Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(43,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.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: | \(6.14848095564\) |
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 | 43.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.43 |
Dual form | 770.2.m.a.197.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −2.00000 | + | 1.00000i | −0.894427 | + | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 1.00000i | ||||||
\(10\) | 2.12132 | + | 0.707107i | 0.670820 | + | 0.223607i | ||||
\(11\) | −3.00000 | + | 1.41421i | −0.904534 | + | 0.426401i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.41421 | − | 1.41421i | 0.392232 | − | 0.392232i | −0.483250 | − | 0.875482i | \(-0.660544\pi\) |
0.875482 | + | 0.483250i | \(0.160544\pi\) | |||||||
\(14\) | − | 1.00000i | − | 0.267261i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(18\) | −2.12132 | + | 2.12132i | −0.500000 | + | 0.500000i | ||||
\(19\) | 4.24264 | 0.973329 | 0.486664 | − | 0.873589i | \(-0.338214\pi\) | ||||
0.486664 | + | 0.873589i | \(0.338214\pi\) | |||||||
\(20\) | −1.00000 | − | 2.00000i | −0.223607 | − | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.12132 | + | 1.12132i | 0.665468 | + | 0.239066i | ||||
\(23\) | −2.00000 | − | 2.00000i | −0.417029 | − | 0.417029i | 0.467150 | − | 0.884178i | \(-0.345281\pi\) |
−0.884178 | + | 0.467150i | \(0.845281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.707107 | + | 0.707107i | −0.133631 | + | 0.133631i | ||||
\(29\) | 7.07107 | 1.31306 | 0.656532 | − | 0.754298i | \(-0.272023\pi\) | ||||
0.656532 | + | 0.754298i | \(0.272023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.12132 | − | 0.707107i | −0.358569 | − | 0.119523i | ||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | 6.00000 | − | 6.00000i | 0.986394 | − | 0.986394i | −0.0135147 | − | 0.999909i | \(-0.504302\pi\) |
0.999909 | + | 0.0135147i | \(0.00430201\pi\) | |||||||
\(38\) | −3.00000 | − | 3.00000i | −0.486664 | − | 0.486664i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.707107 | + | 2.12132i | −0.111803 | + | 0.335410i | ||||
\(41\) | − | 1.41421i | − | 0.220863i | −0.993884 | − | 0.110432i | \(-0.964777\pi\) | ||
0.993884 | − | 0.110432i | \(-0.0352233\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.65685 | − | 5.65685i | 0.862662 | − | 0.862662i | −0.128984 | − | 0.991647i | \(-0.541172\pi\) |
0.991647 | + | 0.128984i | \(0.0411717\pi\) | |||||||
\(44\) | −1.41421 | − | 3.00000i | −0.213201 | − | 0.452267i | ||||
\(45\) | 3.00000 | + | 6.00000i | 0.447214 | + | 0.894427i | ||||
\(46\) | 2.82843i | 0.417029i | ||||||||
\(47\) | 7.00000 | − | 7.00000i | 1.02105 | − | 1.02105i | 0.0212814 | − | 0.999774i | \(-0.493225\pi\) |
0.999774 | − | 0.0212814i | \(-0.00677460\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | −4.94975 | + | 0.707107i | −0.700000 | + | 0.100000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.41421 | + | 1.41421i | 0.196116 | + | 0.196116i | ||||
\(53\) | −4.00000 | − | 4.00000i | −0.549442 | − | 0.549442i | 0.376837 | − | 0.926279i | \(-0.377012\pi\) |
−0.926279 | + | 0.376837i | \(0.877012\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.58579 | − | 5.82843i | 0.618347 | − | 0.785905i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.00000 | − | 5.00000i | −0.656532 | − | 0.656532i | ||||
