Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,6,Mod(63,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.63");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.n (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.6614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 1375 x^{14} + 743087 x^{12} + 198706725 x^{10} + 26872635188 x^{8} + 1612811892960 x^{6} + \cdots + 177426662425600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{41}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 63.1 | ||
Root | \(-19.8299i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.63 |
Dual form | 160.6.n.c.127.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −20.8299 | + | 20.8299i | −1.33624 | + | 1.33624i | −0.436570 | + | 0.899670i | \(0.643807\pi\) |
−0.899670 | + | 0.436570i | \(0.856193\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −55.6057 | − | 5.74531i | −0.994705 | − | 0.102775i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 135.906 | + | 135.906i | 1.04832 | + | 1.04832i | 0.998772 | + | 0.0495445i | \(0.0157770\pi\) |
0.0495445 | + | 0.998772i | \(0.484223\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 624.772i | − | 2.57108i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 629.190i | − | 1.56783i | −0.620866 | − | 0.783917i | \(-0.713219\pi\) | ||
0.620866 | − | 0.783917i | \(-0.286781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.08659 | − | 2.08659i | −0.00342435 | − | 0.00342435i | 0.705393 | − | 0.708817i | \(-0.250771\pi\) |
−0.708817 | + | 0.705393i | \(0.750771\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1277.94 | − | 1038.59i | 1.46650 | − | 1.19183i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −241.044 | + | 241.044i | −0.202290 | + | 0.202290i | −0.800981 | − | 0.598690i | \(-0.795688\pi\) |
0.598690 | + | 0.800981i | \(0.295688\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −372.104 | −0.236472 | −0.118236 | − | 0.992986i | \(-0.537724\pi\) | ||||
−0.118236 | + | 0.992986i | \(0.537724\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5661.81 | −2.80161 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2034.55 | − | 2034.55i | 0.801954 | − | 0.801954i | −0.181447 | − | 0.983401i | \(-0.558078\pi\) |
0.983401 | + | 0.181447i | \(0.0580781\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3058.98 | + | 638.944i | 0.978874 | + | 0.204462i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7952.27 | + | 7952.27i | 2.09934 | + | 2.09934i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 55.2453i | − | 0.0121983i | −0.999981 | − | 0.00609916i | \(-0.998059\pi\) | ||
0.999981 | − | 0.00609916i | \(-0.00194144\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1844.67i | 0.344757i | 0.985031 | + | 0.172379i | \(0.0551453\pi\) | ||||
−0.985031 | + | 0.172379i | \(0.944855\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13106.0 | + | 13106.0i | 2.09500 | + | 2.09500i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6776.31 | − | 8337.95i | −0.935024 | − | 1.15051i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −61.7891 | + | 61.7891i | −0.00742006 | + | 0.00742006i | −0.710807 | − | 0.703387i | \(-0.751670\pi\) |
0.703387 | + | 0.710807i | \(0.251670\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 86.9270 | 0.00915152 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4808.22 | −0.446709 | −0.223355 | − | 0.974737i | \(-0.571701\pi\) | ||||
−0.223355 | + | 0.974737i | \(0.571701\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10658.2 | + | 10658.2i | −0.879048 | + | 0.879048i | −0.993436 | − | 0.114388i | \(-0.963509\pi\) |
0.114388 | + | 0.993436i | \(0.463509\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3589.51 | + | 34740.8i | −0.264243 | + | 2.55746i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12121.5 | + | 12121.5i | 0.800410 | + | 0.800410i | 0.983159 | − | 0.182750i | \(-0.0584998\pi\) |
−0.182750 | + | 0.983159i | \(0.558500\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 20133.7i | 1.19793i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 10041.9i | − | 0.540617i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −21384.1 | − | 21384.1i | −1.04569 | − | 1.04569i | −0.998905 | − | 0.0467821i | \(-0.985103\pi\) |
−0.0467821 | − | 0.998905i | \(-0.514897\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3614.89 | + | 34986.5i | −0.161135 | + | 1.55953i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7750.90 | − | 7750.90i | 0.315984 | − | 0.315984i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 50708.8 | 1.89650 | 0.948252 | − | 0.317519i | \(-0.102850\pi\) | ||||
0.948252 | + | 0.317519i | \(0.102850\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 16164.0 | 0.556191 | 0.278095 | − | 0.960554i | \(-0.410297\pi\) | ||||
0.278095 | + | 0.960554i | \(0.410297\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 84910.0 | − | 84910.0i | 2.69530 | − | 2.69530i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 104.038 | + | 128.014i | 0.00305428 | + | 0.00375816i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 24888.6 | + | 24888.6i | 0.677350 | + | 0.677350i | 0.959400 | − | 0.282050i | \(-0.0910143\pi\) |
−0.282050 | + | 0.959400i | \(0.591014\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 84759.2i | 2.14321i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 58597.1i | − | 1.37953i | −0.724034 | − | 0.689764i | \(-0.757714\pi\) | ||
0.724034 | − | 0.689764i | \(-0.242286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −42184.9 | − | 42184.9i | −0.926509 | − | 0.926509i | 0.0709698 | − | 0.997478i | \(-0.477391\pi\) |
−0.997478 | + | 0.0709698i | \(0.977391\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −77027.5 | + | 50409.2i | −1.58122 | + | 1.03480i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 85510.5 | − | 85510.5i | 1.64359 | − | 1.64359i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 32362.8 | 0.583417 | 0.291708 | − | 0.956507i | \(-0.405776\pi\) | ||||
0.291708 | + | 0.956507i | \(0.405776\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −179471. | −3.03936 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10165.1 | + | 10165.1i | −0.161963 | + | 0.161963i | −0.783436 | − | 0.621473i | \(-0.786535\pi\) |
0.621473 | + | 0.783436i | \(0.286535\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14788.3 | − | 12018.6i | 0.222009 | − | 0.180429i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1150.76 | + | 1150.76i | 0.0162999 | + | 0.0162999i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 32266.2i | 0.431790i | 0.976417 | + | 0.215895i | \(0.0692669\pi\) | ||||
−0.976417 | + | 0.215895i | \(0.930733\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 567.158i | − | 0.00717961i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −38424.3 | − | 38424.3i | −0.460679 | − | 0.460679i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20691.1 | + | 2137.85i | 0.235220 | + | 0.0243035i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 24499.5 | − | 24499.5i | 0.264379 | − | 0.264379i | −0.562451 | − | 0.826830i | \(-0.690142\pi\) |
0.826830 | + | 0.562451i | \(0.190142\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −393100. | −4.03102 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 128187. | 1.25037 | 0.625186 | − | 0.780476i | \(-0.285023\pi\) | ||||
0.625186 | + | 0.780476i | \(0.285023\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8402.08 | + | 8402.08i | −0.0780358 | + | 0.0780358i | −0.745047 | − | 0.667012i | \(-0.767573\pi\) |
0.667012 | + | 0.745047i | \(0.267573\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 314829. | + | 32528.9i | 2.78677 | + | 0.287936i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 54744.5 | + | 54744.5i | 0.462254 | + | 0.462254i | 0.899394 | − | 0.437139i | \(-0.144008\pi\) |
