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.c.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 | \(-0.960142\pi\) | ||
0.992171 | − | 0.124890i | \(-0.0398578\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.585786 | + | 0.585786i | −0.162468 | + | 0.162468i | −0.783659 | − | 0.621191i | \(-0.786649\pi\) |
0.621191 | + | 0.783659i | \(0.286649\pi\) | |||||||
\(14\) | −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 | \(-0.194141\pi\) | ||||
0.819699 | + | 0.572795i | \(0.194141\pi\) | |||||||
\(30\) | 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 | \(0.137547\pi\) |
0.418794 | + | 0.908081i | \(0.362453\pi\) | |||||||
\(38\) | 5.00000 | + | 5.00000i | 0.811107 | + | 0.811107i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.828427i | 0.129379i | 0.997905 | + | 0.0646893i | \(0.0206056\pi\) | ||||
−0.997905 | + | 0.0646893i | \(0.979394\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.58579 | − | 3.58579i | 0.546827 | − | 0.546827i | −0.378694 | − | 0.925522i | \(-0.623627\pi\) |
0.925522 | + | 0.378694i | \(0.123627\pi\) | |||||||
\(44\) | −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 | \(-0.325650\pi\) | ||||
0.520756 | + | 0.853706i | \(0.325650\pi\) | |||||||
\(60\) | 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 | 0.544086 | − | 0.839029i | \(-0.316876\pi\) |
−0.839029 | + | 0.544086i | \(0.816876\pi\) | |||||||
\(68\) | 4.41421 | + | 4.41421i | 0.535302 | + | 0.535302i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.75736i | − | 0.445917i | −0.974828 | − | 0.222958i | \(-0.928429\pi\) | ||
0.974828 | − | 0.222958i | \(-0.0715714\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | + | 6.00000i | −0.702247 | + | 0.702247i | −0.964892 | − | 0.262646i | \(-0.915405\pi\) |
0.262646 | + | 0.964892i | \(0.415405\pi\) | |||||||
\(74\) | 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 | \(-0.664329\pi\) | ||||
−0.493626 | + | 0.869675i | \(0.664329\pi\) | |||||||
\(90\) | 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 | 0.719318 | − | 0.694681i | \(-0.244455\pi\) |
−0.694681 | + | 0.719318i | \(0.744455\pi\) | |||||||
\(98\) | 0.707107 | + | 0.707107i | 0.0714286 | + | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 15.6569i | − | 1.55792i | −0.627077 | − | 0.778958i | \(-0.715749\pi\) | ||
0.627077 | − | 0.778958i | \(-0.284251\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.585786 | − | 0.585786i | 0.0577193 | − | 0.0577193i | −0.677658 | − | 0.735377i | \(-0.737005\pi\) |
0.735377 | + | 0.677658i | \(0.237005\pi\) | |||||||
\(104\) | 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 | 0.941879 | − | 0.335954i | \(-0.109059\pi\) |
−0.335954 | + | 0.941879i | \(0.609059\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000i | 0.524222i | 0.965038 | + | 0.262111i | \(0.0844187\pi\) | ||||
−0.965038 | + | 0.262111i | \(0.915581\pi\) | |||||||
\(132\) | 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 | \(-0.249058\pi\) | ||||
0.709197 | + | 0.705010i | \(0.249058\pi\) | |||||||
\(150\) | 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 | 0.889343 | − | 0.457241i | \(-0.151162\pi\) |
−0.457241 | + | 0.889343i | \(0.651162\pi\) | |||||||
\(158\) | 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 | \(0.558941\pi\) |
−0.982905 | + | 0.184114i | \(0.941059\pi\) | |||||||
\(164\) | 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 | \(-0.386837\pi\) | ||||
0.348070 | + | 0.937469i | \(0.386837\pi\) | |||||||
\(180\) | 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 | \(-0.874898\pi\) | ||
0.923757 | − | 0.382980i | \(-0.125102\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | − | 6.00000i | 0.431889 | − | 0.431889i | −0.457381 | − | 0.889271i | \(-0.651213\pi\) |
0.889271 | + | 0.457381i | \(0.151213\pi\) | |||||||
\(194\) | 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 | −0.982597 | − | 0.185748i | \(-0.940529\pi\) |