\(59\) | 4.00000i | 0.520756i | 0.965507 | + | 0.260378i | \(0.0838471\pi\) | ||||
−0.965507 | + | 0.260378i | \(0.916153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.82843i | − | 0.362143i | −0.983470 | − | 0.181071i | \(-0.942043\pi\) | ||
0.983470 | − | 0.181071i | \(-0.0579565\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.12132 | − | 2.12132i | 0.267261 | − | 0.267261i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −1.41421 | + | 4.24264i | −0.175412 | + | 0.526235i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00000 | + | 3.00000i | −0.366508 | + | 0.366508i | −0.866202 | − | 0.499694i | \(-0.833446\pi\) |
0.499694 | + | 0.866202i | \(0.333446\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.00000 | + | 2.00000i | 0.119523 | + | 0.239046i | ||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | −2.12132 | − | 2.12132i | −0.250000 | − | 0.250000i | ||||
\(73\) | 4.24264 | − | 4.24264i | 0.496564 | − | 0.496564i | −0.413803 | − | 0.910366i | \(-0.635800\pi\) |
0.910366 | + | 0.413803i | \(0.135800\pi\) | |||||||
\(74\) | −8.48528 | −0.986394 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.24264i | 0.486664i | ||||||||
\(77\) | −3.12132 | − | 1.12132i | −0.355707 | − | 0.127786i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.24264 | −0.477334 | −0.238667 | − | 0.971101i | \(-0.576710\pi\) | ||||
−0.238667 | + | 0.971101i | \(0.576710\pi\) | |||||||
\(80\) | 2.00000 | − | 1.00000i | 0.223607 | − | 0.111803i | ||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | −1.00000 | + | 1.00000i | −0.110432 | + | 0.110432i | ||||
\(83\) | 8.48528 | − | 8.48528i | 0.931381 | − | 0.931381i | −0.0664117 | − | 0.997792i | \(-0.521155\pi\) |
0.997792 | + | 0.0664117i | \(0.0211551\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.12132 | + | 3.12132i | −0.119533 | + | 0.332734i | ||||
\(89\) | 14.0000i | 1.48400i | 0.670402 | + | 0.741999i | \(0.266122\pi\) | ||||
−0.670402 | + | 0.741999i | \(0.733878\pi\) | |||||||
\(90\) | 2.12132 | − | 6.36396i | 0.223607 | − | 0.670820i | ||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 2.00000 | − | 2.00000i | 0.208514 | − | 0.208514i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.89949 | −1.02105 | ||||||||
\(95\) | −8.48528 | + | 4.24264i | −0.870572 | + | 0.435286i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | − | 6.00000i | 0.609208 | − | 0.609208i | −0.333531 | − | 0.942739i | \(-0.608240\pi\) |
0.942739 | + | 0.333531i | \(0.108240\pi\) | |||||||
\(98\) | 0.707107 | − | 0.707107i | 0.0714286 | − | 0.0714286i | ||||
\(99\) | 4.24264 | + | 9.00000i | 0.426401 | + | 0.904534i | ||||
\(100\) | 4.00000 | + | 3.00000i | 0.400000 | + | 0.300000i | ||||
\(101\) | − | 5.65685i | − | 0.562878i | −0.959579 | − | 0.281439i | \(-0.909188\pi\) | ||
0.959579 | − | 0.281439i | \(-0.0908117\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.00000 | + | 3.00000i | 0.295599 | + | 0.295599i | 0.839287 | − | 0.543688i | \(-0.182973\pi\) |
−0.543688 | + | 0.839287i | \(0.682973\pi\) | |||||||
\(104\) | − | 2.00000i | − | 0.196116i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.65685i | 0.549442i | ||||||||
\(107\) | 8.48528 | + | 8.48528i | 0.820303 | + | 0.820303i | 0.986151 | − | 0.165848i | \(-0.0530362\pi\) |
−0.165848 | + | 0.986151i | \(0.553036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.7279 | −1.21911 | −0.609557 | − | 0.792742i | \(-0.708653\pi\) | ||||