−0.437139 | + | 0.899394i | \(0.644008\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17456.0i | 0.140728i | 0.997521 | + | 0.0703638i | \(0.0224160\pi\) | ||||
−0.997521 | + | 0.0703638i | \(0.977584\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2574.13i | − | 0.0198300i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 85583.2 | + | 85583.2i | 0.630511 | + | 0.630511i | 0.948196 | − | 0.317686i | \(-0.102906\pi\) |
−0.317686 | + | 0.948196i | \(0.602906\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −124822. | + | 101444.i | −0.880128 | + | 0.715286i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1303.64 | + | 1303.64i | −0.00880427 | + | 0.00880427i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −65518.6 | −0.424128 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −234829. | −1.45810 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 100155. | − | 100155.i | 0.596911 | − | 0.596911i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −166426. | − | 53103.7i | −0.952677 | − | 0.303984i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 96993.9 | + | 96993.9i | 0.533624 | + | 0.533624i | 0.921649 | − | 0.388025i | \(-0.126843\pi\) |
−0.388025 | + | 0.921649i | \(0.626843\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 444019.i | − | 2.34924i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 272784.i | 1.38880i | 0.719588 | + | 0.694402i | \(0.244331\pi\) | ||||
−0.719588 | + | 0.694402i | \(0.755669\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −50571.0 | − | 50571.0i | −0.247898 | − | 0.247898i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −396503. | − | 487880.i | −1.87246 | − | 2.30398i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 164113. | − | 164113.i | 0.747037 | − | 0.747037i | −0.226885 | − | 0.973922i | \(-0.572854\pi\) |
0.973922 | + | 0.226885i | \(0.0728541\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 244627. | 1.07391 | 0.536955 | − | 0.843611i | \(-0.319574\pi\) | ||||
0.536955 | + | 0.843611i | \(0.319574\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −504981. | −2.13908 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1312.86 | + | 1312.86i | −0.00536882 | + | 0.00536882i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −317.402 | + | 3071.95i | −0.00125369 | + | 0.0121337i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −419383. | − | 419383.i | −1.60073 | − | 1.60073i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 130589.i | 0.481883i | 0.970540 | + | 0.240941i | \(0.0774562\pi\) | ||||
−0.970540 | + | 0.240941i | \(0.922544\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12502.0i | 0.0446208i | 0.999751 | + | 0.0223104i | \(0.00710221\pi\) | ||||
−0.999751 | + | 0.0223104i | \(0.992898\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 150598. | + | 150598.i | 0.520104 | + | 0.520104i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10598.2 | − | 102574.i | 0.0354326 | − | 0.342932i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 402134. | − | 402134.i | 1.30203 | − | 1.30203i | 0.375012 | − | 0.927020i | \(-0.377638\pi\) |
0.927020 | − | 0.375012i | \(-0.122362\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 890859. | 2.79458 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 553014. | 1.68140 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6089.60 | + | 6089.60i | −0.0179523 | + | 0.0179523i | −0.716026 | − | 0.698074i | \(-0.754041\pi\) |
0.698074 | + | 0.716026i | \(0.254041\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −653469. | − | 804065.i | −1.86859 | − | 2.29922i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −179899. | − | 179899.i | −0.499156 | − | 0.499156i | 0.412019 | − | 0.911175i | \(-0.364824\pi\) |
−0.911175 | + | 0.412019i | \(0.864824\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 371284.i | − | 0.999977i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 232480.i | 0.607988i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 85872.0 | + | 85872.0i | 0.218140 | + | 0.218140i | 0.807714 | − | 0.589574i | \(-0.200704\pi\) |
−0.589574 | + | 0.807714i | \(0.700704\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 328897. | + | 502569.i | 0.811829 | + | 1.24051i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.05626e6 | + | 1.05626e6i | −2.53418 | + | 2.53418i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 230684. | 0.538127 | 0.269064 | − | 0.963122i | \(-0.413286\pi\) | ||||
0.269064 | + | 0.963122i | \(0.413286\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 601745. | 1.36526 | 0.682631 | − | 0.730763i | \(-0.260836\pi\) | ||||
0.682631 | + | 0.730763i | \(0.260836\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −336694. | + | 336694.i | −0.743204 | + | 0.743204i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3790.82 | − | 3080.83i | 0.00814337 | − | 0.00661817i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 151663. | + | 151663.i | 0.317157 | + | 0.317157i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.16152e6i | 4.40154i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 573479.i | 1.13746i | 0.822526 | + | 0.568728i | \(0.192564\pi\) | ||||
−0.822526 | + | 0.568728i | \(0.807436\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 617099. | + | 617099.i | 1.19251 | + | 1.19251i | 0.976361 | + | 0.216148i | \(0.0693494\pi\) |
0.216148 | + | 0.976361i | \(0.430651\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4833.63 | − | 499.423i | −0.00910306 | − | 0.000940550i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 283085. | − | 283085.i | 0.519698 | − | 0.519698i | −0.397782 | − | 0.917480i | \(-0.630220\pi\) |
0.917480 | + | 0.397782i | \(0.130220\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −125350. | −0.224385 | −0.112192 | − | 0.993687i | \(-0.535787\pi\) | ||||
−0.112192 | + | 0.993687i | \(0.535787\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.03685e6 | −1.81020 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7508.15 | − | 7508.15i | 0.0127877 | − | 0.0127877i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 267364. | + | 27624.7i | 0.444344 | + | 0.0459107i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.27113e6 | − | 1.27113e6i | −2.06188 | − | 2.06188i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 234124.i | 0.370749i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4378.03i | − | 0.00676974i | −0.999994 | − | 0.00338487i | \(-0.998923\pi\) | ||
0.999994 | − | 0.00338487i | \(-0.00107744\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.22057e6 | + | 1.22057e6i | 1.84338 | + | 1.84338i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 653891. | − | 531421.i | 0.964737 | − | 0.784048i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −250701. | + | 250701.i | −0.361415 | + | 0.361415i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.75742e6 | 2.47608 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1005.92 | 0.00138543 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 298702. | − | 298702.i | 0.402231 | − | 0.402231i | −0.476787 | − | 0.879019i | \(-0.658199\pi\) |
0.879019 | + | 0.476787i | \(0.158199\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 399194. | − | 1.91117e6i | 0.525688 | − | 2.51676i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 605799. | + | 605799.i | 0.780304 | + | 0.780304i | 0.979882 | − | 0.199578i | \(-0.0639572\pi\) |
−0.199578 | + | 0.979882i | \(0.563957\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 527570.i | − | 0.664801i | −0.943138 | − | 0.332400i | \(-0.892141\pi\) | ||
0.943138 | − | 0.332400i | \(-0.107859\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.56235e6i | 4.39245i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 214988. | + | 214988.i | 0.259432 | + | 0.259432i | 0.824823 | − | 0.565391i | \(-0.191275\pi\) |
