Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1457,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.m (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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1457.2 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.1457 |
Dual form | 3150.2.m.f.2843.2 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.828427i | 0.249780i | 0.992171 | + | 0.124890i | \(0.0398578\pi\) | ||||
−0.992171 | + | 0.124890i | \(0.960142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.585786 | − | 0.585786i | 0.162468 | − | 0.162468i | −0.621191 | − | 0.783659i | \(-0.713351\pi\) |
0.783659 | + | 0.621191i | \(0.213351\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.41421 | + | 4.41421i | −1.07060 | + | 1.07060i | −0.0732936 | + | 0.997310i | \(0.523351\pi\) |
−0.997310 | + | 0.0732936i | \(0.976649\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.07107i | 1.62221i | 0.584898 | + | 0.811107i | \(0.301135\pi\) | ||||
−0.584898 | + | 0.811107i | \(0.698865\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.585786 | + | 0.585786i | 0.124890 | + | 0.124890i | ||||
\(23\) | 0.828427 | + | 0.828427i | 0.172739 | + | 0.172739i | 0.788182 | − | 0.615443i | \(-0.211023\pi\) |
−0.615443 | + | 0.788182i | \(0.711023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 0.828427i | − | 0.162468i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.707107 | − | 0.707107i | 0.133631 | − | 0.133631i | ||||
\(29\) | −8.82843 | −1.63940 | −0.819699 | − | 0.572795i | \(-0.805859\pi\) | ||||
−0.819699 | + | 0.572795i | \(0.805859\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.17157 | −0.569631 | −0.284816 | − | 0.958582i | \(-0.591932\pi\) | ||||
−0.284816 | + | 0.958582i | \(0.591932\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.24264i | 1.07060i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.07107 | − | 8.07107i | −1.32688 | − | 1.32688i | −0.908081 | − | 0.418794i | \(-0.862453\pi\) |
−0.418794 | − | 0.908081i | \(-0.637547\pi\) | |||||||
\(38\) | 5.00000 | + | 5.00000i | 0.811107 | + | 0.811107i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.828427i | − | 0.129379i | −0.997905 | − | 0.0646893i | \(-0.979394\pi\) | ||
0.997905 | − | 0.0646893i | \(-0.0206056\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.58579 | + | 3.58579i | −0.546827 | + | 0.546827i | −0.925522 | − | 0.378694i | \(-0.876373\pi\) |
0.378694 | + | 0.925522i | \(0.376373\pi\) | |||||||
\(44\) | 0.828427 | 0.124890 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.17157 | 0.172739 | ||||||||
\(47\) | −3.58579 | + | 3.58579i | −0.523041 | + | 0.523041i | −0.918488 | − | 0.395448i | \(-0.870589\pi\) |
0.395448 | + | 0.918488i | \(0.370589\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.585786 | − | 0.585786i | −0.0812340 | − | 0.0812340i | ||||
\(53\) | −0.828427 | − | 0.828427i | −0.113793 | − | 0.113793i | 0.647917 | − | 0.761711i | \(-0.275640\pi\) |
−0.761711 | + | 0.647917i | \(0.775640\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 1.00000i | − | 0.133631i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.24264 | + | 6.24264i | −0.819699 | + | 0.819699i | ||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.41421 | 1.20537 | 0.602683 | − | 0.797981i | \(-0.294098\pi\) | ||||
0.602683 | + | 0.797981i | \(0.294098\pi\) | |||||||
\(62\) | −2.24264 | + | 2.24264i | −0.284816 | + | 0.284816i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.41421 | + | 2.41421i | 0.294943 | + | 0.294943i | 0.839029 | − | 0.544086i | \(-0.183124\pi\) |
−0.544086 | + | 0.839029i | \(0.683124\pi\) | |||||||
\(68\) | 4.41421 | + | 4.41421i | 0.535302 | + | 0.535302i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.75736i | 0.445917i | 0.974828 | + | 0.222958i | \(0.0715714\pi\) | ||||
−0.974828 | + | 0.222958i | \(0.928429\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | − | 6.00000i | 0.702247 | − | 0.702247i | −0.262646 | − | 0.964892i | \(-0.584595\pi\) |
0.964892 | + | 0.262646i | \(0.0845950\pi\) | |||||||
\(74\) | −11.4142 | −1.32688 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.07107 | 0.811107 | ||||||||
\(77\) | −0.585786 | + | 0.585786i | −0.0667566 | + | 0.0667566i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.31371i | 1.04787i | 0.851757 | + | 0.523937i | \(0.175537\pi\) | ||||
−0.851757 | + | 0.523937i | \(0.824463\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.585786 | − | 0.585786i | −0.0646893 | − | 0.0646893i | ||||
\(83\) | −1.65685 | − | 1.65685i | −0.181863 | − | 0.181863i | 0.610304 | − | 0.792167i | \(-0.291047\pi\) |
−0.792167 | + | 0.610304i | \(0.791047\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.07107i | 0.546827i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.585786 | − | 0.585786i | 0.0624450 | − | 0.0624450i | ||||
\(89\) | 9.31371 | 0.987251 | 0.493626 | − | 0.869675i | \(-0.335671\pi\) | ||||
0.493626 | + | 0.869675i | \(0.335671\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.828427 | 0.0868428 | ||||||||
\(92\) | 0.828427 | − | 0.828427i | 0.0863695 | − | 0.0863695i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.07107i | 0.523041i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.242641 | − | 0.242641i | −0.0246364 | − | 0.0246364i | 0.694681 | − | 0.719318i | \(-0.255545\pi\) |
−0.719318 | + | 0.694681i | \(0.755545\pi\) | |||||||
\(98\) | 0.707107 | + | 0.707107i | 0.0714286 | + | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.6569i | 1.55792i | 0.627077 | + | 0.778958i | \(0.284251\pi\) | ||||
−0.627077 | + | 0.778958i | \(0.715749\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.585786 | + | 0.585786i | −0.0577193 | + | 0.0577193i | −0.735377 | − | 0.677658i | \(-0.762995\pi\) |
0.677658 | + | 0.735377i | \(0.262995\pi\) | |||||||
\(104\) | −0.828427 | −0.0812340 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.17157 | −0.113793 | ||||||||
\(107\) | 5.07107 | − | 5.07107i | 0.490239 | − | 0.490239i | −0.418143 | − | 0.908381i | \(-0.637319\pi\) |
0.908381 | + | 0.418143i | \(0.137319\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.14214i | 0.779875i | 0.920841 | + | 0.389938i | \(0.127503\pi\) | ||||
−0.920841 | + | 0.389938i | \(0.872497\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.707107 | − | 0.707107i | −0.0668153 | − | 0.0668153i | ||||
\(113\) | −2.58579 | − | 2.58579i | −0.243250 | − | 0.243250i | 0.574943 | − | 0.818193i | \(-0.305024\pi\) |
−0.818193 | + | 0.574943i | \(0.805024\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.82843i | 0.819699i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.65685 | + | 5.65685i | −0.520756 | + | 0.520756i | ||||
\(119\) | −6.24264 | −0.572262 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3137 | 0.937610 | ||||||||