−0.609557 | + | 0.792742i | \(0.708653\pi\) | |||||||
\(110\) | −7.36396 | + | 0.878680i | −0.702126 | + | 0.0837788i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.707107 | − | 0.707107i | −0.0668153 | − | 0.0668153i | ||||
\(113\) | −9.00000 | − | 9.00000i | −0.846649 | − | 0.846649i | 0.143065 | − | 0.989713i | \(-0.454304\pi\) |
−0.989713 | + | 0.143065i | \(0.954304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.00000 | + | 2.00000i | 0.559503 | + | 0.186501i | ||||
\(116\) | 7.07107i | 0.656532i | ||||||||
\(117\) | −4.24264 | − | 4.24264i | −0.392232 | − | 0.392232i | ||||
\(118\) | 2.82843 | − | 2.82843i | 0.260378 | − | 0.260378i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | − | 8.48528i | 0.636364 | − | 0.771389i | ||||
\(122\) | −2.00000 | + | 2.00000i | −0.181071 | + | 0.181071i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.00000 | + | 11.0000i | −0.178885 | + | 0.983870i | ||||
\(126\) | −3.00000 | −0.267261 | ||||||||
\(127\) | −9.89949 | − | 9.89949i | −0.878438 | − | 0.878438i | 0.114935 | − | 0.993373i | \(-0.463334\pi\) |
−0.993373 | + | 0.114935i | \(0.963334\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.00000 | − | 2.00000i | 0.350823 | − | 0.175412i | ||||
\(131\) | 1.41421i | 0.123560i | 0.998090 | + | 0.0617802i | \(0.0196778\pi\) | ||||
−0.998090 | + | 0.0617802i | \(0.980322\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | + | 3.00000i | 0.260133 | + | 0.260133i | ||||
\(134\) | 4.24264 | 0.366508 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.00000 | − | 5.00000i | 0.427179 | − | 0.427179i | −0.460487 | − | 0.887666i | \(-0.652325\pi\) |
0.887666 | + | 0.460487i | \(0.152325\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.3848 | 1.55938 | 0.779688 | − | 0.626168i | \(-0.215378\pi\) | ||||
0.779688 | + | 0.626168i | \(0.215378\pi\) | |||||||
\(140\) | 0.707107 | − | 2.12132i | 0.0597614 | − | 0.179284i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.65685 | + | 5.65685i | 0.474713 | + | 0.474713i | ||||
\(143\) | −2.24264 | + | 6.24264i | −0.187539 | + | 0.522036i | ||||
\(144\) | 3.00000i | 0.250000i | ||||||||
\(145\) | −14.1421 | + | 7.07107i | −1.17444 | + | 0.587220i | ||||
\(146\) | −6.00000 | −0.496564 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00000 | + | 6.00000i | 0.493197 | + | 0.493197i | ||||
\(149\) | 9.89949 | 0.810998 | 0.405499 | − | 0.914095i | \(-0.367098\pi\) | ||||
0.405499 | + | 0.914095i | \(0.367098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3848i | 1.49613i | 0.663624 | + | 0.748066i | \(0.269017\pi\) | ||||
−0.663624 | + | 0.748066i | \(0.730983\pi\) | |||||||
\(152\) | 3.00000 | − | 3.00000i | 0.243332 | − | 0.243332i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.41421 | + | 3.00000i | 0.113961 | + | 0.241747i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.00000 | − | 7.00000i | 0.558661 | − | 0.558661i | −0.370265 | − | 0.928926i | \(-0.620733\pi\) |
0.928926 | + | 0.370265i | \(0.120733\pi\) | |||||||
\(158\) | 3.00000 | + | 3.00000i | 0.238667 | + | 0.238667i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.12132 | − | 0.707107i | −0.167705 | − | 0.0559017i | ||||
\(161\) | − | 2.82843i | − | 0.222911i | ||||||
\(162\) | 6.36396 | + | 6.36396i | 0.500000 | + | 0.500000i | ||||
\(163\) | 1.00000 | + | 1.00000i | 0.0783260 | + | 0.0783260i | 0.745184 | − | 0.666858i | \(-0.232361\pi\) |
