0.947872 | − | 0.318651i | \(-0.896770\pi\) | ||
0.947872 | − | 0.318651i | \(-0.103230\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.32420e6 | + | 2.67689e6i | −0.131355 | + | 0.265535i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.16041e6i | 0.507867i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 90663.7i | 0.00885289i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.89528e6 | + | 6.41234e6i | 0.474270 | + | 0.621247i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.98600e6i | 0.767687i | 0.923398 | + | 0.383844i | \(0.125400\pi\) | ||||
−0.923398 | + | 0.383844i | \(0.874600\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.81890e6 | 0.745793 | 0.372897 | − | 0.927873i | \(-0.378365\pi\) | ||||
0.372897 | + | 0.927873i | \(0.378365\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.59603e6 | − | 1.33339e7i | 0.624285 | − | 1.26200i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.38044e6 | 0.787057 | 0.393528 | − | 0.919313i | \(-0.371254\pi\) | ||||
0.393528 | + | 0.919313i | \(0.371254\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.54413e6 | 0.237097 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.38503e6 | − | 1.08859e7i | 0.498007 | − | 1.00673i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.01923e6 | −0.277085 | −0.138542 | − | 0.990357i | \(-0.544242\pi\) | ||||
−0.138542 | + | 0.990357i | \(0.544242\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.30779e6i | − | 0.210181i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.18449e7 | + | 1.55157e7i | 1.07058 | + | 1.40236i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.78900e6i | 0.698664i | 0.936999 | + | 0.349332i | \(0.113591\pi\) | ||||
−0.936999 | + | 0.349332i | \(0.886409\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.90709e6i | 0.525860i | 0.964815 | + | 0.262930i | \(0.0846888\pi\) | ||||
−0.964815 | + | 0.262930i | \(0.915311\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.26694e6 | − | 8.62568e6i | 0.376993 | − | 0.762095i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 5.47787e6i | − | 0.480350i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.40592e6 | −0.122362 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.27642e6 | + | 3.10482e6i | 0.542184 | + | 0.268207i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.59940e7 | −2.22878 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.71964e6 | 0.742097 | 0.371049 | − | 0.928613i | \(-0.378998\pi\) | ||||
0.371049 | + | 0.928613i | \(0.378998\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 351781. | − | 68621.7i | 0.0297176 | − | 0.00579698i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.44508e7 | −1.21177 | −0.605887 | − | 0.795551i | \(-0.707181\pi\) | ||||
−0.605887 | + | 0.795551i | \(0.707181\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.90619e7i | 1.58669i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.08106e6 | − | 3.99754e6i | −0.667730 | − | 0.330312i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.40378e7i | − | 1.15145i | −0.817642 | − | 0.575727i | \(-0.804719\pi\) | ||
0.817642 | − | 0.575727i | \(-0.195281\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.87602e7i | − | 1.52761i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.78446e6 | + | 2.36677e6i | 0.386759 | + | 0.191322i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.79112e7i | 1.43739i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.42291e7 | −1.13366 | −0.566828 | − | 0.823836i | \(-0.691830\pi\) | ||||
−0.566828 | + | 0.823836i | \(0.691830\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.30831e6 | − | 1.21930e7i | −0.736271 | − | 0.964443i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.00233e7 | −0.787136 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.66343e7 | 1.29695 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.01163e7 | + | 5.00432e6i | 0.783119 | + | 0.387393i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.47356e6 | 0.190120 | 0.0950598 | − | 0.995472i | \(-0.469696\pi\) | ||||
0.0950598 | + | 0.995472i | \(0.469696\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.56882e6i | 0.196041i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.71707e6 | − | 1.56001e7i | 0.584763 | − | 1.18210i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1.47383e7i | − | 1.10891i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.27275e6i | 0.244510i | 0.992499 | + | 0.122255i | \(0.0390126\pi\) | ||||
−0.992499 | + | 0.122255i | \(0.960987\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.75944e6 | + | 2.87001e6i | −0.278900 | + | 0.212917i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.74676e6i | 0.202347i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.52861e7 | −1.11823 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.13591e7 | + | 2.29626e7i | −0.825176 | + | 1.66810i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.25182e7 | −0.903067 | −0.451534 | − | 0.892254i | \(-0.649123\pi\) | ||||
−0.451534 | + | 0.892254i | \(0.649123\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.08144e7 | 1.49116 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.12689e7 | + | 2.27801e7i | −0.801741 | + | 1.62073i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 289644. | 0.0204654 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.09674e7i | − | 1.47132i | −0.677349 | − | 0.735661i | \(-0.736871\pi\) | ||