−0.565391 | + | 0.824823i | \(0.691275\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −604383. | − | 743667.i | −0.713909 | − | 0.878434i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −674116. | + | 674116.i | −0.779585 | + | 0.779585i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.17211e6 | −1.32731 | −0.663656 | − | 0.748038i | \(-0.730996\pi\) | ||||
−0.663656 | + | 0.748038i | \(0.730996\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.37526e6 | −1.52525 | −0.762625 | − | 0.646841i | \(-0.776090\pi\) | ||||
−0.762625 | + | 0.646841i | \(0.776090\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.80597e6 | − | 1.80597e6i | 1.96198 | − | 1.96198i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 115674. | − | 1.11955e6i | 0.123118 | − | 1.19159i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 776.428 | + | 776.428i | 0.000809765 | + | 0.000809765i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 423476.i | − | 0.432843i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 305774.i | − | 0.306349i | −0.988199 | − | 0.153174i | \(-0.951050\pi\) | ||
0.988199 | − | 0.153174i | \(-0.0489496\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.28012e6 | − | 1.28012e6i | −1.25733 | − | 1.25733i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −57693.7 | + | 558385.i | −0.0555620 | + | 0.537754i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −964285. | + | 964285.i | −0.910694 | + | 0.910694i | −0.996327 | − | 0.0856328i | \(-0.972709\pi\) |
0.0856328 | + | 0.996327i | \(0.472709\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16795.0 | −0.0155572 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −34515.7 | −0.0313628 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.19814e6 | − | 1.19814e6i | 1.06812 | − | 1.06812i | 0.0706129 | − | 0.997504i | \(-0.477504\pi\) |
0.997504 | − | 0.0706129i | \(-0.0224955\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.06622e6 | + | 1.31194e6i | 0.932679 | + | 1.14762i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −672102. | − | 672102.i | −0.576975 | − | 0.576975i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.22133e6i | − | 1.02909i | −0.857463 | − | 0.514546i | \(-0.827961\pi\) | ||
0.857463 | − | 0.514546i | \(-0.172039\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 501303.i | − | 0.414646i | −0.978273 | − | 0.207323i | \(-0.933525\pi\) | ||
0.978273 | − | 0.207323i | \(-0.0664751\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11813.9 | + | 11813.9i | 0.00959369 | + | 0.00959369i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 402017. | − | 1.92468e6i | 0.320563 | − | 1.53471i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −314343. | + | 314343.i | −0.246153 | + | 0.246153i | −0.819390 | − | 0.573237i | \(-0.805687\pi\) |
0.573237 | + | 0.819390i | \(0.305687\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.15250e6 | 0.886398 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.00305e6 | 0.757807 | 0.378904 | − | 0.925436i | \(-0.376301\pi\) | ||||
0.378904 | + | 0.925436i | \(0.376301\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −575269. | + | 575269.i | −0.426977 | + | 0.426977i | −0.887597 | − | 0.460620i | \(-0.847627\pi\) |
0.460620 | + | 0.887597i | \(0.347627\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −475525. | + | 386463.i | −0.346786 | + | 0.281835i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −653465. | − | 653465.i | −0.468293 | − | 0.468293i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.30365e6i | 0.918157i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.02064e6i | 0.706548i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 738761. | + | 738761.i | 0.502730 | + | 0.502730i | 0.912285 | − | 0.409555i | \(-0.134316\pi\) |
−0.409555 | + | 0.912285i | \(0.634316\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.81970e6 | − | 291338.i | −1.88646 | − | 0.194914i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.00349e6 | − | 5.00349e6i | 3.29141 | − | 3.29141i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8490.55 | −0.00549235 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.89702e6 | −1.84304 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.67012e6 | + | 2.67012e6i | −1.67080 | + | 1.67080i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −898809. | − | 92867.1i | −0.553245 | − | 0.0571626i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.06010e6 | + | 2.06010e6i | 1.24750 | + | 1.24750i | 0.956819 | + | 0.290686i | \(0.0938834\pi\) |
0.290686 | + | 0.956819i | \(0.406117\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 350030.i | − | 0.208549i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 891640.i | − | 0.522744i | −0.965238 | − | 0.261372i | \(-0.915825\pi\) | ||
0.965238 | − | 0.261372i | \(-0.0841749\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 910965. | + | 910965.i | 0.525582 | + | 0.525582i | 0.919252 | − | 0.393670i | \(-0.128795\pi\) |
−0.393670 | + | 0.919252i | \(0.628795\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.20931e6 | + | 4.23364e6i | −2.95804 | + | 2.40402i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.21076e6 | − | 1.21076e6i | 0.676721 | − | 0.676721i | −0.282536 | − | 0.959257i | \(-0.591176\pi\) |
0.959257 | + | 0.282536i | \(0.0911757\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −34759.8 | −0.0191249 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.28065e6 | −1.23537 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 89693.6 | − | 89693.6i | 0.0478360 | − | 0.0478360i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5049.63 | − | 7716.05i | −0.00265186 | − | 0.00405216i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −363608. | − | 363608.i | −0.188046 | − | 0.188046i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.29477e6i | 1.67817i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.52738e6i | − | 0.766262i | −0.923694 | − | 0.383131i | \(-0.874846\pi\) | ||
0.923694 | − | 0.383131i | \(-0.125154\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 38604.1 | + | 38604.1i | 0.0190776 | + | 0.0190776i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.24095e6 | − | 1.52694e6i | −0.604148 | − | 0.743378i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.27407e6 | − | 2.27407e6i | 1.09076 | − | 1.09076i | 0.0953146 | − | 0.995447i | \(-0.469614\pi\) |
0.995447 | − | 0.0953146i | \(-0.0303857\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.56538e6 | −1.68503 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.16065e6 | 0.540522 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −452116. | + | 452116.i | −0.207498 | + | 0.207498i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 486968. | − | 4.71309e6i | 0.220269 | − | 2.13186i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.68164e6 | − | 2.68164e6i | −1.19558 | − | 1.19558i | −0.975478 | − | 0.220097i | \(-0.929363\pi\) |
−0.220097 | − | 0.975478i | \(-0.570637\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 951948.i | 0.418359i | 0.977877 | + | 0.209180i | \(0.0670794\pi\) | ||||
−0.977877 | + | 0.209180i | \(0.932921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 33186.2i | − | 0.0143777i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4882.13 | + | 4882.13i | 0.00208532 | + | 0.00208532i | 0.708149 | − | 0.706063i | \(-0.249531\pi\) |
−0.706063 | + | 0.708149i | \(0.749531\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −336659. | + | 3.25833e6i | −0.141781 | + | 1.37222i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.36475e6 | − | 1.36475e6i | 0.566737 | − | 0.566737i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.85803e6 | 1.57990 | 0.789951 | − | 0.613170i | \(-0.210106\pi\) | ||||