−0.666858 | + | 0.745184i | \(0.732361\pi\) | |||||||
\(164\) | 1.41421 | 0.110432 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0000 | −0.931381 | ||||||||
\(167\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000i | 0.692308i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 12.7279i | − | 0.973329i | ||||||
\(172\) | 5.65685 | + | 5.65685i | 0.431331 | + | 0.431331i | ||||
\(173\) | −12.7279 | + | 12.7279i | −0.967686 | + | 0.967686i | −0.999494 | − | 0.0318080i | \(-0.989873\pi\) |
0.0318080 | + | 0.999494i | \(0.489873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.94975 | − | 0.707107i | 0.374166 | − | 0.0534522i | ||||
\(176\) | 3.00000 | − | 1.41421i | 0.226134 | − | 0.106600i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.89949 | − | 9.89949i | 0.741999 | − | 0.741999i | ||||
\(179\) | − | 2.00000i | − | 0.149487i | −0.997203 | − | 0.0747435i | \(-0.976186\pi\) | ||
0.997203 | − | 0.0747435i | \(-0.0238138\pi\) | |||||||
\(180\) | −6.00000 | + | 3.00000i | −0.447214 | + | 0.223607i | ||||
\(181\) | 4.00000 | 0.297318 | 0.148659 | − | 0.988889i | \(-0.452504\pi\) | ||||
0.148659 | + | 0.988889i | \(0.452504\pi\) | |||||||
\(182\) | −1.41421 | − | 1.41421i | −0.104828 | − | 0.104828i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.82843 | −0.208514 | ||||||||
\(185\) | −6.00000 | + | 18.0000i | −0.441129 | + | 1.32339i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.00000 | + | 7.00000i | 0.510527 | + | 0.510527i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.00000 | + | 3.00000i | 0.652929 | + | 0.217643i | ||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.07107 | + | 7.07107i | −0.508987 | + | 0.508987i | −0.914215 | − | 0.405229i | \(-0.867192\pi\) |
0.405229 | + | 0.914215i | \(0.367192\pi\) | |||||||
\(194\) | −8.48528 | −0.609208 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | −8.48528 | − | 8.48528i | −0.604551 | − | 0.604551i | 0.336966 | − | 0.941517i | \(-0.390599\pi\) |
−0.941517 | + | 0.336966i | \(0.890599\pi\) | |||||||
\(198\) | 3.36396 | − | 9.36396i | 0.239066 | − | 0.665468i | ||||
\(199\) | 22.0000i | 1.55954i | 0.626067 | + | 0.779769i | \(0.284664\pi\) | ||||
−0.626067 | + | 0.779769i | \(0.715336\pi\) | |||||||
\(200\) | −0.707107 | − | 4.94975i | −0.0500000 | − | 0.350000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.00000 | + | 4.00000i | −0.281439 | + | 0.281439i | ||||
\(203\) | 5.00000 | + | 5.00000i | 0.350931 | + | 0.350931i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.41421 | + | 2.82843i | 0.0987730 | + | 0.197546i | ||||
\(206\) | − | 4.24264i | − | 0.295599i | ||||||
\(207\) | −6.00000 | + | 6.00000i | −0.417029 | + | 0.417029i | ||||
\(208\) | −1.41421 | + | 1.41421i | −0.0980581 | + | 0.0980581i | ||||
\(209\) | −12.7279 | + | 6.00000i | −0.880409 | + | 0.415029i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.65685i | 0.389434i | 0.980859 | + | 0.194717i | \(0.0623788\pi\) | ||||
−0.980859 | + | 0.194717i | \(0.937621\pi\) | |||||||
\(212\) | 4.00000 | − | 4.00000i | 0.274721 | − | 0.274721i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 12.0000i | − | 0.820303i | ||||||
\(215\) | −5.65685 | + | 16.9706i | −0.385794 | + | 1.15738i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.00000 | + | 9.00000i | 0.609557 | + | 0.609557i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.82843 | + | 4.58579i | 0.392952 | + | 0.309174i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.00000 | − | 7.00000i | −0.468755 | − | 0.468755i | 0.432756 | − | 0.901511i | \(-0.357541\pi\) |