0.677349 | − | 0.735661i | \(-0.263129\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.32969e7 | − | 5.39285e6i | 0.926686 | − | 0.375837i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.86763e7i | − | 1.29270i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 2.37515e7i | − | 1.63279i | −0.577491 | − | 0.816397i | \(-0.695968\pi\) | ||
0.577491 | − | 0.816397i | \(-0.304032\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −63960.2 | + | 129296.i | −0.00436709 | + | 0.00882811i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.22850e7i | − | 2.18944i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.98341e7 | −1.33598 | −0.667991 | − | 0.744170i | \(-0.732845\pi\) | ||||
−0.667991 | + | 0.744170i | \(0.732845\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.75647e6 | − | 2.84761e6i | −0.385133 | − | 0.190517i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.45507e6 | 0.561882 | 0.280941 | − | 0.959725i | \(-0.409353\pi\) | ||||
0.280941 | + | 0.959725i | \(0.409353\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.18992e6 | −0.210567 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.41673e6 | + | 3.37180e6i | −0.289601 | + | 0.221086i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.20792e6 | 0.143807 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.69261e7i | 1.74210i | 0.491193 | + | 0.871051i | \(0.336561\pi\) | ||||
−0.491193 | + | 0.871051i | \(0.663439\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.10295e7 | − | 1.04029e7i | −1.35158 | − | 0.668599i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.98414e6i | 0.637446i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.12014e7i | − | 1.34470i | −0.740234 | − | 0.672350i | \(-0.765285\pi\) | ||
0.740234 | − | 0.672350i | \(-0.234715\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.10965e6 | + | 1.53828e6i | 0.195933 | + | 0.0969241i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.80031e7i | − | 1.12690i | −0.826151 | − | 0.563449i | \(-0.809474\pi\) | ||
0.826151 | − | 0.563449i | \(-0.190526\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.98711e7 | 1.23570 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.21703e7 | − | 9.29096e6i | 0.751875 | − | 0.573994i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.91866e6 | −0.179141 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.91227e6 | 0.482486 | 0.241243 | − | 0.970465i | \(-0.422445\pi\) | ||||
0.241243 | + | 0.970465i | \(0.422445\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.68551e7 | − | 8.33786e6i | −1.02116 | − | 0.505148i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.31768e7 | −1.39510 | −0.697548 | − | 0.716538i | \(-0.745726\pi\) | ||||
−0.697548 | + | 0.716538i | \(0.745726\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 565882.i | − | 0.0338432i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.12106e6 | − | 6.30926e6i | 0.185460 | − | 0.374909i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1.11012e7i | − | 0.655427i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1.60879e7i | − | 0.943781i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.13813e7 | − | 2.22014e6i | 0.663419 | − | 0.129412i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 4.46773e6i | − | 0.258769i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.36874e7 | 1.36327 | 0.681634 | − | 0.731693i | \(-0.261270\pi\) | ||||
0.681634 | + | 0.731693i | \(0.261270\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.12384e7 | − | 2.27186e7i | 0.642706 | − | 1.29924i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.89532e7 | −1.07706 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.98207e7 | 1.68397 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.26357e7 | + | 2.55432e7i | −0.709058 | + | 1.43337i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.45597e7 | −0.811907 | −0.405953 | − | 0.913894i | \(-0.633060\pi\) | ||||
−0.405953 | + | 0.913894i | \(0.633060\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.18505e7i | − | 1.21086i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.47811e6 | − | 4.94549e6i | 0.356753 | − | 0.272351i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 3.89273e7i | − | 2.13042i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 3.39478e6i | − | 0.184639i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 952584. | − | 1.92566e6i | 0.0514896 | − | 0.104087i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.22475e7i | 1.73231i | 0.499779 | + | 0.866153i | \(0.333415\pi\) | ||||
−0.499779 | + | 0.866153i | \(0.666585\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.06545e7 | −0.568828 | −0.284414 | − | 0.958702i | \(-0.591799\pi\) | ||||
−0.284414 | + | 0.958702i | \(0.591799\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.07374e7 | + | 1.02584e7i | 1.10034 | + | 0.544316i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.25241e6 | −0.382462 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.24639e7 | −0.653280 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.06786e7 | + | 1.39879e7i | 0.556295 | + | 0.728692i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.14818e7 | 0.594498 | 0.297249 | − | 0.954800i | \(-0.403931\pi\) | ||||
0.297249 | + | 0.954800i | \(0.403931\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.52972e7i | 1.30189i | 0.759126 | + | 0.650944i | \(0.225627\pi\) | ||||