0.789951 | + | 0.613170i | \(0.210106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.33764e6 | −0.944081 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.89147e6 | − | 4.89147e6i | 1.94838 | − | 1.94838i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.10335e6 | + | 2.58808e6i | 0.826380 | + | 1.01682i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 701915. | + | 701915.i | 0.272032 | + | 0.272032i | 0.829918 | − | 0.557886i | \(-0.188387\pi\) |
−0.557886 | + | 0.829918i | \(0.688387\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.00404e6i | 1.14852i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 5.81245e6i | − | 2.19242i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.74504e6 | − | 2.74504e6i | −1.02159 | − | 1.02159i | −0.999762 | − | 0.0218283i | \(-0.993051\pi\) |
−0.0218283 | − | 0.999762i | \(-0.506949\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.57279e6 | − | 2.36049e6i | 1.67920 | − | 0.866811i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −115.274 | + | 115.274i | −4.17714e−5 | + | 4.17714e-5i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.26919e6 | −0.811472 | −0.405736 | − | 0.913990i | \(-0.632985\pi\) | ||||
−0.405736 | + | 0.913990i | \(0.632985\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.04075e6 | −1.42610 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.29183e6 | + | 1.29183e6i | −0.449997 | + | 0.449997i | −0.895353 | − | 0.445356i | \(-0.853077\pi\) |
0.445356 | + | 0.895353i | \(0.353077\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.24615e6 | + | 4.26358e6i | −1.80380 | + | 1.46596i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.65894e6 | + | 6.65894e6i | 2.26010 | + | 2.26010i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 5.08803e6i | − | 1.70481i | −0.522884 | − | 0.852404i | \(-0.675144\pi\) | ||
0.522884 | − | 0.852404i | \(-0.324856\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 980835.i | 0.324455i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.68207e6 | − | 5.68207e6i | −1.85578 | − | 1.85578i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.79956e6 | − | 185935.i | −0.580327 | − | 0.0599608i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −424803. | + | 424803.i | −0.135273 | + | 0.135273i | −0.771501 | − | 0.636228i | \(-0.780494\pi\) |
0.636228 | + | 0.771501i | \(0.280494\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.10678e6 | 0.662502 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.57875e6 | 0.490289 | 0.245145 | − | 0.969487i | \(-0.421165\pi\) | ||||
0.245145 | + | 0.969487i | \(0.421165\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3849.06 | − | 3849.06i | 0.00118057 | − | 0.00118057i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.97961e6 | + | 1.03112e6i | 3.02326 | + | 0.312371i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 38877.1 | + | 38877.1i | 0.0116334 | + | 0.0116334i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 2.15206e6i | − | 0.636130i | −0.948069 | − | 0.318065i | \(-0.896967\pi\) | ||
0.948069 | − | 0.318065i | \(-0.103033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.83693e6i | 1.99644i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.89162e6 | + | 6.89162e6i | 1.98814 | + | 1.98814i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 623639. | − | 506835.i | 0.177751 | − | 0.144460i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.09557e6 | + | 5.09557e6i | −1.43500 | + | 1.43500i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.70273e6 | −0.752087 | −0.376043 | − | 0.926602i | \(-0.622716\pi\) | ||||
−0.376043 | + | 0.926602i | \(0.622716\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.60276e6 | −0.990673 | −0.495337 | − | 0.868701i | \(-0.664955\pi\) | ||||
−0.495337 | + | 0.868701i | \(0.664955\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.57318e6 | − | 7.57318e6i | 2.05791 | − | 2.05791i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −891365. | + | 583337.i | −0.239377 | + | 0.156656i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.19678e6 | + | 2.19678e6i | 0.583064 | + | 0.583064i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 54693.6i | − | 0.0143481i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 3.84787e6i | − | 0.997763i | −0.866670 | − | 0.498882i | \(-0.833744\pi\) | ||
0.866670 | − | 0.498882i | \(-0.166256\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.93938e6 | − | 1.93938e6i | −0.497100 | − | 0.497100i | 0.413434 | − | 0.910534i | \(-0.364329\pi\) |
−0.910534 | + | 0.413434i | \(0.864329\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −57377.1 | − | 70600.0i | −0.0145384 | − | 0.0178888i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −757065. | + | 757065.i | −0.189640 | + | 0.189640i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.92588e6 | −0.476945 | −0.238472 | − | 0.971149i | \(-0.576647\pi\) | ||||
−0.238472 | + | 0.971149i | \(0.576647\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.25790e7 | 3.07998 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 655444. | − | 655444.i | 0.158681 | − | 0.158681i | −0.623301 | − | 0.781982i | \(-0.714209\pi\) |
0.781982 | + | 0.623301i | \(0.214209\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 185379. | − | 1.79418e6i | 0.0443774 | − | 0.429504i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.72016e6 | − | 2.72016e6i | −0.643911 | − | 0.643911i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.59016e6i | 1.07451i | 0.843418 | + | 0.537257i | \(0.180540\pi\) | ||||
−0.843418 | + | 0.537257i | \(0.819460\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.02528e6i | 0.700366i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −260416. | − | 260416.i | −0.0596241 | − | 0.0596241i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3258.50 | + | 31537.2i | −0.000737887 | + | 0.00714159i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.50178e6 | + | 2.50178e6i | −0.560349 | + | 0.560349i | −0.929407 | − | 0.369057i | \(-0.879681\pi\) |
0.369057 | + | 0.929407i | \(0.379681\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.83370e6 | −0.849350 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.98032e6 | −0.653145 | −0.326573 | − | 0.945172i | \(-0.605894\pi\) | ||||
−0.326573 | + | 0.945172i | \(0.605894\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −268149. | + | 268149.i | −0.0581331 | + | 0.0581331i | −0.735576 | − | 0.677443i | \(-0.763088\pi\) |
0.677443 | + | 0.735576i | \(0.263088\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.91585e6 | + | 2.35737e6i | 0.410893 | + | 0.505586i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.69656e6 | − | 4.69656e6i | −0.996525 | − | 0.996525i | 0.00346931 | − | 0.999994i | \(-0.498896\pi\) |
−0.999994 | + | 0.00346931i | \(0.998896\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.76500e6i | 1.42015i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.67528e7i | 3.47966i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.70603e6 | + | 6.70603e6i | 1.37820 | + | 1.37820i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.13826e6 | − | 237754.i | −0.231477 | − | 0.0483496i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.33602e7 | + | 1.33602e7i | −2.68854 | + | 2.68854i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.68594e6 | 1.13231 | 0.566153 | − | 0.824300i | \(-0.308431\pi\) | ||||
0.566153 | + | 0.824300i | \(0.308431\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 257.857 | 5.08178e−5 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.15192e7 | + | 1.15192e7i | −2.24676 | + | 2.24676i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.50307e6 | + | 1.22155e6i | −0.290151 | + | 0.235807i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.35039e6 | − | 4.35039e6i | −0.831200 | − | 0.831200i | 0.156481 | − | 0.987681i | \(-0.449985\pi\) |