\(122\) | 6.65685 | − | 6.65685i | 0.602683 | − | 0.602683i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.17157i | 0.284816i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.82843 | − | 6.82843i | −0.605925 | − | 0.605925i | 0.335954 | − | 0.941879i | \(-0.390941\pi\) |
−0.941879 | + | 0.335954i | \(0.890941\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.00000i | − | 0.524222i | −0.965038 | − | 0.262111i | \(-0.915581\pi\) | ||
0.965038 | − | 0.262111i | \(-0.0844187\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.00000 | + | 5.00000i | −0.433555 | + | 0.433555i | ||||
\(134\) | 3.41421 | 0.294943 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.24264 | 0.535302 | ||||||||
\(137\) | −13.0711 | + | 13.0711i | −1.11674 | + | 1.11674i | −0.124520 | + | 0.992217i | \(0.539739\pi\) |
−0.992217 | + | 0.124520i | \(0.960261\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.24264i | 0.699132i | 0.936912 | + | 0.349566i | \(0.113671\pi\) | ||||
−0.936912 | + | 0.349566i | \(0.886329\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.65685 | + | 2.65685i | 0.222958 | + | 0.222958i | ||||
\(143\) | 0.485281 | + | 0.485281i | 0.0405813 | + | 0.0405813i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 8.48528i | − | 0.702247i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.07107 | + | 8.07107i | −0.663438 | + | 0.663438i | ||||
\(149\) | −17.3137 | −1.41839 | −0.709197 | − | 0.705010i | \(-0.750942\pi\) | ||||
−0.709197 | + | 0.705010i | \(0.750942\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.31371 | 0.757939 | 0.378969 | − | 0.925409i | \(-0.376279\pi\) | ||||
0.378969 | + | 0.925409i | \(0.376279\pi\) | |||||||
\(152\) | 5.00000 | − | 5.00000i | 0.405554 | − | 0.405554i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.828427i | 0.0667566i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.41421 | − | 5.41421i | −0.432101 | − | 0.432101i | 0.457241 | − | 0.889343i | \(-0.348838\pi\) |
−0.889343 | + | 0.457241i | \(0.848838\pi\) | |||||||
\(158\) | 6.58579 | + | 6.58579i | 0.523937 | + | 0.523937i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.17157i | 0.0923329i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.8995 | − | 14.8995i | 1.16702 | − | 1.16702i | 0.184114 | − | 0.982905i | \(-0.441059\pi\) |
0.982905 | − | 0.184114i | \(-0.0589414\pi\) | |||||||
\(164\) | −0.828427 | −0.0646893 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.34315 | −0.181863 | ||||||||
\(167\) | −12.8995 | + | 12.8995i | −0.998193 | + | 0.998193i | −0.999998 | − | 0.00180548i | \(-0.999425\pi\) |
0.00180548 | + | 0.999998i | \(0.499425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.3137i | 0.947208i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.58579 | + | 3.58579i | 0.273414 | + | 0.273414i | ||||
\(173\) | −8.00000 | − | 8.00000i | −0.608229 | − | 0.608229i | 0.334254 | − | 0.942483i | \(-0.391516\pi\) |
−0.942483 | + | 0.334254i | \(0.891516\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.828427i | − | 0.0624450i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.58579 | − | 6.58579i | 0.493626 | − | 0.493626i | ||||
\(179\) | −9.31371 | −0.696139 | −0.348070 | − | 0.937469i | \(-0.613163\pi\) | ||||
−0.348070 | + | 0.937469i | \(0.613163\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.07107 | 0.228271 | 0.114135 | − | 0.993465i | \(-0.463590\pi\) | ||||
0.114135 | + | 0.993465i | \(0.463590\pi\) | |||||||
\(182\) | 0.585786 | − | 0.585786i | 0.0434214 | − | 0.0434214i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 1.17157i | − | 0.0863695i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.65685 | − | 3.65685i | −0.267416 | − | 0.267416i | ||||
\(188\) | 3.58579 | + | 3.58579i | 0.261520 | + | 0.261520i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5858i | 0.765961i | 0.923757 | + | 0.382980i | \(0.125102\pi\) | ||||
−0.923757 | + | 0.382980i | \(0.874898\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.00000 | + | 6.00000i | −0.431889 | + | 0.431889i | −0.889271 | − | 0.457381i | \(-0.848787\pi\) |
0.457381 | + | 0.889271i | \(0.348787\pi\) | |||||||
\(194\) | −0.343146 | −0.0246364 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −8.82843 | + | 8.82843i | −0.628999 | + | 0.628999i | −0.947816 | − | 0.318817i | \(-0.896714\pi\) |
0.318817 | + | 0.947816i | \(0.396714\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.6569i | 0.826332i | 0.910656 | + | 0.413166i | \(0.135577\pi\) | ||||
−0.910656 | + | 0.413166i | \(0.864423\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.0711 | + | 11.0711i | 0.778958 | + | 0.778958i | ||||
\(203\) | −6.24264 | − | 6.24264i | −0.438147 | − | 0.438147i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.828427i | 0.0577193i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.585786 | + | 0.585786i | −0.0406170 | + | 0.0406170i | ||||
\(209\) | −5.85786 | −0.405197 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.4853 | 1.41026 | 0.705132 | − | 0.709076i | \(-0.250888\pi\) | ||||
0.705132 | + | 0.709076i | \(0.250888\pi\) | |||||||
\(212\) | −0.828427 | + | 0.828427i | −0.0568966 | + | 0.0568966i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 7.17157i | − | 0.490239i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.24264 | − | 2.24264i | −0.152240 | − | 0.152240i | ||||
\(218\) | 5.75736 | + | 5.75736i | 0.389938 | + | 0.389938i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.17157i | 0.347878i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.8995 | − | 11.8995i | 0.796849 | − | 0.796849i | −0.185748 | − | 0.982597i | \(-0.559471\pi\) |
0.982597 | + | 0.185748i | \(0.0594709\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.65685 | −0.243250 | ||||||||
\(227\) | 15.6569 | − | 15.6569i | 1.03918 | − | 1.03918i | 0.0399815 | − | 0.999200i | \(-0.487270\pi\) |
0.999200 | − | 0.0399815i | \(-0.0127299\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.0711i | 1.26025i | 0.776493 | + | 0.630126i | \(0.216997\pi\) | ||||
−0.776493 | + | 0.630126i | \(0.783003\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.24264 | + | 6.24264i | 0.409849 | + | 0.409849i | ||||
\(233\) | 2.58579 | + | 2.58579i | 0.169401 | + | 0.169401i | 0.786716 | − | 0.617315i | \(-0.211780\pi\) |
−0.617315 | + | 0.786716i | \(0.711780\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.00000i | 0.520756i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.41421 | + | 4.41421i | −0.286131 | + | 0.286131i | ||||
\(239\) | 17.2132 | 1.11343 | 0.556715 | − | 0.830704i | \(-0.312062\pi\) | ||||
0.556715 | + | 0.830704i | \(0.312062\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.65685 | 0.235559 | 0.117779 | − | 0.993040i | \(-0.462422\pi\) | ||||
0.117779 | + | 0.993040i | \(0.462422\pi\) | |||||||
\(242\) | 7.29289 | − | 7.29289i | 0.468805 | − | 0.468805i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 9.41421i | − | 0.602683i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.14214 | + | 4.14214i | 0.263558 | + | 0.263558i | ||||