−0.901511 | + | 0.432756i | \(0.857541\pi\) | |||||||
\(224\) | 1.00000i | 0.0668153i | ||||||||
\(225\) | −12.0000 | − | 9.00000i | −0.800000 | − | 0.600000i | ||||
\(226\) | 12.7279i | 0.846649i | ||||||||
\(227\) | 15.5563 | + | 15.5563i | 1.03251 | + | 1.03251i | 0.999453 | + | 0.0330577i | \(0.0105245\pi\) |
0.0330577 | + | 0.999453i | \(0.489475\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.00000i | − | 0.132164i | −0.997814 | − | 0.0660819i | \(-0.978950\pi\) | ||
0.997814 | − | 0.0660819i | \(-0.0210498\pi\) | |||||||
\(230\) | −2.82843 | − | 5.65685i | −0.186501 | − | 0.373002i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.00000 | − | 5.00000i | 0.328266 | − | 0.328266i | ||||
\(233\) | −18.3848 | + | 18.3848i | −1.20443 | + | 1.20443i | −0.231621 | + | 0.972806i | \(0.574403\pi\) |
−0.972806 | + | 0.231621i | \(0.925597\pi\) | |||||||
\(234\) | 6.00000i | 0.392232i | ||||||||
\(235\) | −7.00000 | + | 21.0000i | −0.456630 | + | 1.36989i | ||||
\(236\) | −4.00000 | −0.260378 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.7279 | 0.823301 | 0.411650 | − | 0.911342i | \(-0.364952\pi\) | ||||
0.411650 | + | 0.911342i | \(0.364952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 21.2132i | − | 1.36646i | −0.730202 | − | 0.683231i | \(-0.760574\pi\) | ||
0.730202 | − | 0.683231i | \(-0.239426\pi\) | |||||||
\(242\) | −10.9497 | + | 1.05025i | −0.703876 | + | 0.0675128i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.82843 | 0.181071 | ||||||||
\(245\) | −1.00000 | − | 2.00000i | −0.0638877 | − | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000 | − | 6.00000i | 0.381771 | − | 0.381771i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.19239 | − | 6.36396i | 0.581378 | − | 0.402492i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 2.12132 | + | 2.12132i | 0.133631 | + | 0.133631i | ||||
\(253\) | 8.82843 | + | 3.17157i | 0.555038 | + | 0.199395i | ||||
\(254\) | 14.0000i | 0.878438i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.00000 | − | 8.00000i | 0.499026 | − | 0.499026i | −0.412108 | − | 0.911135i | \(-0.635208\pi\) |
0.911135 | + | 0.412108i | \(0.135208\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.48528 | 0.527250 | ||||||||
\(260\) | −4.24264 | − | 1.41421i | −0.263117 | − | 0.0877058i | ||||
\(261\) | − | 21.2132i | − | 1.31306i | ||||||
\(262\) | 1.00000 | − | 1.00000i | 0.0617802 | − | 0.0617802i | ||||
\(263\) | −9.89949 | + | 9.89949i | −0.610429 | + | 0.610429i | −0.943058 | − | 0.332629i | \(-0.892064\pi\) |
0.332629 | + | 0.943058i | \(0.392064\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.0000 | + | 4.00000i | 0.737154 | + | 0.245718i | ||||
\(266\) | − | 4.24264i | − | 0.260133i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.00000 | − | 3.00000i | −0.183254 | − | 0.183254i | ||||
\(269\) | − | 18.0000i | − | 1.09748i | −0.835993 | − | 0.548740i | \(-0.815108\pi\) | ||
0.835993 | − | 0.548740i | \(-0.184892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.1127i | 1.88996i | 0.327125 | + | 0.944981i | \(0.393920\pi\) | ||||
−0.327125 | + | 0.944981i | \(0.606080\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.07107 | −0.427179 | ||||||||