−0.987681 | + | 0.156481i | \(0.949985\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 253692.i | − | 0.0479772i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.84948e6i | − | 0.720606i | −0.932835 | − | 0.360303i | \(-0.882673\pi\) | ||
0.932835 | − | 0.360303i | \(-0.117327\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13316.6 | + | 13316.6i | 0.00246760 | + | 0.00246760i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.18586e7 | + | 2.25848e6i | 4.00967 | + | 0.414289i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.96368e6 | − | 7.96368e6i | 1.44618 | − | 1.44618i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.16271e6 | 1.46752 | 0.733758 | − | 0.679411i | \(-0.237765\pi\) | ||||
0.733758 | + | 0.679411i | \(0.237765\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.49455e6 | 1.33399 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.68480e6 | + | 2.68480e6i | −0.473143 | + | 0.473143i | −0.902930 | − | 0.429787i | \(-0.858589\pi\) |
0.429787 | + | 0.902930i | \(0.358589\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.12790e6 | − | 736472.i | −1.24375 | − | 0.128507i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.73382e6 | + | 7.73382e6i | 1.33621 | + | 1.33621i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 9.38152e6i | − | 1.60501i | −0.596643 | − | 0.802507i | \(-0.703499\pi\) | ||
0.596643 | − | 0.802507i | \(-0.296501\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1.14663e7i | − | 1.94255i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.95907e6 | − | 2.95907e6i | −0.496435 | − | 0.496435i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 515476. | − | 418931.i | 0.0856427 | − | 0.0696024i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.62674e6 | − | 7.62674e6i | 1.25491 | − | 1.25491i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.57741e6 | −0.582976 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.02177e7 | 1.64914 | 0.824572 | − | 0.565757i | \(-0.191416\pi\) | ||||
0.824572 | + | 0.565757i | \(0.191416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −638202. | + | 638202.i | −0.102024 | + | 0.102024i | −0.756277 | − | 0.654252i | \(-0.772984\pi\) |
0.654252 | + | 0.756277i | \(0.272984\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.73194e7 | − | 3.61758e6i | −2.74242 | − | 0.572822i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −444647. | − | 444647.i | −0.0697411 | − | 0.0697411i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1.84246e6i | − | 0.286260i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 3.16814e7i | − | 4.87606i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10032.8 | + | 10032.8i | 0.00152969 | + | 0.00152969i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.72958e6 | − | 3.35863e6i | −0.412298 | − | 0.507315i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.80513e6 | + | 4.80513e6i | −0.719068 | + | 0.719068i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.26679e7 | 1.87816 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.81061e6 | 1.14734 | 0.573669 | − | 0.819087i | \(-0.305519\pi\) | ||||
0.573669 | + | 0.819087i | \(0.305519\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.25343e7 | + | 1.25343e7i | −1.82432 | + | 1.82432i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 100290. | − | 970655.i | 0.0144633 | − | 0.139982i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.78434e6 | + | 4.78434e6i | 0.683682 | + | 0.683682i | 0.960828 | − | 0.277146i | \(-0.0893886\pi\) |
−0.277146 | + | 0.960828i | \(0.589389\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 1.00988e7i | − | 1.43001i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20557.0i | 0.00288457i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.39829e6 | + | 4.39829e6i | 0.611605 | + | 0.611605i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14789.2 | + | 143136.i | −0.00203803 | + | 0.0197250i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.45559e6 | + | 5.45559e6i | −0.745082 | + | 0.745082i | −0.973551 | − | 0.228469i | \(-0.926628\pi\) |
0.228469 | + | 0.973551i | \(0.426628\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44478.5 | 0.00602034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.31825e6 | −0.847597 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 970144. | − | 970144.i | 0.128993 | − | 0.128993i | −0.639663 | − | 0.768656i | \(-0.720926\pi\) |
0.768656 | + | 0.639663i | \(0.220926\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.26721e6 | − | 5.25061e6i | −0.562371 | − | 0.691973i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.43911e7 | − | 2.43911e7i | −3.18621 | − | 3.18621i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.24295e7i | − | 1.60943i | −0.593661 | − | 0.804715i | \(-0.702318\pi\) | ||
0.593661 | − | 0.804715i | \(-0.297682\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.36788e7i | 1.75573i | 0.478909 | + | 0.877864i | \(0.341032\pi\) | ||||
−0.478909 | + | 0.877864i | \(0.658968\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.19455e7 | − | 1.19455e7i | −1.51991 | − | 1.51991i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.52363e6 | − | 4.92370e6i | 0.948981 | − | 0.621043i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.07760e6 | − | 1.07760e6i | 0.134747 | − | 0.134747i | −0.636516 | − | 0.771263i | \(-0.719625\pi\) |
0.771263 | + | 0.636516i | \(0.219625\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.57083e7 | −3.18696 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.76299e6 | −0.339577 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.34547e7 | + | 1.34547e7i | −1.63946 | + | 1.63946i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 79979.7 | − | 65000.0i | 0.00966251 | − | 0.00785279i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −998920. | − | 998920.i | −0.119656 | − | 0.119656i | 0.644743 | − | 0.764399i | \(-0.276964\pi\) |
−0.764399 | + | 0.644743i | \(0.776964\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 686408.i | − | 0.0815256i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.17933e7i | 1.38888i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.60583e6 | − | 9.60583e6i | −1.12176 | − | 1.12176i | −0.991478 | − | 0.130278i | \(-0.958413\pi\) |
−0.130278 | − | 0.991478i | \(-0.541587\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.64321e6 | + | 376425.i | 0.421882 | + | 0.0435899i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.61104e6 | − | 2.61104e6i | 0.299832 | − | 0.299832i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.45847e6 | 1.07709 | 0.538547 | − | 0.842595i | \(-0.318973\pi\) | ||||
0.538547 | + | 0.842595i | \(0.318973\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.44386e6 | −0.163057 | −0.0815287 | − | 0.996671i | \(-0.525980\pi\) | ||||
−0.0815287 | + | 0.996671i | \(0.525980\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.55497e7 | − | 1.55497e7i | 1.74152 | − | 1.74152i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.30578e7 | + | 1.34917e6i | 1.45038 | + | 0.149857i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.07148e7 | + | 1.07148e7i | 1.18036 | + | 1.18036i | 0.979651 | + | 0.200707i | \(0.0643240\pi\) |
0.200707 | + | 0.979651i | \(0.435676\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 312788.i | 0.0341749i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 50585.3i | − | 0.00548177i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.16515e7 | + | 1.16515e7i | 1.25237 | + | 1.25237i | 0.954656 | + | 0.297711i | \(0.0962233\pi\) |
0.297711 | + | 0.954656i | \(0.403777\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.14460e6 | + | 4.99376e6i | −0.655098 | + | 0.532402i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −250447. | + | 250447.i | −0.0264852 | + | 0.0264852i | −0.720225 | − | 0.693740i | \(-0.755962\pi\) |