\(248\) | 2.24264 | + | 2.24264i | 0.142408 | + | 0.142408i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.9706i | 1.70237i | 0.524868 | + | 0.851183i | \(0.324115\pi\) | ||||
−0.524868 | + | 0.851183i | \(0.675885\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.686292 | + | 0.686292i | −0.0431468 | + | 0.0431468i | ||||
\(254\) | −9.65685 | −0.605925 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.8995 | − | 12.8995i | 0.804648 | − | 0.804648i | −0.179170 | − | 0.983818i | \(-0.557341\pi\) |
0.983818 | + | 0.179170i | \(0.0573411\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 11.4142i | − | 0.709245i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.24264 | − | 4.24264i | −0.262111 | − | 0.262111i | ||||
\(263\) | −22.0000 | − | 22.0000i | −1.35658 | − | 1.35658i | −0.878099 | − | 0.478479i | \(-0.841188\pi\) |
−0.478479 | − | 0.878099i | \(-0.658812\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.07107i | 0.433555i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.41421 | − | 2.41421i | 0.147472 | − | 0.147472i | ||||
\(269\) | −1.31371 | −0.0800982 | −0.0400491 | − | 0.999198i | \(-0.512751\pi\) | ||||
−0.0400491 | + | 0.999198i | \(0.512751\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.8284 | 0.779271 | 0.389636 | − | 0.920969i | \(-0.372601\pi\) | ||||
0.389636 | + | 0.920969i | \(0.372601\pi\) | |||||||
\(272\) | 4.41421 | − | 4.41421i | 0.267651 | − | 0.267651i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.4853i | 1.11674i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.92893 | + | 3.92893i | 0.236067 | + | 0.236067i | 0.815219 | − | 0.579153i | \(-0.196616\pi\) |
−0.579153 | + | 0.815219i | \(0.696616\pi\) | |||||||
\(278\) | 5.82843 | + | 5.82843i | 0.349566 | + | 0.349566i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 27.0711i | − | 1.61492i | −0.589919 | − | 0.807462i | \(-0.700840\pi\) | ||
0.589919 | − | 0.807462i | \(-0.299160\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.0000 | − | 18.0000i | 1.06999 | − | 1.06999i | 0.0726300 | − | 0.997359i | \(-0.476861\pi\) |
0.997359 | − | 0.0726300i | \(-0.0231392\pi\) | |||||||
\(284\) | 3.75736 | 0.222958 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.686292 | 0.0405813 | ||||||||
\(287\) | 0.585786 | − | 0.585786i | 0.0345779 | − | 0.0345779i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 21.9706i | − | 1.29239i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.00000 | − | 6.00000i | −0.351123 | − | 0.351123i | ||||
\(293\) | −5.51472 | − | 5.51472i | −0.322173 | − | 0.322173i | 0.527427 | − | 0.849600i | \(-0.323157\pi\) |
−0.849600 | + | 0.527427i | \(0.823157\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 11.4142i | 0.663438i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.2426 | + | 12.2426i | −0.709197 | + | 0.709197i | ||||
\(299\) | 0.970563 | 0.0561291 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.07107 | −0.292291 | ||||||||
\(302\) | 6.58579 | − | 6.58579i | 0.378969 | − | 0.378969i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 7.07107i | − | 0.405554i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.4853 | + | 24.4853i | 1.39745 | + | 1.39745i | 0.807279 | + | 0.590169i | \(0.200939\pi\) |
0.590169 | + | 0.807279i | \(0.299061\pi\) | |||||||
\(308\) | 0.585786 | + | 0.585786i | 0.0333783 | + | 0.0333783i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 16.0000i | − | 0.907277i | −0.891186 | − | 0.453638i | \(-0.850126\pi\) | ||
0.891186 | − | 0.453638i | \(-0.149874\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.34315 | − | 8.34315i | 0.471582 | − | 0.471582i | −0.430844 | − | 0.902426i | \(-0.641784\pi\) |
0.902426 | + | 0.430844i | \(0.141784\pi\) | |||||||
\(314\) | −7.65685 | −0.432101 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.31371 | 0.523937 | ||||||||
\(317\) | −3.75736 | + | 3.75736i | −0.211034 | + | 0.211034i | −0.804707 | − | 0.593672i | \(-0.797677\pi\) |
0.593672 | + | 0.804707i | \(0.297677\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 7.31371i | − | 0.409489i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.828427 | + | 0.828427i | 0.0461664 | + | 0.0461664i | ||||
\(323\) | −31.2132 | − | 31.2132i | −1.73675 | − | 1.73675i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 21.0711i | − | 1.16702i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.585786 | + | 0.585786i | −0.0323446 | + | 0.0323446i | ||||
\(329\) | −5.07107 | −0.279577 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.1421 | −1.65676 | −0.828381 | − | 0.560165i | \(-0.810738\pi\) | ||||
−0.828381 | + | 0.560165i | \(0.810738\pi\) | |||||||
\(332\) | −1.65685 | + | 1.65685i | −0.0909317 | + | 0.0909317i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 18.2426i | 0.998193i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.4853 | + | 18.4853i | 1.00696 | + | 1.00696i | 0.999976 | + | 0.00698181i | \(0.00222240\pi\) |
0.00698181 | + | 0.999976i | \(0.497778\pi\) | |||||||
\(338\) | 8.70711 | + | 8.70711i | 0.473604 | + | 0.473604i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.62742i | − | 0.142283i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 5.07107 | 0.273414 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.3137 | −0.608229 | ||||||||
\(347\) | 9.17157 | − | 9.17157i | 0.492356 | − | 0.492356i | −0.416692 | − | 0.909048i | \(-0.636811\pi\) |
0.909048 | + | 0.416692i | \(0.136811\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.7279i | 0.895425i | 0.894178 | + | 0.447713i | \(0.147761\pi\) | ||||
−0.894178 | + | 0.447713i | \(0.852239\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.585786 | − | 0.585786i | −0.0312225 | − | 0.0312225i | ||||
\(353\) | 21.3848 | + | 21.3848i | 1.13820 | + | 1.13820i | 0.988773 | + | 0.149424i | \(0.0477418\pi\) |
0.149424 | + | 0.988773i | \(0.452258\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 9.31371i | − | 0.493626i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.58579 | + | 6.58579i | −0.348070 | + | 0.348070i | ||||
\(359\) | −4.72792 | −0.249530 | −0.124765 | − | 0.992186i | \(-0.539818\pi\) | ||||
−0.124765 | + | 0.992186i | \(0.539818\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −31.0000 | −1.63158 | ||||||||
\(362\) | 2.17157 | − | 2.17157i | 0.114135 | − | 0.114135i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 0.828427i | − | 0.0434214i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.0000 | − | 20.0000i | −1.04399 | − | 1.04399i | −0.998987 | − | 0.0450047i | \(-0.985670\pi\) |
−0.0450047 | − | 0.998987i | \(-0.514330\pi\) | |||||||
\(368\) | −0.828427 | − | 0.828427i | −0.0431847 | − | 0.0431847i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.17157i | − | 0.0608250i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.75736 | − | 2.75736i | 0.142771 | − | 0.142771i | −0.632109 | − | 0.774880i | \(-0.717810\pi\) |