\(275\) | −3.34315 | + | 16.2426i | −0.201599 | + | 0.979468i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.65685 | + | 5.65685i | 0.339887 | + | 0.339887i | 0.856325 | − | 0.516437i | \(-0.172742\pi\) |
−0.516437 | + | 0.856325i | \(0.672742\pi\) | |||||||
\(278\) | −13.0000 | − | 13.0000i | −0.779688 | − | 0.779688i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.00000 | + | 1.00000i | −0.119523 | + | 0.0597614i | ||||
\(281\) | − | 28.2843i | − | 1.68730i | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||
0.536895 | − | 0.843649i | \(-0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.24264 | − | 4.24264i | 0.252199 | − | 0.252199i | −0.569673 | − | 0.821872i | \(-0.692930\pi\) |
0.821872 | + | 0.569673i | \(0.192930\pi\) | |||||||
\(284\) | − | 8.00000i | − | 0.474713i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.00000 | − | 2.82843i | 0.354787 | − | 0.167248i | ||||
\(287\) | 1.00000 | − | 1.00000i | 0.0590281 | − | 0.0590281i | ||||
\(288\) | 2.12132 | − | 2.12132i | 0.125000 | − | 0.125000i | ||||
\(289\) | − | 17.0000i | − | 1.00000i | ||||||
\(290\) | 15.0000 | + | 5.00000i | 0.880830 | + | 0.293610i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.24264 | + | 4.24264i | 0.248282 | + | 0.248282i | ||||
\(293\) | 21.2132 | − | 21.2132i | 1.23929 | − | 1.23929i | 0.278996 | − | 0.960292i | \(-0.409998\pi\) |
0.960292 | − | 0.278996i | \(-0.0900018\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | − | 8.00000i | −0.232889 | − | 0.465778i | ||||
\(296\) | − | 8.48528i | − | 0.493197i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.00000 | − | 7.00000i | −0.405499 | − | 0.405499i | ||||
\(299\) | −5.65685 | −0.327144 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | 0.461112 | ||||||||
\(302\) | 13.0000 | − | 13.0000i | 0.748066 | − | 0.748066i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.24264 | −0.243332 | ||||||||
\(305\) | 2.82843 | + | 5.65685i | 0.161955 | + | 0.323911i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.3848 | + | 18.3848i | 1.04927 | + | 1.04927i | 0.998721 | + | 0.0505532i | \(0.0160985\pi\) |
0.0505532 | + | 0.998721i | \(0.483902\pi\) | |||||||
\(308\) | 1.12132 | − | 3.12132i | 0.0638932 | − | 0.177854i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.0000 | −1.70114 | −0.850572 | − | 0.525859i | \(-0.823744\pi\) | ||||
−0.850572 | + | 0.525859i | \(0.823744\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.0000 | − | 12.0000i | −0.678280 | − | 0.678280i | 0.281331 | − | 0.959611i | \(-0.409224\pi\) |
−0.959611 | + | 0.281331i | \(0.909224\pi\) | |||||||
\(314\) | −9.89949 | −0.558661 | ||||||||
\(315\) | −2.12132 | + | 6.36396i | −0.119523 | + | 0.358569i | ||||
\(316\) | − | 4.24264i | − | 0.238667i | ||||||
\(317\) | 8.00000 | − | 8.00000i | 0.449325 | − | 0.449325i | −0.445805 | − | 0.895130i | \(-0.647083\pi\) |
0.895130 | + | 0.445805i | \(0.147083\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.2132 | + | 10.0000i | −1.18771 | + | 0.559893i | ||||
\(320\) | 1.00000 | + | 2.00000i | 0.0559017 | + | 0.111803i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.00000 | + | 2.00000i | −0.111456 | + | 0.111456i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | − | 9.00000i | − | 0.500000i | ||||||
\(325\) | −1.41421 | − | 9.89949i | −0.0784465 | − | 0.549125i | ||||
\(326\) | − | 1.41421i | − | 0.0783260i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.00000 | − | 1.00000i | −0.0552158 | − | 0.0552158i | ||||