0.693740 | + | 0.720225i | \(0.255962\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.33339e6 | 0.244771 | 0.122386 | − | 0.992483i | \(-0.460946\pi\) | ||||
0.122386 | + | 0.992483i | \(0.460946\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.23586e7 | 3.36714 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.38516e6 | + | 4.38516e6i | −0.452653 | + | 0.452653i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.94913e6 | + | 3.90904e6i | 0.916390 | + | 0.400286i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.87679e6 | − | 4.87679e6i | −0.495410 | − | 0.495410i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 29787.9i | − | 0.00300201i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.87636e6i | 0.587536i | 0.955877 | + | 0.293768i | \(0.0949094\pi\) | ||||
−0.955877 | + | 0.293768i | \(0.905091\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 91194.0 | + | 91194.0i | 0.00904601 | + | 0.00904601i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.83615e6 | − | 5.95067e6i | −0.475954 | − | 0.585641i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 42010.7 | − | 42010.7i | 0.00410215 | − | 0.00410215i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.66098e7 | −3.54687 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.87093e6 | 0.179851 | 0.0899254 | − | 0.995949i | \(-0.471337\pi\) | ||||
0.0899254 | + | 0.995949i | \(0.471337\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.11386e6 | + | 8.11386e6i | −0.773927 | + | 0.773927i | −0.978791 | − | 0.204864i | \(-0.934325\pi\) |
0.204864 | + | 0.978791i | \(0.434325\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.55103e6 | + | 2.46900e7i | −0.241444 | + | 2.33680i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.28000e7 | + | 1.28000e7i | 1.20213 | + | 1.20213i | 0.973518 | + | 0.228610i | \(0.0734179\pi\) |
0.228610 | + | 0.973518i | \(0.426582\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 3.19055e7i | − | 2.97340i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1.04442e7i | − | 0.965874i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.18312e6 | + | 7.18312e6i | 0.659220 | + | 0.659220i | 0.955196 | − | 0.295975i | \(-0.0956447\pi\) |
−0.295975 | + | 0.955196i | \(0.595645\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.56723e6 | − | 1.51683e7i | 0.142735 | − | 1.38145i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.63559e7 | + | 2.63559e7i | −2.38212 | + | 2.38212i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.69340e7 | −1.51895 | −0.759477 | − | 0.650534i | \(-0.774545\pi\) | ||||
−0.759477 | + | 0.650534i | \(0.774545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.24863e7 | 1.11156 | 0.555778 | − | 0.831331i | \(-0.312421\pi\) | ||||
0.555778 | + | 0.831331i | \(0.312421\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −20953.3 | + | 20953.3i | −0.00185126 | + | 0.00185126i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.52149e6 | + | 3.10258e6i | 0.221107 | + | 0.272063i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −112399. | − | 112399.i | −0.00978249 | − | 0.00978249i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.24439e7i | 1.07496i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.01702e7i | − | 0.872014i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.56500e6 | + | 2.56500e6i | 0.218298 | + | 0.218298i | 0.807781 | − | 0.589483i | \(-0.200668\pi\) |
−0.589483 | + | 0.807781i | \(0.700668\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.92448e7 | + | 2.94069e7i | 1.62575 | + | 2.48422i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.86486e6 | − | 6.86486e6i | 0.575652 | − | 0.575652i | −0.358050 | − | 0.933702i | \(-0.616558\pi\) |
0.933702 | + | 0.358050i | \(0.116558\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.65923e6 | 0.554306 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.52375e7 | −2.08535 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.80708e6 | − | 9.80708e6i | 0.804430 | − | 0.804430i | −0.179355 | − | 0.983784i | \(-0.557401\pi\) |
0.983784 | + | 0.179355i | \(0.0574010\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.00685e7 | + | 8.18274e6i | −0.819858 | + | 0.666304i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.09892e7 | + | 1.09892e7i | 0.888334 | + | 0.888334i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 89239.8i | 0.00716160i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 5.31783e6i | − | 0.423681i | −0.977304 | − | 0.211841i | \(-0.932054\pi\) | ||
0.977304 | − | 0.211841i | \(-0.0679458\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.34245e7 | − | 5.34245e7i | −4.22579 | − | 4.22579i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.36027e7 | − | 1.40546e6i | −1.06822 | − | 0.110371i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.15900e6 | − | 1.15900e6i | 0.0903649 | − | 0.0903649i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.95636e6 | −0.693328 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.52528e6 | −0.732121 | −0.366060 | − | 0.930591i | \(-0.619294\pi\) | ||||
−0.366060 | + | 0.930591i | \(0.619294\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22992.0 | − | 22992.0i | 0.00175464 | − | 0.00175464i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.80798e7 | + | 2.90127e6i | 2.12775 | + | 0.219845i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.74213e7 | + | 1.74213e7i | 1.31078 | + | 1.31078i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.71196e6i | 0.725590i | 0.931869 | + | 0.362795i | \(0.118177\pi\) | ||||
−0.931869 | + | 0.362795i | \(0.881823\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 2.02194e7i | − | 1.50001i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.75307e6 | + | 3.75307e6i | 0.276480 | + | 0.276480i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 80545.3 | − | 65459.7i | 0.00589217 | − | 0.00478860i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.44149e7 | − | 2.44149e7i | 1.77361 | − | 1.77361i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.73163e6 | −0.702042 | −0.351021 | − | 0.936368i | \(-0.614165\pi\) | ||||
−0.351021 | + | 0.936368i | \(0.614165\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.28378e6 | −0.163612 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.86465e7 | − | 2.86465e7i | 2.03810 | − | 2.03810i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 35298.7 | − | 168994.i | 0.00249410 | − | 0.0119406i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.43193e7 | − | 1.43193e7i | −1.00482 | − | 1.00482i | −0.999988 | − | 0.00482795i | \(-0.998463\pi\) |
−0.00482795 | − | 0.999988i | \(-0.501537\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.16248e7i | 2.20399i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 5.13820e6i | − | 0.355646i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.05150e6 | − | 6.05150e6i | −0.416009 | − | 0.416009i | 0.467816 | − | 0.883826i | \(-0.345041\pi\) |
−0.883826 | + | 0.467816i | \(0.845041\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.09106e7 | + | 2.57296e7i | 1.42774 | + | 1.75677i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.56596e7 | − | 1.56596e7i | 1.06197 | − | 1.06197i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.40664e7 | 1.62107 | 0.810533 | − | 0.585693i | \(-0.199178\pi\) | ||||
0.810533 | + | 0.585693i | \(0.199178\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −32345.9 | −0.00216408 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −431915. | + | 431915.i | −0.0287029 | + | 0.0287029i | −0.721313 | − | 0.692610i | \(-0.756461\pi\) |