0.185748 | + | 0.982597i | \(0.440529\pi\) | |||||||
\(224\) | 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 | \(-0.687938\pi\) | ||||
−0.556715 | + | 0.830704i | \(0.687938\pi\) | |||||||
\(240\) | 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 | \(-0.675885\pi\) | ||
0.524868 | − | 0.851183i | \(-0.324115\pi\) | |||||||
\(252\) | 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 | \(-0.487249\pi\) | ||||
0.0400491 | + | 0.999198i | \(0.487249\pi\) | |||||||
\(270\) | 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 | 0.579153 | − | 0.815219i | \(-0.303384\pi\) |
−0.815219 | + | 0.579153i | \(0.803384\pi\) | |||||||
\(278\) | 5.82843 | + | 5.82843i | 0.349566 | + | 0.349566i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.0711i | 1.61492i | 0.589919 | + | 0.807462i | \(0.299160\pi\) | ||||
−0.589919 | + | 0.807462i | \(0.700840\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.0000 | + | 18.0000i | −1.06999 | + | 1.06999i | −0.0726300 | + | 0.997359i | \(0.523139\pi\) |
−0.997359 | + | 0.0726300i | \(0.976861\pi\) | |||||||
\(284\) | −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 | \(-0.799061\pi\) |
−0.590169 | − | 0.807279i | \(-0.700939\pi\) | |||||||
\(308\) | 0.585786 | + | 0.585786i | 0.0333783 | + | 0.0333783i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.0000i | 0.907277i | 0.891186 | + | 0.453638i | \(0.149874\pi\) | ||||
−0.891186 | + | 0.453638i | \(0.850126\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.34315 | + | 8.34315i | −0.471582 | + | 0.471582i | −0.902426 | − | 0.430844i | \(-0.858216\pi\) |
0.430844 | + | 0.902426i | \(0.358216\pi\) | |||||||
\(314\) | 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 | \(-0.997778\pi\) |
−0.00698181 | − | 0.999976i | \(-0.502222\pi\) | |||||||
\(338\) | 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 | \(-0.460182\pi\) | ||||
0.124765 | + | 0.992186i | \(0.460182\pi\) | |||||||
\(360\) | 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 | \(0.0143303\pi\) |
0.0450047 | + | 0.998987i | \(0.485670\pi\) | |||||||
\(368\) | −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 | −0.774880 | − | 0.632109i | \(-0.782190\pi\) |
0.632109 | + | 0.774880i | \(0.282190\pi\) | |||||||
\(374\) | 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 | \(-0.355361\pi\) | ||||
0.438920 | + | 0.898526i | \(0.355361\pi\) | |||||||
\(390\) | 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 | \(0.0459854\pi\) |
0.143965 | + | 0.989583i | \(0.454015\pi\) | |||||||
\(398\) | 8.24264 | + | 8.24264i | 0.413166 | + | 0.413166i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.9289i | 0.845391i | 0.906272 | + | 0.422695i | \(0.138916\pi\) | ||||
−0.906272 | + | 0.422695i | \(0.861084\pi\) | |||||||
\(402\) | 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 | \(-0.662467\pi\) | ||||
−0.488532 | + | 0.872546i | \(0.662467\pi\) | |||||||
\(420\) | 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 | \(-0.751586\pi\) | ||
0.710621 | − | 0.703575i | \(-0.248414\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.7574 | − | 15.7574i | 0.757250 | − | 0.757250i | −0.218571 | − | 0.975821i | \(-0.570139\pi\) |
0.975821 | + | 0.218571i | \(0.0701394\pi\) | |||||||
\(434\) | 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 | \(-0.689425\pi\) | ||||
−0.560590 | + | 0.828094i | \(0.689425\pi\) | |||||||
\(450\) | 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 | \(0.0504793\pi\) |
0.157921 | + | 0.987452i | \(0.449521\pi\) | |||||||
\(458\) | 13.4853 | + | 13.4853i | 0.630126 | + | 0.630126i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.6863i | 0.684009i | 0.939698 | + | 0.342004i | \(0.111106\pi\) | ||||
−0.939698 | + | 0.342004i | \(0.888894\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.4853 | − | 22.4853i | 1.04498 | − | 1.04498i | 0.0460401 | − | 0.998940i | \(-0.485340\pi\) |