0.774880 | + | 0.632109i | \(0.217810\pi\) | |||||||
\(374\) | −5.17157 | −0.267416 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.07107 | 0.261520 | ||||||||
\(377\) | −5.17157 | + | 5.17157i | −0.266350 | + | 0.266350i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.65685i | 0.290573i | 0.989390 | + | 0.145287i | \(0.0464104\pi\) | ||||
−0.989390 | + | 0.145287i | \(0.953590\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.48528 | + | 7.48528i | 0.382980 | + | 0.382980i | ||||
\(383\) | 3.24264 | + | 3.24264i | 0.165691 | + | 0.165691i | 0.785082 | − | 0.619391i | \(-0.212621\pi\) |
−0.619391 | + | 0.785082i | \(0.712621\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.48528i | 0.431889i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.242641 | + | 0.242641i | −0.0123182 | + | 0.0123182i | ||||
\(389\) | −17.3137 | −0.877840 | −0.438920 | − | 0.898526i | \(-0.644639\pi\) | ||||
−0.438920 | + | 0.898526i | \(0.644639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.31371 | −0.369870 | ||||||||
\(392\) | 0.707107 | − | 0.707107i | 0.0357143 | − | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.4853i | 0.628999i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.5858 | − | 22.5858i | −1.13355 | − | 1.13355i | −0.989583 | − | 0.143965i | \(-0.954015\pi\) |
−0.143965 | − | 0.989583i | \(-0.545985\pi\) | |||||||
\(398\) | 8.24264 | + | 8.24264i | 0.413166 | + | 0.413166i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 16.9289i | − | 0.845391i | −0.906272 | − | 0.422695i | \(-0.861084\pi\) | ||
0.906272 | − | 0.422695i | \(-0.138916\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.85786 | + | 1.85786i | −0.0925468 | + | 0.0925468i | ||||
\(404\) | 15.6569 | 0.778958 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.82843 | −0.438147 | ||||||||
\(407\) | 6.68629 | − | 6.68629i | 0.331427 | − | 0.331427i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 14.6863i | − | 0.726190i | −0.931752 | − | 0.363095i | \(-0.881720\pi\) | ||
0.931752 | − | 0.363095i | \(-0.118280\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.585786 | + | 0.585786i | 0.0288596 | + | 0.0288596i | ||||
\(413\) | −5.65685 | − | 5.65685i | −0.278356 | − | 0.278356i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.828427i | 0.0406170i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.14214 | + | 4.14214i | −0.202598 | + | 0.202598i | ||||
\(419\) | 20.0000 | 0.977064 | 0.488532 | − | 0.872546i | \(-0.337533\pi\) | ||||
0.488532 | + | 0.872546i | \(0.337533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.142136 | −0.00692727 | −0.00346363 | − | 0.999994i | \(-0.501103\pi\) | ||||
−0.00346363 | + | 0.999994i | \(0.501103\pi\) | |||||||
\(422\) | 14.4853 | − | 14.4853i | 0.705132 | − | 0.705132i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.17157i | 0.0568966i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.65685 | + | 6.65685i | 0.322148 | + | 0.322148i | ||||
\(428\) | −5.07107 | − | 5.07107i | −0.245119 | − | 0.245119i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.2132i | 1.40715i | 0.710621 | + | 0.703575i | \(0.248414\pi\) | ||||
−0.710621 | + | 0.703575i | \(0.751586\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.7574 | + | 15.7574i | −0.757250 | + | 0.757250i | −0.975821 | − | 0.218571i | \(-0.929861\pi\) |
0.218571 | + | 0.975821i | \(0.429861\pi\) | |||||||
\(434\) | −3.17157 | −0.152240 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.14214 | 0.389938 | ||||||||
\(437\) | −5.85786 | + | 5.85786i | −0.280220 | + | 0.280220i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13.7990i | − | 0.658590i | −0.944227 | − | 0.329295i | \(-0.893189\pi\) | ||
0.944227 | − | 0.329295i | \(-0.106811\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.65685 | + | 3.65685i | 0.173939 | + | 0.173939i | ||||
\(443\) | −7.51472 | − | 7.51472i | −0.357035 | − | 0.357035i | 0.505684 | − | 0.862719i | \(-0.331240\pi\) |
−0.862719 | + | 0.505684i | \(0.831240\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 16.8284i | − | 0.796849i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.707107 | + | 0.707107i | −0.0334077 | + | 0.0334077i | ||||
\(449\) | 23.7574 | 1.12118 | 0.560590 | − | 0.828094i | \(-0.310575\pi\) | ||||
0.560590 | + | 0.828094i | \(0.310575\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.686292 | 0.0323162 | ||||||||
\(452\) | −2.58579 | + | 2.58579i | −0.121625 | + | 0.121625i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 22.1421i | − | 1.03918i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.4853 | − | 24.4853i | −1.14537 | − | 1.14537i | −0.987452 | − | 0.157921i | \(-0.949521\pi\) |
−0.157921 | − | 0.987452i | \(-0.550479\pi\) | |||||||
\(458\) | 13.4853 | + | 13.4853i | 0.630126 | + | 0.630126i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 14.6863i | − | 0.684009i | −0.939698 | − | 0.342004i | \(-0.888894\pi\) | ||
0.939698 | − | 0.342004i | \(-0.111106\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.4853 | + | 22.4853i | −1.04498 | + | 1.04498i | −0.0460401 | + | 0.998940i | \(0.514660\pi\) |
−0.998940 | + | 0.0460401i | \(0.985340\pi\) | |||||||
\(464\) | 8.82843 | 0.409849 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.65685 | 0.169401 | ||||||||
\(467\) | −1.65685 | + | 1.65685i | −0.0766701 | + | 0.0766701i | −0.744402 | − | 0.667732i | \(-0.767265\pi\) |
0.667732 | + | 0.744402i | \(0.267265\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.41421i | 0.157654i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.65685 | + | 5.65685i | 0.260378 | + | 0.260378i | ||||
\(473\) | −2.97056 | − | 2.97056i | −0.136587 | − | 0.136587i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.24264i | 0.286131i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.1716 | − | 12.1716i | 0.556715 | − | 0.556715i | ||||
\(479\) | 1.65685 | 0.0757036 | 0.0378518 | − | 0.999283i | \(-0.487949\pi\) | ||||
0.0378518 | + | 0.999283i | \(0.487949\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.45584 | −0.431149 | ||||||||
\(482\) | 2.58579 | − | 2.58579i | 0.117779 | − | 0.117779i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 10.3137i | − | 0.468805i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0000 | + | 20.0000i | 0.906287 | + | 0.906287i | 0.995970 | − | 0.0896838i | \(-0.0285856\pi\) |
−0.0896838 | + | 0.995970i | \(0.528586\pi\) | |||||||
\(488\) | −6.65685 | − | 6.65685i | −0.301342 | − | 0.301342i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 10.9706i | − | 0.495095i | −0.968876 | − | 0.247547i | \(-0.920375\pi\) | ||
0.968876 | − | 0.247547i | \(-0.0796246\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38.9706 | − | 38.9706i | 1.75515 | − | 1.75515i | ||||
\(494\) | 5.85786 | 0.263558 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.17157 | 0.142408 | ||||||||