0.692610 | + | 0.721313i | \(0.256461\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 750276. | − | 7.26150e6i | 0.0495257 | − | 0.479331i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.35086e6 | + | 6.35086e6i | 0.416420 | + | 0.416420i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.48802e7i | 0.969178i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 6.74056e6i | − | 0.436110i | −0.975936 | − | 0.218055i | \(-0.930029\pi\) | ||
0.975936 | − | 0.218055i | \(-0.0699712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.36925e6 | + | 6.36925e6i | 0.409355 | + | 0.409355i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 71827.9 | − | 695182.i | 0.00458591 | − | 0.0443845i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.62480e7 | + | 1.62480e7i | −1.03053 | + | 1.03053i | −0.0310107 | + | 0.999519i | \(0.509873\pi\) |
−0.999519 | + | 0.0310107i | \(0.990127\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.33296e7 | 3.36019 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.16648e6 | 0.0730156 | 0.0365078 | − | 0.999333i | \(-0.488377\pi\) | ||||
0.0365078 | + | 0.999333i | \(0.488377\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.37237e6 | + | 2.37237e6i | −0.147527 | + | 0.147527i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.50886e6 | − | 9.23932e6i | −0.463896 | − | 0.570803i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −105809. | − | 105809.i | −0.00649430 | − | 0.00649430i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.27850e7i | − | 0.779626i | −0.920894 | − | 0.389813i | \(-0.872540\pi\) | ||
0.920894 | − | 0.389813i | \(-0.127460\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 4.01720e7i | − | 2.43381i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.30426e7 | + | 2.30426e7i | 1.38702 | + | 1.38702i | 0.831514 | + | 0.555504i | \(0.187475\pi\) |
0.555504 | + | 0.831514i | \(0.312525\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.17864e6 | + | 5.64280e6i | −0.0704898 | + | 0.337474i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 349838. | − | 349838.i | 0.0207881 | − | 0.0207881i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.78916e6 | 0.105634 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.68687e7 | −2.16287 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 439326. | − | 439326.i | 0.0256084 | − | 0.0256084i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.46713e7 | + | 2.00505e7i | −1.42895 | + | 1.16132i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.89243e7 | + | 1.89243e7i | 1.08914 | + | 1.08914i | 0.995617 | + | 0.0935222i | \(0.0298126\pi\) |
0.0935222 | + | 0.995617i | \(0.470187\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.99144e7i | 2.85452i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.32625e7i | 1.32195i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33727.6 | − | 33727.6i | −0.00190459 | − | 0.00190459i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.95368e7 | − | 5.11827e6i | −2.77978 | − | 0.287214i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.83940e7 | − | 1.83940e7i | 1.02572 | − | 1.02572i | 0.0260618 | − | 0.999660i | \(-0.491703\pi\) |
0.999660 | − | 0.0260618i | \(-0.00829668\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.84365e6 | −0.323830 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.01590e7 | 1.11017 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.65423e7 | + | 2.65423e7i | −1.45261 | + | 1.45261i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.07507e7 | − | 3.17724e6i | −1.67250 | − | 0.172807i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.54403e7 | + | 2.54403e7i | 1.37511 | + | 1.37511i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 2.81220e6i | − | 0.151069i | −0.997143 | − | 0.0755344i | \(-0.975934\pi\) | ||
0.997143 | − | 0.0755344i | \(-0.0240663\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.65169e6i | 0.301736i | 0.988554 | + | 0.150868i | \(0.0482068\pi\) | ||||
−0.988554 | + | 0.150868i | \(0.951793\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.04421e7 | + | 1.04421e7i | 0.554067 | + | 0.554067i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 373603. | − | 303630.i | 0.0197023 | − | 0.0160122i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.96596e6 | − | 3.96596e6i | 0.207870 | − | 0.207870i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −354344. | −0.0184593 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.26086e7 | −0.652844 | −0.326422 | − | 0.945224i | \(-0.605843\pi\) | ||||
−0.326422 | + | 0.945224i | \(0.605843\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.12950e7 | − | 1.12950e7i | 0.581282 | − | 0.581282i | −0.353974 | − | 0.935255i | \(-0.615170\pi\) |
0.935255 | + | 0.353974i | \(0.115170\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.17170e7 | + | 4.84650e7i | 1.62240 | + | 2.47909i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.08514e6 | + | 8.08514e6i | 0.411078 | + | 0.411078i | 0.882114 | − | 0.471036i | \(-0.156120\pi\) |
−0.471036 | + | 0.882114i | \(0.656120\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 7.84537e6i | − | 0.396485i | −0.980153 | − | 0.198243i | \(-0.936477\pi\) | ||
0.980153 | − | 0.198243i | \(-0.0635234\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1.30955e7i | − | 0.657839i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.85312e6 | − | 4.85312e6i | −0.242331 | − | 0.242331i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.96981e6 | + | 1.10370e7i | 0.445212 | + | 0.547814i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.46693e7 | + | 1.46693e7i | −0.723762 | + | 0.723762i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.47278e7 | −1.21278 | −0.606389 | − | 0.795168i | \(-0.707383\pi\) | ||||
−0.606389 | + | 0.795168i | \(0.707383\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.05081e7 | 0.999851 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.08936e7 | + | 2.08936e7i | −1.01261 | + | 1.01261i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.13314e6 | + | 2.06455e7i | −0.102773 | + | 0.994681i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.19146e7 | − | 3.19146e7i | −1.52855 | − | 1.52855i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 2.39656e7i | − | 1.14109i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 251426.i | 0.0119011i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.59901e7 | + | 1.59901e7i | 0.752452 | + | 0.752452i | 0.974936 | − | 0.222484i | \(-0.0714166\pi\) |
−0.222484 | + | 0.974936i | \(0.571417\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.33567e6 | − | 1.29272e7i | 0.0624862 | − | 0.604769i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.17808e6 | − | 2.17808e6i | 0.101303 | − | 0.101303i | −0.654639 | − | 0.755942i | \(-0.727179\pi\) |
0.755942 | + | 0.654639i | \(0.227179\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.18655e7 | 0.548659 | 0.274329 | − | 0.961636i | \(-0.411544\pi\) | ||||
0.274329 | + | 0.961636i | \(0.411544\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.72232e7 | 1.25150 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.71183e7 | − | 1.71183e7i | 0.782411 | − | 0.782411i | −0.197827 | − | 0.980237i | \(-0.563388\pi\) |
0.980237 | + | 0.197827i | \(0.0633883\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.28161e6 | − | 5.26833e6i | −0.194566 | − | 0.239405i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.71550e7 | − | 2.71550e7i | −1.22688 | − | 1.22688i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.03624e7i | − | 0.914701i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 103864.i | − | 0.00463897i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.53066e7 | − | 1.53066e7i | −0.679739 | − | 0.679739i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.54011e7 | − | 2.98353e7i | −0.680036 | − | 1.31738i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.01657e7 | − | 2.01657e7i | 0.885347 | − | 0.885347i | −0.108725 | − | 0.994072i | \(-0.534677\pi\) |