−0.759126 | + | 0.650944i | \(0.774373\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −640645. | − | 316914.i | −0.0327704 | − | 0.0162109i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.83375e6i | 0.449140i | 0.974458 | + | 0.224570i | \(0.0720977\pi\) | ||||
−0.974458 | + | 0.224570i | \(0.927902\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 4.86456e6i | − | 0.245843i | −0.992416 | − | 0.122921i | \(-0.960774\pi\) | ||
0.992416 | − | 0.122921i | \(-0.0392263\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.25554e7 | + | 1.11577e7i | 1.13305 | + | 0.560495i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 181100.i | 0.00904288i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.74425e7 | −0.865749 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.33752e6 | − | 2.22358e7i | −0.214007 | − | 1.09708i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.36695e7 | −1.16087 | −0.580436 | − | 0.814306i | \(-0.697118\pi\) | ||||
−0.580436 | + | 0.814306i | \(0.697118\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.11402e7 | −0.543128 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.54927e6 | − | 766390.i | −0.0750857 | − | 0.0371433i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.53139e6 | −0.170139 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.61087e6i | 0.460314i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.61113e6 | − | 1.74075e7i | 0.410007 | − | 0.828833i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.59197e6i | 0.0753548i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.69049e7i | 0.795498i | 0.917494 | + | 0.397749i | \(0.130209\pi\) | ||||
−0.917494 | + | 0.397749i | \(0.869791\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.20046e6 | − | 8.12199e6i | −0.290074 | − | 0.379968i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2.33438e7i | − | 1.08572i | −0.839822 | − | 0.542861i | \(-0.817341\pi\) | ||
0.839822 | − | 0.542861i | \(-0.182659\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.96996e7 | 0.910908 | 0.455454 | − | 0.890259i | \(-0.349477\pi\) | ||||
0.455454 | + | 0.890259i | \(0.349477\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.34876e7 | + | 2.72654e7i | −0.620052 | + | 1.25344i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.42226e6 | 0.156418 | 0.0782088 | − | 0.996937i | \(-0.475080\pi\) | ||||
0.0782088 | + | 0.996937i | \(0.475080\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.60730e7 | 0.730395 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.29062e6 | + | 2.60900e6i | −0.0583111 | + | 0.117876i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.43203e6 | 0.423697 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.70378e7i | 1.65425i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.15764e7 | + | 2.82630e7i | 0.958171 | + | 1.25511i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 2.23997e7i | − | 0.989057i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.82299e7i | − | 0.800361i | −0.916436 | − | 0.400181i | \(-0.868947\pi\) | ||
0.916436 | − | 0.400181i | \(-0.131053\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.92417e7 | − | 3.88974e7i | 0.839986 | − | 1.69804i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.79378e7i | 1.64677i | 0.567483 | + | 0.823385i | \(0.307917\pi\) | ||||
−0.567483 | + | 0.823385i | \(0.692083\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.47312e7 | 1.49906 | 0.749529 | − | 0.661972i | \(-0.230280\pi\) | ||||
0.749529 | + | 0.661972i | \(0.230280\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.16232e6 | − | 2.05901e6i | −0.178639 | − | 0.0883692i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.89149e6 | −0.379459 | −0.189730 | − | 0.981836i | \(-0.560761\pi\) | ||||
−0.189730 | + | 0.981836i | \(0.560761\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.18474e7 | −0.502771 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.76027e7 | − | 7.54225e6i | −1.16482 | − | 0.318278i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.45822e7 | −0.611922 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.13570e7i | − | 0.891216i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.56744e6 | − | 1.76474e6i | −0.148039 | − | 0.0732317i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1.83082e7i | − | 0.755520i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.57774e7i | 1.46824i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.06125e7 | + | 1.51434e7i | 1.24934 | + | 0.618021i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 3.96449e7i | − | 1.60904i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.17482e7 | 1.68508 | 0.842539 | − | 0.538636i | \(-0.181060\pi\) | ||||
0.842539 | + | 0.538636i | \(0.181060\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.66824e7 | − | 2.18523e7i | −0.669650 | − | 0.877176i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.26866e6 | 0.170410 | 0.0852052 | − | 0.996363i | \(-0.472845\pi\) | ||||
0.0852052 | + | 0.996363i | \(0.472845\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.10811e7 | 0.439953 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.25275e7 | + | 2.10375e7i | 1.67926 | + | 0.830695i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.29830e6 | 0.208072 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.88729e7i | − | 0.737138i | −0.929600 | − | 0.368569i | \(-0.879848\pi\) | ||