\(497\) | −2.65685 | + | 2.65685i | −0.119176 | + | 0.119176i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 24.0000i | − | 1.07439i | −0.843459 | − | 0.537194i | \(-0.819484\pi\) | ||
0.843459 | − | 0.537194i | \(-0.180516\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 19.0711 | + | 19.0711i | 0.851183 | + | 0.851183i | ||||
\(503\) | −17.5858 | − | 17.5858i | −0.784111 | − | 0.784111i | 0.196410 | − | 0.980522i | \(-0.437072\pi\) |
−0.980522 | + | 0.196410i | \(0.937072\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.970563i | 0.0431468i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.82843 | + | 6.82843i | −0.302962 | + | 0.302962i | ||||
\(509\) | 29.6569 | 1.31452 | 0.657258 | − | 0.753665i | \(-0.271716\pi\) | ||||
0.657258 | + | 0.753665i | \(0.271716\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.48528 | 0.375367 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 18.2426i | − | 0.804648i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.97056 | − | 2.97056i | −0.130645 | − | 0.130645i | ||||
\(518\) | −8.07107 | − | 8.07107i | −0.354622 | − | 0.354622i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.9706i | 1.18160i | 0.806817 | + | 0.590801i | \(0.201188\pi\) | ||||
−0.806817 | + | 0.590801i | \(0.798812\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.2843 | − | 26.2843i | 1.14933 | − | 1.14933i | 0.162647 | − | 0.986684i | \(-0.447997\pi\) |
0.986684 | − | 0.162647i | \(-0.0520030\pi\) | |||||||
\(524\) | −6.00000 | −0.262111 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −31.1127 | −1.35658 | ||||||||
\(527\) | 14.0000 | − | 14.0000i | 0.609850 | − | 0.609850i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 21.6274i | − | 0.940322i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.00000 | + | 5.00000i | 0.216777 | + | 0.216777i | ||||
\(533\) | −0.485281 | − | 0.485281i | −0.0210199 | − | 0.0210199i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 3.41421i | − | 0.147472i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.928932 | + | 0.928932i | −0.0400491 | + | 0.0400491i | ||||
\(539\) | −0.828427 | −0.0356829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.4853 | 1.13869 | 0.569346 | − | 0.822098i | \(-0.307197\pi\) | ||||
0.569346 | + | 0.822098i | \(0.307197\pi\) | |||||||
\(542\) | 9.07107 | − | 9.07107i | 0.389636 | − | 0.389636i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 6.24264i | − | 0.267651i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.72792 | − | 1.72792i | −0.0738806 | − | 0.0738806i | 0.669201 | − | 0.743082i | \(-0.266637\pi\) |
−0.743082 | + | 0.669201i | \(0.766637\pi\) | |||||||
\(548\) | 13.0711 | + | 13.0711i | 0.558368 | + | 0.558368i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 62.4264i | − | 2.65945i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.58579 | + | 6.58579i | −0.280056 | + | 0.280056i | ||||
\(554\) | 5.55635 | 0.236067 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.24264 | 0.349566 | ||||||||
\(557\) | −21.8995 | + | 21.8995i | −0.927911 | + | 0.927911i | −0.997571 | − | 0.0696594i | \(-0.977809\pi\) |
0.0696594 | + | 0.997571i | \(0.477809\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.20101i | 0.177684i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.1421 | − | 19.1421i | −0.807462 | − | 0.807462i | ||||
\(563\) | 8.14214 | + | 8.14214i | 0.343150 | + | 0.343150i | 0.857550 | − | 0.514400i | \(-0.171985\pi\) |
−0.514400 | + | 0.857550i | \(0.671985\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 25.4558i | − | 1.06999i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.65685 | − | 2.65685i | 0.111479 | − | 0.111479i | ||||
\(569\) | −26.3848 | −1.10611 | −0.553054 | − | 0.833146i | \(-0.686538\pi\) | ||||
−0.553054 | + | 0.833146i | \(0.686538\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.9706 | −1.04499 | −0.522493 | − | 0.852644i | \(-0.674998\pi\) | ||||
−0.522493 | + | 0.852644i | \(0.674998\pi\) | |||||||
\(572\) | 0.485281 | − | 0.485281i | 0.0202906 | − | 0.0202906i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 0.828427i | − | 0.0345779i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.8284 | − | 16.8284i | −0.700577 | − | 0.700577i | 0.263958 | − | 0.964534i | \(-0.414972\pi\) |
−0.964534 | + | 0.263958i | \(0.914972\pi\) | |||||||
\(578\) | −15.5355 | − | 15.5355i | −0.646193 | − | 0.646193i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2.34315i | − | 0.0972101i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.686292 | − | 0.686292i | 0.0284233 | − | 0.0284233i | ||||
\(584\) | −8.48528 | −0.351123 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.79899 | −0.322173 | ||||||||
\(587\) | 14.0000 | − | 14.0000i | 0.577842 | − | 0.577842i | −0.356466 | − | 0.934308i | \(-0.616019\pi\) |
0.934308 | + | 0.356466i | \(0.116019\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 22.4264i | − | 0.924064i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.07107 | + | 8.07107i | 0.331719 | + | 0.331719i | ||||
\(593\) | 11.5858 | + | 11.5858i | 0.475771 | + | 0.475771i | 0.903776 | − | 0.428005i | \(-0.140783\pi\) |
−0.428005 | + | 0.903776i | \(0.640783\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.3137i | 0.709197i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.686292 | − | 0.686292i | 0.0280645 | − | 0.0280645i | ||||
\(599\) | −19.0711 | −0.779223 | −0.389611 | − | 0.920979i | \(-0.627391\pi\) | ||||
−0.389611 | + | 0.920979i | \(0.627391\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.0000 | −0.734235 | −0.367118 | − | 0.930175i | \(-0.619655\pi\) | ||||
−0.367118 | + | 0.930175i | \(0.619655\pi\) | |||||||
\(602\) | −3.58579 | + | 3.58579i | −0.146146 | + | 0.146146i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 9.31371i | − | 0.378969i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.3848 | + | 24.3848i | 0.989748 | + | 0.989748i | 0.999948 | − | 0.0102004i | \(-0.00324696\pi\) |
−0.0102004 | + | 0.999948i | \(0.503247\pi\) | |||||||
\(608\) | −5.00000 | − | 5.00000i | −0.202777 | − | 0.202777i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.20101i | 0.169955i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.41421 | + | 6.41421i | −0.259068 | + | 0.259068i | −0.824675 | − | 0.565607i | \(-0.808642\pi\) |
0.565607 | + | 0.824675i | \(0.308642\pi\) | |||||||
\(614\) | 34.6274 | 1.39745 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.828427 | 0.0333783 | ||||||||
\(617\) | −27.4142 | + | 27.4142i | −1.10365 | + | 1.10365i | −0.109689 | + | 0.993966i | \(0.534985\pi\) |
−0.993966 | + | 0.109689i | \(0.965015\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 18.8701i | − | 0.758452i | −0.925304 | − | 0.379226i | \(-0.876190\pi\) | ||
0.925304 | − | 0.379226i | \(-0.123810\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.3137 | − | 11.3137i | −0.453638 | − | 0.453638i | ||||