0.998940 | − | 0.0460401i | \(-0.0146602\pi\) | |||||||
\(464\) | −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 | \(-0.512051\pi\) | ||||
−0.0378518 | + | 0.999283i | \(0.512051\pi\) | |||||||
\(480\) | 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 | 0.0896838 | − | 0.995970i | \(-0.471414\pi\) |
−0.995970 | + | 0.0896838i | \(0.971414\pi\) | |||||||
\(488\) | −6.65685 | − | 6.65685i | −0.301342 | − | 0.301342i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.9706i | 0.495095i | 0.968876 | + | 0.247547i | \(0.0796246\pi\) | ||||
−0.968876 | + | 0.247547i | \(0.920375\pi\) | |||||||
\(492\) | 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 | \(-0.728284\pi\) | ||||
−0.657258 | + | 0.753665i | \(0.728284\pi\) | |||||||
\(510\) | 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 | \(-0.798812\pi\) | ||
0.806817 | − | 0.590801i | \(-0.201188\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.2843 | + | 26.2843i | −1.14933 | + | 1.14933i | −0.162647 | + | 0.986684i | \(0.552003\pi\) |
−0.986684 | + | 0.162647i | \(0.947997\pi\) | |||||||
\(524\) | 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 | 0.743082 | − | 0.669201i | \(-0.233363\pi\) |
−0.669201 | + | 0.743082i | \(0.733363\pi\) | |||||||
\(548\) | 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 | \(-0.313462\pi\) | ||||
0.553054 | + | 0.833146i | \(0.313462\pi\) | |||||||
\(570\) | 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 | 0.964534 | − | 0.263958i | \(-0.0850279\pi\) |
−0.263958 | + | 0.964534i | \(0.585028\pi\) | |||||||
\(578\) | −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 | \(-0.372609\pi\) | ||||
0.389611 | + | 0.920979i | \(0.372609\pi\) | |||||||
\(600\) | 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 | 0.0102004 | − | 0.999948i | \(-0.496753\pi\) |
−0.999948 | + | 0.0102004i | \(0.996753\pi\) | |||||||
\(608\) | −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 | −0.565607 | − | 0.824675i | \(-0.691358\pi\) |
0.824675 | + | 0.565607i | \(0.191358\pi\) | |||||||
\(614\) | −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 | \(-0.839046\pi\) | ||
0.874859 | − | 0.484377i | \(-0.160954\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.1421 | − | 28.1421i | 1.10982 | − | 1.10982i | 0.116644 | − | 0.993174i | \(-0.462786\pi\) |
0.993174 | − | 0.116644i | \(-0.0372135\pi\) | |||||||
\(644\) | −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 | \(-0.360420\pi\) | ||||
0.424584 | + | 0.905389i | \(0.360420\pi\) | |||||||
\(660\) | 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 | −0.00550686 | − | 0.999985i | \(-0.501753\pi\) |
0.999985 | + | 0.00550686i | \(0.00175290\pi\) | |||||||
\(674\) | −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 | \(-0.942493\pi\) | ||
0.983725 | − | 0.179683i | \(-0.0575072\pi\) | |||||||
\(702\) | 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 | \(-0.821958\pi\) | ||||
−0.847608 | + | 0.530622i | \(0.821958\pi\) | |||||||
\(720\) | 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 | 0.738944 | − | 0.673767i | \(-0.235325\pi\) |
−0.673767 | + | 0.738944i | \(0.735325\pi\) | |||||||
\(728\) | −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 | −0.614380 | − | 0.789010i | \(-0.710594\pi\) |
0.789010 | + | 0.614380i | \(0.210594\pi\) | |||||||
\(734\) | 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 | 0.503261 | − | 0.864134i | \(-0.332133\pi\) |
−0.864134 | + | 0.503261i | \(0.832133\pi\) | |||||||
\(758\) | 4.00000 | + | 4.00000i | 0.145287 | + | 0.145287i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.34315i | 0.157439i | 0.996897 | + | 0.0787195i | \(0.0250831\pi\) | ||||
−0.996897 | + | 0.0787195i | \(0.974917\pi\) | |||||||
\(762\) | 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 | 0.896090 | − | 0.443872i | \(-0.146396\pi\) |