0.994072 | + | 0.108725i | \(0.0346769\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.07767e7 | −1.34354 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.91597e6 | −0.343609 | −0.171804 | − | 0.985131i | \(-0.554960\pi\) | ||||
−0.171804 | + | 0.985131i | \(0.554960\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.14814e7 | + | 3.14814e7i | −1.35879 | + | 1.35879i | −0.483380 | + | 0.875410i | \(0.660591\pi\) |
−0.875410 | + | 0.483380i | \(0.839409\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.48027e7 | − | 5.26656e7i | 2.78122 | − | 2.26031i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.71941e7 | + | 1.71941e7i | 0.733787 | + | 0.733787i | 0.971368 | − | 0.237581i | \(-0.0763545\pi\) |
−0.237581 | + | 0.971368i | \(0.576354\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.63640e7i | 1.11881i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.12921e8i | 4.76521i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.51047e6 | − | 4.51047e6i | −0.189275 | − | 0.189275i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.28273e7 | − | 1.32535e6i | −0.535278 | − | 0.0553062i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 176858. | − | 176858.i | 0.00733909 | − | 0.00733909i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 101909. | 0.00420546 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.03091e7 | 0.423065 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.03446e7 | − | 6.03446e7i | 2.46274 | − | 2.46274i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.34605e7 | − | 3.45722e6i | −1.35803 | − | 0.140315i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.12763e7 | − | 1.12763e7i | −0.455143 | − | 0.455143i | 0.441914 | − | 0.897057i | \(-0.354300\pi\) |
−0.897057 | + | 0.441914i | \(0.854300\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 8.00873e7i | − | 3.21480i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 5.86631e6i | − | 0.234190i | −0.993121 | − | 0.117095i | \(-0.962642\pi\) | ||
0.993121 | − | 0.117095i | \(-0.0373583\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.39578e6 | + | 6.39578e6i | 0.253931 | + | 0.253931i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.06565e7 | − | 1.67877e7i | 0.815652 | − | 0.662886i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.70729e7 | + | 3.70729e7i | −1.45591 | + | 1.45591i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.68789e7 | 1.04984 | 0.524919 | − | 0.851152i | \(-0.324096\pi\) | ||||
0.524919 | + | 0.851152i | \(0.324096\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.58234e7 | −3.33393 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −122268. | + | 122268.i | −0.00472399 | + | 0.00472399i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −228492. | + | 149532.i | −0.00878043 | + | 0.00574619i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.24938e6 | + | 5.24938e6i | 0.200636 | + | 0.200636i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 2.10476e7i | − | 0.800134i | −0.916486 | − | 0.400067i | \(-0.868987\pi\) | ||
0.916486 | − | 0.400067i | \(-0.131013\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 7.49183e6i | − | 0.283278i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.85728e7 | + | 1.85728e7i | 0.698511 | + | 0.698511i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.56196e6 | − | 9.30466e6i | −0.282882 | − | 0.348074i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.37746e7 | + | 2.37746e7i | −0.884637 | + | 0.884637i | −0.994002 | − | 0.109365i | \(-0.965118\pi\) |
0.109365 | + | 0.994002i | \(0.465118\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.79507e7 | −1.40461 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.62621e7 | −0.966843 | −0.483421 | − | 0.875388i | \(-0.660606\pi\) | ||||
−0.483421 | + | 0.875388i | \(0.660606\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.78258e6 | + | 9.78258e6i | −0.358240 | + | 0.358240i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.24186e7 | − | 1.20193e8i | 0.452369 | − | 4.37823i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.23513e7 | − | 1.23513e7i | −0.447545 | − | 0.447545i | 0.446993 | − | 0.894538i | \(-0.352495\pi\) |
−0.894538 | + | 0.446993i | \(0.852495\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 176045.i | 0.00634539i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.04400e7i | 1.80852i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.58367e7 | − | 1.58367e7i | −0.564850 | − | 0.564850i | 0.365831 | − | 0.930681i | \(-0.380785\pi\) |
−0.930681 | + | 0.365831i | \(0.880785\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.29482e6 | − | 3.18887e7i | 0.116902 | − | 1.13143i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 724044. | − | 724044.i | 0.0255555 | − | 0.0255555i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.46078e7 | 1.56626 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.52264e7 | 0.881142 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.42028e7 | − | 3.42028e7i | 1.18849 | − | 1.18849i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.07688e7 | − | 3.78596e7i | −1.06363 | − | 1.30875i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.52477e7 | − | 3.52477e7i | −1.21217 | − | 1.21217i | −0.970311 | − | 0.241862i | \(-0.922242\pi\) |
−0.241862 | − | 0.970311i | \(-0.577758\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.73662e6i | 0.127841i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 3.28671e7i | − | 1.11870i | −0.828932 | − | 0.559350i | \(-0.811051\pi\) | ||
0.828932 | − | 0.559350i | \(-0.188949\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.32462e7 | + | 3.32462e7i | 1.12580 | + | 1.12580i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 265908. | + | 55541.5i | 0.00895819 | + | 0.00187114i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.09369e6 | + | 4.09369e6i | −0.137208 | + | 0.137208i | −0.772375 | − | 0.635167i | \(-0.780931\pi\) |
0.635167 | + | 0.772375i | \(0.280931\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.03016e7 | 0.676975 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.09060e7 | 0.361821 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.92387e7 | + | 2.92387e7i | −0.965105 | + | 0.965105i | −0.999411 | − | 0.0343062i | \(-0.989078\pi\) |
0.0343062 | + | 0.999411i | \(0.489078\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.73675e7 | + | 1.41147e7i | −0.570358 | + | 0.463534i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.86297e7 | − | 6.86297e7i | −2.24243 | − | 2.24243i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.33693e7i | 1.40991i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 4.98205e7i | − | 1.61148i | −0.592271 | − | 0.805739i | \(-0.701768\pi\) | ||
0.592271 | − | 0.805739i | \(-0.298232\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.18152e7 | + | 3.18152e7i | 1.02391 | + | 1.02391i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.97019e6 | + | 720177.i | 0.223196 | + | 0.0230612i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.22401e7 | − | 1.22401e7i | 0.389985 | − | 0.389985i | −0.484697 | − | 0.874682i | \(-0.661070\pi\) |
0.874682 | + | 0.484697i | \(0.161070\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −982728. | −0.0311544 |
(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 | 160.6.n.c.63.1 | ✓ | 16 | |
4.3 | odd | 2 | 160.6.n.d.63.8 | yes | 16 | ||
5.2 | odd | 4 | 160.6.n.d.127.8 | yes | 16 | ||
20.7 | even | 4 | inner | 160.6.n.c.127.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.n.c.63.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
160.6.n.c.127.1 | yes | 16 | 20.7 | even | 4 | inner | |
160.6.n.d.63.8 | yes | 16 | 4.3 | odd | 2 | ||
160.6.n.d.127.8 | yes | 16 | 5.2 | odd | 4 |