\(623\) | 6.58579 | + | 6.58579i | 0.263854 | + | 0.263854i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 11.7990i | − | 0.471582i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.41421 | + | 5.41421i | −0.216051 | + | 0.216051i | ||||
\(629\) | 71.2548 | 2.84112 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.9706 | −1.15330 | −0.576650 | − | 0.816991i | \(-0.695640\pi\) | ||||
−0.576650 | + | 0.816991i | \(0.695640\pi\) | |||||||
\(632\) | 6.58579 | − | 6.58579i | 0.261969 | − | 0.261969i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.31371i | 0.211034i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.585786 | + | 0.585786i | 0.0232097 | + | 0.0232097i | ||||
\(638\) | −5.17157 | − | 5.17157i | −0.204745 | − | 0.204745i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.5269i | 0.968755i | 0.874859 | + | 0.484377i | \(0.160954\pi\) | ||||
−0.874859 | + | 0.484377i | \(0.839046\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.1421 | + | 28.1421i | −1.10982 | + | 1.10982i | −0.116644 | + | 0.993174i | \(0.537214\pi\) |
−0.993174 | + | 0.116644i | \(0.962786\pi\) | |||||||
\(644\) | 1.17157 | 0.0461664 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −44.1421 | −1.73675 | ||||||||
\(647\) | 24.2132 | − | 24.2132i | 0.951919 | − | 0.951919i | −0.0469767 | − | 0.998896i | \(-0.514959\pi\) |
0.998896 | + | 0.0469767i | \(0.0149587\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6.62742i | − | 0.260149i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.8995 | − | 14.8995i | −0.583509 | − | 0.583509i | ||||
\(653\) | −5.41421 | − | 5.41421i | −0.211875 | − | 0.211875i | 0.593189 | − | 0.805063i | \(-0.297869\pi\) |
−0.805063 | + | 0.593189i | \(0.797869\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.828427i | 0.0323446i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.58579 | + | 3.58579i | −0.139789 | + | 0.139789i | ||||
\(659\) | −21.7990 | −0.849168 | −0.424584 | − | 0.905389i | \(-0.639580\pi\) | ||||
−0.424584 | + | 0.905389i | \(0.639580\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.2426 | −1.40968 | −0.704838 | − | 0.709369i | \(-0.748980\pi\) | ||||
−0.704838 | + | 0.709369i | \(0.748980\pi\) | |||||||
\(662\) | −21.3137 | + | 21.3137i | −0.828381 | + | 0.828381i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.34315i | 0.0909317i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.31371 | − | 7.31371i | −0.283188 | − | 0.283188i | ||||
\(668\) | 12.8995 | + | 12.8995i | 0.499096 | + | 0.499096i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.79899i | 0.301077i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.7990 | + | 25.7990i | −0.994478 | + | 0.994478i | −0.999985 | − | 0.00550686i | \(-0.998247\pi\) |
0.00550686 | + | 0.999985i | \(0.498247\pi\) | |||||||
\(674\) | 26.1421 | 1.00696 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.3137 | 0.473604 | ||||||||
\(677\) | −24.4853 | + | 24.4853i | −0.941046 | + | 0.941046i | −0.998356 | − | 0.0573106i | \(-0.981747\pi\) |
0.0573106 | + | 0.998356i | \(0.481747\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 0.343146i | − | 0.0131687i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.85786 | − | 1.85786i | −0.0711413 | − | 0.0711413i | ||||
\(683\) | 15.8995 | + | 15.8995i | 0.608377 | + | 0.608377i | 0.942522 | − | 0.334145i | \(-0.108447\pi\) |
−0.334145 | + | 0.942522i | \(0.608447\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.58579 | − | 3.58579i | 0.136707 | − | 0.136707i | ||||
\(689\) | −0.970563 | −0.0369755 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.2132 | 0.959155 | 0.479578 | − | 0.877499i | \(-0.340790\pi\) | ||||
0.479578 | + | 0.877499i | \(0.340790\pi\) | |||||||
\(692\) | −8.00000 | + | 8.00000i | −0.304114 | + | 0.304114i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 12.9706i | − | 0.492356i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.65685 | + | 3.65685i | 0.138513 | + | 0.138513i | ||||
\(698\) | 11.8284 | + | 11.8284i | 0.447713 | + | 0.447713i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.51472i | 0.359366i | 0.983725 | + | 0.179683i | \(0.0575072\pi\) | ||||
−0.983725 | + | 0.179683i | \(0.942493\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 57.0711 | − | 57.0711i | 2.15248 | − | 2.15248i | ||||
\(704\) | −0.828427 | −0.0312225 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.2426 | 1.13820 | ||||||||
\(707\) | −11.0711 | + | 11.0711i | −0.416370 | + | 0.416370i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 17.3137i | − | 0.650230i | −0.945674 | − | 0.325115i | \(-0.894597\pi\) | ||
0.945674 | − | 0.325115i | \(-0.105403\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.58579 | − | 6.58579i | −0.246813 | − | 0.246813i | ||||
\(713\) | −2.62742 | − | 2.62742i | −0.0983975 | − | 0.0983975i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.31371i | 0.348070i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.34315 | + | 3.34315i | −0.124765 | + | 0.124765i | ||||
\(719\) | 45.4558 | 1.69522 | 0.847608 | − | 0.530622i | \(-0.178042\pi\) | ||||
0.847608 | + | 0.530622i | \(0.178042\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.828427 | −0.0308522 | ||||||||
\(722\) | −21.9203 | + | 21.9203i | −0.815789 | + | 0.815789i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 3.07107i | − | 0.114135i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.75736 | − | 1.75736i | −0.0651768 | − | 0.0651768i | 0.673767 | − | 0.738944i | \(-0.264675\pi\) |
−0.738944 | + | 0.673767i | \(0.764675\pi\) | |||||||
\(728\) | −0.585786 | − | 0.585786i | −0.0217107 | − | 0.0217107i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 31.6569i | − | 1.17087i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.72792 | + | 4.72792i | −0.174630 | + | 0.174630i | −0.789010 | − | 0.614380i | \(-0.789406\pi\) |
0.614380 | + | 0.789010i | \(0.289406\pi\) | |||||||
\(734\) | −28.2843 | −1.04399 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.17157 | −0.0431847 | ||||||||
\(737\) | −2.00000 | + | 2.00000i | −0.0736709 | + | 0.0736709i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 42.6274i | − | 1.56807i | −0.620714 | − | 0.784037i | \(-0.713157\pi\) | ||
0.620714 | − | 0.784037i | \(-0.286843\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.828427 | − | 0.828427i | −0.0304125 | − | 0.0304125i | ||||
\(743\) | −10.1421 | − | 10.1421i | −0.372079 | − | 0.372079i | 0.496155 | − | 0.868234i | \(-0.334745\pi\) |
−0.868234 | + | 0.496155i | \(0.834745\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 3.89949i | − | 0.142771i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.65685 | + | 3.65685i | −0.133708 | + | 0.133708i | ||||
\(749\) | 7.17157 | 0.262044 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.0294 | 0.402470 | 0.201235 | − | 0.979543i | \(-0.435505\pi\) | ||||
0.201235 | + | 0.979543i | \(0.435505\pi\) | |||||||