−0.443872 | + | 0.896090i | \(0.646396\pi\) | |||||||
\(788\) | 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 | \(-0.838255\pi\) | ||||
−0.873653 | + | 0.486550i | \(0.838255\pi\) | |||||||
\(810\) | 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 | \(0.247033\pi\) | ||||
−0.713667 | + | 0.700485i | \(0.752967\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.3137 | − | 37.3137i | 1.30067 | − | 1.30067i | 0.372737 | − | 0.927937i | \(-0.378419\pi\) |
0.927937 | − | 0.372737i | \(-0.121581\pi\) | |||||||
\(824\) | −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 | \(-0.619089\pi\) | ||||
−0.365462 | + | 0.930826i | \(0.619089\pi\) | |||||||
\(840\) | 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 | −0.0549762 | − | 0.998488i | \(-0.517508\pi\) |
0.998488 | + | 0.0549762i | \(0.0175083\pi\) | |||||||
\(854\) | −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 | 0.603753 | − | 0.797171i | \(-0.293671\pi\) |
−0.797171 | + | 0.603753i | \(0.793671\pi\) | |||||||
\(878\) | −9.75736 | − | 9.75736i | −0.329295 | − | 0.329295i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 25.5147i | − | 0.859613i | −0.902921 | − | 0.429806i | \(-0.858582\pi\) | ||
0.902921 | − | 0.429806i | \(-0.141418\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.1005 | − | 19.1005i | 0.642783 | − | 0.642783i | −0.308456 | − | 0.951239i | \(-0.599812\pi\) |
0.951239 | + | 0.308456i | \(0.0998121\pi\) | |||||||
\(884\) | −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 | 0.868680 | − | 0.495374i | \(-0.164969\pi\) |
−0.495374 | + | 0.868680i | \(0.664969\pi\) | |||||||
\(908\) | −15.6569 | − | 15.6569i | −0.519591 | − | 0.519591i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.8995i | 0.990614i | 0.868718 | + | 0.495307i | \(0.164945\pi\) | ||||
−0.868718 | + | 0.495307i | \(0.835055\pi\) | |||||||
\(912\) | 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 | \(-0.373139\pi\) | ||||
0.388078 | + | 0.921626i | \(0.373139\pi\) | |||||||
\(930\) | 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 | 0.927318 | − | 0.374274i | \(-0.122108\pi\) |
−0.374274 | + | 0.927318i | \(0.622108\pi\) | |||||||
\(938\) | 2.41421 | + | 2.41421i | 0.0788269 | + | 0.0788269i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 13.3137i | − | 0.434014i | −0.976170 | − | 0.217007i | \(-0.930370\pi\) | ||
0.976170 | − | 0.217007i | \(-0.0696295\pi\) | |||||||
\(942\) | 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 | \(-0.868387\pi\) |
−0.401795 | − | 0.915730i | \(-0.631613\pi\) | |||||||
\(968\) | −7.29289 | − | 7.29289i | −0.234402 | − | 0.234402i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 24.3431i | − | 0.781209i | −0.920559 | − | 0.390604i | \(-0.872266\pi\) | ||
0.920559 | − | 0.390604i | \(-0.127734\pi\) | |||||||
\(972\) | 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 | \(0.0549141\pi\) |
0.171663 | + | 0.985156i | \(0.445086\pi\) | |||||||
\(998\) | −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.c.1457.2 | ✓ | 4 | |
3.2 | odd | 2 | 3150.2.m.d.1457.1 | yes | 4 | ||
5.2 | odd | 4 | 3150.2.m.f.2843.2 | yes | 4 | ||
5.3 | odd | 4 | 3150.2.m.d.2843.1 | yes | 4 | ||
5.4 | even | 2 | 3150.2.m.e.1457.1 | yes | 4 | ||
15.2 | even | 4 | 3150.2.m.e.2843.1 | yes | 4 | ||
15.8 | even | 4 | inner | 3150.2.m.c.2843.2 | yes | 4 | |
15.14 | odd | 2 | 3150.2.m.f.1457.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.m.c.1457.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3150.2.m.c.2843.2 | yes | 4 | 15.8 | even | 4 | inner | |
3150.2.m.d.1457.1 | yes | 4 | 3.2 | odd | 2 | ||
3150.2.m.d.2843.1 | yes | 4 | 5.3 | odd | 4 | ||
3150.2.m.e.1457.1 | yes | 4 | 5.4 | even | 2 | ||
3150.2.m.e.2843.1 | yes | 4 | 15.2 | even | 4 | ||
3150.2.m.f.1457.2 | yes | 4 | 15.14 | odd | 2 | ||
3150.2.m.f.2843.2 | yes | 4 | 5.2 | odd | 4 |