0.929600 | − | 0.368569i | \(-0.120152\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.06410e6 | + | 8.21562e6i | −0.157876 | + | 0.319147i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.84562e7i | 0.713081i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 327974.i | − | 0.0126033i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.08613e7 | − | 2.35600e7i | 1.17954 | − | 0.900483i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.24738e7i | 0.474197i | 0.971486 | + | 0.237098i | \(0.0761964\pi\) | ||||
−0.971486 | + | 0.237098i | \(0.923804\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 120860. | 0.00456991 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.76059e6 | + | 1.77096e7i | −0.329480 | + | 0.666048i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.05339e7 | −1.14223 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.08166e7 | −0.774570 | −0.387285 | − | 0.921960i | \(-0.626587\pi\) | ||||
−0.387285 | + | 0.921960i | \(0.626587\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.87210e7 | + | 3.78447e7i | −0.692890 | + | 1.40069i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.20794e6 | −0.0444703 | −0.0222351 | − | 0.999753i | \(-0.507078\pi\) | ||||
−0.0222351 | + | 0.999753i | \(0.507078\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 6.87968e6i | − | 0.251935i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.36084e6 | + | 2.74817e7i | 0.195278 | + | 1.00107i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.75552e7i | 1.72315i | 0.507631 | + | 0.861574i | \(0.330521\pi\) | ||||
−0.507631 | + | 0.861574i | \(0.669479\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.46579e7i | 1.60965i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.83047e6 | − | 3.70031e6i | 0.0656313 | − | 0.132674i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.18909e7i | 0.780784i | 0.920649 | + | 0.390392i | \(0.127661\pi\) | ||||
−0.920649 | + | 0.390392i | \(0.872339\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.96255e7 | −1.76075 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.07270e7 | − | 1.02532e7i | −0.731571 | − | 0.361893i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.30704e7 | 1.51228 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.13973e6 | −0.249387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.27367e6 | − | 2.49917e6i | 0.113755 | − | 0.0868421i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.03544e7 | 0.357936 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.28485e7i | − | 1.12967i | −0.825205 | − | 0.564833i | \(-0.808941\pi\) | ||
0.825205 | − | 0.564833i | \(-0.191059\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.14985e7 | − | 5.68808e6i | −0.393398 | − | 0.194606i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.25929e7i | − | 0.428624i | −0.976765 | − | 0.214312i | \(-0.931249\pi\) | ||
0.976765 | − | 0.214312i | \(-0.0687509\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2.30119e7i | − | 0.779237i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 734956. | + | 363568.i | 0.0247600 | + | 0.0122482i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.98034e6i | 0.133408i | 0.997773 | + | 0.0667042i | \(0.0212484\pi\) | ||||
−0.997773 | + | 0.0667042i | \(0.978752\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.62529e7 | −0.541968 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.94628e7 | − | 2.24923e7i | 0.977465 | − | 0.746212i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.24394e7 | −1.73091 | −0.865453 | − | 0.500989i | \(-0.832970\pi\) | ||||
−0.865453 | + | 0.500989i | \(0.832970\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.63808e7 | −0.537954 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.58153e7 | + | 1.77171e7i | 1.17024 | + | 0.578895i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.72422e6 | −0.251110 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.65620e7i | − | 0.535708i | −0.963459 | − | 0.267854i | \(-0.913685\pi\) | ||
0.963459 | − | 0.267854i | \(-0.0863146\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.69632e6 | − | 7.47214e6i | 0.118959 | − | 0.240476i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 5.45720e7i | − | 1.74748i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.73906e7i | 0.554087i | 0.960857 | + | 0.277043i | \(0.0893545\pi\) | ||||
−0.960857 | + | 0.277043i | \(0.910645\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.51394e6 | − | 1.28874e7i | −0.0796969 | − | 0.408557i |
(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 | 384.6.f.e.191.8 | yes | 20 | |
3.2 | odd | 2 | 384.6.f.f.191.7 | yes | 20 | ||
4.3 | odd | 2 | 384.6.f.f.191.13 | yes | 20 | ||
8.3 | odd | 2 | 384.6.f.f.191.8 | yes | 20 | ||
8.5 | even | 2 | inner | 384.6.f.e.191.13 | yes | 20 | |
12.11 | even | 2 | inner | 384.6.f.e.191.14 | yes | 20 | |
24.5 | odd | 2 | 384.6.f.f.191.14 | yes | 20 | ||
24.11 | even | 2 | inner | 384.6.f.e.191.7 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.f.e.191.7 | ✓ | 20 | 24.11 | even | 2 | inner | |
384.6.f.e.191.8 | yes | 20 | 1.1 | even | 1 | trivial | |
384.6.f.e.191.13 | yes | 20 | 8.5 | even | 2 | inner | |
384.6.f.e.191.14 | yes | 20 | 12.11 | even | 2 | inner | |
384.6.f.f.191.7 | yes | 20 | 3.2 | odd | 2 | ||
384.6.f.f.191.8 | yes | 20 | 8.3 | odd | 2 | ||
384.6.f.f.191.13 | yes | 20 | 4.3 | odd | 2 | ||
384.6.f.f.191.14 | yes | 20 | 24.5 | odd | 2 |