\(752\) | 3.58579 | − | 3.58579i | 0.130760 | − | 0.130760i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.31371i | 0.266350i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.92893 | + | 9.92893i | 0.360873 | + | 0.360873i | 0.864134 | − | 0.503261i | \(-0.167867\pi\) |
−0.503261 | + | 0.864134i | \(0.667867\pi\) | |||||||
\(758\) | 4.00000 | + | 4.00000i | 0.145287 | + | 0.145287i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.34315i | − | 0.157439i | −0.996897 | − | 0.0787195i | \(-0.974917\pi\) | ||
0.996897 | − | 0.0787195i | \(-0.0250831\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.75736 | + | 5.75736i | −0.208430 | + | 0.208430i | ||||
\(764\) | 10.5858 | 0.382980 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.58579 | 0.165691 | ||||||||
\(767\) | −4.68629 | + | 4.68629i | −0.169212 | + | 0.169212i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 16.1421i | − | 0.582100i | −0.956708 | − | 0.291050i | \(-0.905995\pi\) | ||
0.956708 | − | 0.291050i | \(-0.0940047\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.00000 | + | 6.00000i | 0.215945 | + | 0.215945i | ||||
\(773\) | 35.9411 | + | 35.9411i | 1.29271 | + | 1.29271i | 0.933103 | + | 0.359610i | \(0.117090\pi\) |
0.359610 | + | 0.933103i | \(0.382910\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.343146i | 0.0123182i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.2426 | + | 12.2426i | −0.438920 | + | 0.438920i | ||||
\(779\) | 5.85786 | 0.209880 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.11270 | −0.111381 | ||||||||
\(782\) | −5.17157 | + | 5.17157i | −0.184935 | + | 0.184935i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.6863 | − | 12.6863i | −0.452217 | − | 0.452217i | 0.443872 | − | 0.896090i | \(-0.353604\pi\) |
−0.896090 | + | 0.443872i | \(0.853604\pi\) | |||||||
\(788\) | 8.82843 | + | 8.82843i | 0.314500 | + | 0.314500i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3.65685i | − | 0.130023i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.51472 | − | 5.51472i | 0.195833 | − | 0.195833i | ||||
\(794\) | −31.9411 | −1.13355 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.6569 | 0.413166 | ||||||||
\(797\) | −35.7990 | + | 35.7990i | −1.26807 | + | 1.26807i | −0.320979 | + | 0.947086i | \(0.604012\pi\) |
−0.947086 | + | 0.320979i | \(0.895988\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 31.6569i | − | 1.11994i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.9706 | − | 11.9706i | −0.422695 | − | 0.422695i | ||||
\(803\) | 4.97056 | + | 4.97056i | 0.175407 | + | 0.175407i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.62742i | 0.0925468i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.0711 | − | 11.0711i | 0.389479 | − | 0.389479i | ||||
\(809\) | 49.6985 | 1.74731 | 0.873653 | − | 0.486550i | \(-0.161745\pi\) | ||||
0.873653 | + | 0.486550i | \(0.161745\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.2426 | −1.13219 | −0.566096 | − | 0.824339i | \(-0.691547\pi\) | ||||
−0.566096 | + | 0.824339i | \(0.691547\pi\) | |||||||
\(812\) | −6.24264 | + | 6.24264i | −0.219074 | + | 0.219074i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 9.45584i | − | 0.331427i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.3553 | − | 25.3553i | −0.887071 | − | 0.887071i | ||||
\(818\) | −10.3848 | − | 10.3848i | −0.363095 | − | 0.363095i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 40.1421i | − | 1.40097i | −0.713667 | − | 0.700485i | \(-0.752967\pi\) | ||
0.713667 | − | 0.700485i | \(-0.247033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.3137 | + | 37.3137i | −1.30067 | + | 1.30067i | −0.372737 | + | 0.927937i | \(0.621581\pi\) |
−0.927937 | + | 0.372737i | \(0.878419\pi\) | |||||||
\(824\) | 0.828427 | 0.0288596 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | 10.8284 | − | 10.8284i | 0.376541 | − | 0.376541i | −0.493311 | − | 0.869853i | \(-0.664214\pi\) |
0.869853 | + | 0.493311i | \(0.164214\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 34.8701i | − | 1.21109i | −0.795812 | − | 0.605544i | \(-0.792956\pi\) | ||
0.795812 | − | 0.605544i | \(-0.207044\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.585786 | + | 0.585786i | 0.0203085 | + | 0.0203085i | ||||
\(833\) | −4.41421 | − | 4.41421i | −0.152943 | − | 0.152943i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.85786i | 0.202598i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.1421 | − | 14.1421i | 0.488532 | − | 0.488532i | ||||
\(839\) | 21.1716 | 0.730924 | 0.365462 | − | 0.930826i | \(-0.380911\pi\) | ||||
0.365462 | + | 0.930826i | \(0.380911\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 48.9411 | 1.68763 | ||||||||
\(842\) | −0.100505 | + | 0.100505i | −0.00346363 | + | 0.00346363i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 20.4853i | − | 0.705132i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.29289 | + | 7.29289i | 0.250587 | + | 0.250587i | ||||
\(848\) | 0.828427 | + | 0.828427i | 0.0284483 | + | 0.0284483i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 13.3726i | − | 0.458406i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.5563 | + | 27.5563i | −0.943511 | + | 0.943511i | −0.998488 | − | 0.0549762i | \(-0.982492\pi\) |
0.0549762 | + | 0.998488i | \(0.482492\pi\) | |||||||
\(854\) | 9.41421 | 0.322148 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.17157 | −0.245119 | ||||||||
\(857\) | 21.0416 | − | 21.0416i | 0.718768 | − | 0.718768i | −0.249585 | − | 0.968353i | \(-0.580294\pi\) |
0.968353 | + | 0.249585i | \(0.0802941\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.7279i | 1.38962i | 0.719194 | + | 0.694809i | \(0.244511\pi\) | ||||
−0.719194 | + | 0.694809i | \(0.755489\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.6569 | + | 20.6569i | 0.703575 | + | 0.703575i | ||||
\(863\) | 26.6274 | + | 26.6274i | 0.906408 | + | 0.906408i | 0.995980 | − | 0.0895725i | \(-0.0285501\pi\) |
−0.0895725 | + | 0.995980i | \(0.528550\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 22.2843i | 0.757250i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.24264 | + | 2.24264i | −0.0761202 | + | 0.0761202i | ||||
\(869\) | −7.71573 | −0.261738 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.82843 | 0.0958376 | ||||||||
\(872\) | 5.75736 | − | 5.75736i | 0.194969 | − | 0.194969i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.28427i | 0.280220i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.72792 | + | 5.72792i | 0.193418 | + | 0.193418i | 0.797171 | − | 0.603753i | \(-0.206329\pi\) |
−0.603753 | + | 0.797171i | \(0.706329\pi\) | |||||||
\(878\) | −9.75736 | − | 9.75736i | −0.329295 | − | 0.329295i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.5147i | 0.859613i | 0.902921 | + | 0.429806i | \(0.141418\pi\) | ||||
−0.902921 | + | 0.429806i | \(0.858582\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.1005 | + | 19.1005i | −0.642783 | + | 0.642783i | −0.951239 | − | 0.308456i | \(-0.900188\pi\) |
0.308456 | + | 0.951239i | \(0.400188\pi\) | |||||||
\(884\) | 5.17157 | 0.173939 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.6274 | −0.357035 | ||||||||
\(887\) | 37.3848 | − | 37.3848i | 1.25526 | − | 1.25526i | 0.301927 | − | 0.953331i | \(-0.402370\pi\) |
0.953331 | − | 0.301927i | \(-0.0976298\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 9.65685i | − | 0.323880i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.8995 | − | 11.8995i | −0.398425 | − | 0.398425i | ||||
\(893\) | −25.3553 | − | 25.3553i | −0.848484 | − | 0.848484i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000i | 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.7990 | − | 16.7990i | 0.560590 | − | 0.560590i | ||||
\(899\) | 28.0000 | 0.933852 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.31371 | 0.243655 | ||||||||
\(902\) | 0.485281 | − | 0.485281i | 0.0161581 | − | 0.0161581i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.65685i | 0.121625i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.2426 | − | 11.2426i | −0.373306 | − | 0.373306i | 0.495374 | − | 0.868680i | \(-0.335031\pi\) |
−0.868680 | + | 0.495374i | \(0.835031\pi\) | |||||||
\(908\) | −15.6569 | − | 15.6569i | −0.519591 | − | 0.519591i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 29.8995i | − | 0.990614i | −0.868718 | − | 0.495307i | \(-0.835055\pi\) | ||
0.868718 | − | 0.495307i | \(-0.164945\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.37258 | − | 1.37258i | 0.0454259 | − | 0.0454259i | ||||
\(914\) | −34.6274 | −1.14537 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.0711 | 0.630126 | ||||||||
\(917\) | 4.24264 | − | 4.24264i | 0.140104 | − | 0.140104i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 8.68629i | − | 0.286534i | −0.989684 | − | 0.143267i | \(-0.954239\pi\) | ||
0.989684 | − | 0.143267i | \(-0.0457608\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.3848 | − | 10.3848i | −0.342004 | − | 0.342004i | ||||
\(923\) | 2.20101 | + | 2.20101i | 0.0724471 | + | 0.0724471i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 31.7990i | 1.04498i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.24264 | − | 6.24264i | 0.204925 | − | 0.204925i | ||||
\(929\) | −23.6569 | −0.776156 | −0.388078 | − | 0.921626i | \(-0.626861\pi\) | ||||
−0.388078 | + | 0.921626i | \(0.626861\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.07107 | −0.231745 | ||||||||
\(932\) | 2.58579 | − | 2.58579i | 0.0847003 | − | 0.0847003i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.34315i | 0.0766701i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.9289 | − | 16.9289i | −0.553044 | − | 0.553044i | 0.374274 | − | 0.927318i | \(-0.377892\pi\) |
−0.927318 | + | 0.374274i | \(0.877892\pi\) | |||||||
\(938\) | 2.41421 | + | 2.41421i | 0.0788269 | + | 0.0788269i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.3137i | 0.434014i | 0.976170 | + | 0.217007i | \(0.0696295\pi\) | ||||
−0.976170 | + | 0.217007i | \(0.930370\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.686292 | − | 0.686292i | 0.0223487 | − | 0.0223487i | ||||
\(944\) | 8.00000 | 0.260378 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.20101 | −0.136587 | ||||||||
\(947\) | −8.58579 | + | 8.58579i | −0.279001 | + | 0.279001i | −0.832710 | − | 0.553709i | \(-0.813212\pi\) |
0.553709 | + | 0.832710i | \(0.313212\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 7.02944i | − | 0.228185i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.41421 | + | 4.41421i | 0.143065 | + | 0.143065i | ||||
\(953\) | 3.61522 | + | 3.61522i | 0.117109 | + | 0.117109i | 0.763233 | − | 0.646124i | \(-0.223611\pi\) |
−0.646124 | + | 0.763233i | \(0.723611\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 17.2132i | − | 0.556715i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.17157 | − | 1.17157i | 0.0378518 | − | 0.0378518i | ||||
\(959\) | −18.4853 | −0.596921 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.9411 | −0.675520 | ||||||||
\(962\) | −6.68629 | + | 6.68629i | −0.215575 | + | 0.215575i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 3.65685i | − | 0.117779i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.9706 | + | 40.9706i | 1.31752 | + | 1.31752i | 0.915730 | + | 0.401795i | \(0.131613\pi\) |
0.401795 | + | 0.915730i | \(0.368387\pi\) | |||||||
\(968\) | −7.29289 | − | 7.29289i | −0.234402 | − | 0.234402i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.3431i | 0.781209i | 0.920559 | + | 0.390604i | \(0.127734\pi\) | ||||
−0.920559 | + | 0.390604i | \(0.872266\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.82843 | + | 5.82843i | −0.186851 | + | 0.186851i | ||||
\(974\) | 28.2843 | 0.906287 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.41421 | −0.301342 | ||||||||
\(977\) | 1.61522 | − | 1.61522i | 0.0516756 | − | 0.0516756i | −0.680797 | − | 0.732472i | \(-0.738366\pi\) |
0.732472 | + | 0.680797i | \(0.238366\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.71573i | 0.246596i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.75736 | − | 7.75736i | −0.247547 | − | 0.247547i | ||||
\(983\) | 24.4142 | + | 24.4142i | 0.778692 | + | 0.778692i | 0.979608 | − | 0.200916i | \(-0.0643918\pi\) |
−0.200916 | + | 0.979608i | \(0.564392\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 55.1127i | − | 1.75515i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.14214 | − | 4.14214i | 0.131779 | − | 0.131779i | ||||
\(989\) | −5.94113 | −0.188917 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.3137 | −0.740584 | −0.370292 | − | 0.928915i | \(-0.620742\pi\) | ||||
−0.370292 | + | 0.928915i | \(0.620742\pi\) | |||||||
\(992\) | 2.24264 | − | 2.24264i | 0.0712039 | − | 0.0712039i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.75736i | 0.119176i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.5269 | − | 36.5269i | −1.15682 | − | 1.15682i | −0.985156 | − | 0.171663i | \(-0.945086\pi\) |
−0.171663 | − | 0.985156i | \(-0.554914\pi\) | |||||||
\(998\) | −16.9706 | − | 16.9706i | −0.537194 | − | 0.537194i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3150.2.m.f.1457.2 | yes | 4 | |
3.2 | odd | 2 | 3150.2.m.e.1457.1 | yes | 4 | ||
5.2 | odd | 4 | 3150.2.m.c.2843.2 | yes | 4 | ||
5.3 | odd | 4 | 3150.2.m.e.2843.1 | yes | 4 | ||
5.4 | even | 2 | 3150.2.m.d.1457.1 | yes | 4 | ||
15.2 | even | 4 | 3150.2.m.d.2843.1 | yes | 4 | ||
15.8 | even | 4 | inner | 3150.2.m.f.2843.2 | yes | 4 | |
15.14 | odd | 2 | 3150.2.m.c.1457.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.m.c.1457.2 | ✓ | 4 | 15.14 | odd | 2 | ||
3150.2.m.c.2843.2 | yes | 4 | 5.2 | odd | 4 | ||
3150.2.m.d.1457.1 | yes | 4 | 5.4 | even | 2 | ||
3150.2.m.d.2843.1 | yes | 4 | 15.2 | even | 4 | ||
3150.2.m.e.1457.1 | yes | 4 | 3.2 | odd | 2 | ||
3150.2.m.e.2843.1 | yes | 4 | 5.3 | odd | 4 | ||
3150.2.m.f.1457.2 | yes | 4 | 1.1 | even | 1 | trivial | |
3150.2.m.f.2843.2 | yes | 4 | 15.8 | even | 4 | inner |