\(329\) | 9.89949 | 0.545777 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | 0.219860 | 0.109930 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109930 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(332\) | 8.48528 | + | 8.48528i | 0.465690 | + | 0.465690i | ||||
\(333\) | −18.0000 | − | 18.0000i | −0.986394 | − | 0.986394i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.00000 | − | 9.00000i | 0.163908 | − | 0.491723i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.5563 | − | 15.5563i | −0.847408 | − | 0.847408i | 0.142401 | − | 0.989809i | \(-0.454518\pi\) |
−0.989809 | + | 0.142401i | \(0.954518\pi\) | |||||||
\(338\) | 6.36396 | − | 6.36396i | 0.346154 | − | 0.346154i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −9.00000 | + | 9.00000i | −0.486664 | + | 0.486664i | ||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | − | 8.00000i | − | 0.431331i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.0000 | 0.967686 | ||||||||
\(347\) | −2.82843 | − | 2.82843i | −0.151838 | − | 0.151838i | 0.627100 | − | 0.778938i | \(-0.284242\pi\) |
−0.778938 | + | 0.627100i | \(0.784242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.9411 | −1.81683 | −0.908413 | − | 0.418073i | \(-0.862706\pi\) | ||||
−0.908413 | + | 0.418073i | \(0.862706\pi\) | |||||||
\(350\) | −4.00000 | − | 3.00000i | −0.213809 | − | 0.160357i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.12132 | − | 1.12132i | −0.166367 | − | 0.0597666i | ||||
\(353\) | −4.00000 | − | 4.00000i | −0.212899 | − | 0.212899i | 0.592599 | − | 0.805498i | \(-0.298102\pi\) |
−0.805498 | + | 0.592599i | \(0.798102\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.0000 | − | 8.00000i | 0.849192 | − | 0.424596i | ||||
\(356\) | −14.0000 | −0.741999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.41421 | + | 1.41421i | −0.0747435 | + | 0.0747435i | ||||
\(359\) | 9.89949 | 0.522475 | 0.261238 | − | 0.965275i | \(-0.415869\pi\) | ||||
0.261238 | + | 0.965275i | \(0.415869\pi\) | |||||||
\(360\) | 6.36396 | + | 2.12132i | 0.335410 | + | 0.111803i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | −2.82843 | − | 2.82843i | −0.148659 | − | 0.148659i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.00000i | 0.104828i | ||||||||
\(365\) | −4.24264 | + | 12.7279i | −0.222070 | + | 0.666210i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.0000 | − | 25.0000i | 1.30499 | − | 1.30499i | 0.380005 | − | 0.924984i | \(-0.375922\pi\) |
0.924984 | − | 0.380005i | \(-0.124078\pi\) | |||||||
\(368\) | 2.00000 | + | 2.00000i | 0.104257 | + | 0.104257i | ||||
\(369\) | −4.24264 | −0.220863 | ||||||||
\(370\) | 16.9706 | − | 8.48528i | 0.882258 | − | 0.441129i | ||||
\(371\) | − | 5.65685i | − | 0.293689i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.1421 | + | 14.1421i | −0.732252 | + | 0.732252i | −0.971065 | − | 0.238813i | \(-0.923242\pi\) |
0.238813 | + | 0.971065i | \(0.423242\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 9.89949i | − | 0.510527i | ||||||
\(377\) | 10.0000 | − | 10.0000i | 0.515026 | − | 0.515026i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 30.0000i | − | 1.54100i | −0.637442 | − | 0.770498i | \(-0.720007\pi\) | ||
0.637442 | − | 0.770498i | \(-0.279993\pi\) | |||||||
\(380\) | −4.24264 | − | 8.48528i | −0.217643 | − | 0.435286i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.3137 | + | 11.3137i | 0.578860 | + | 0.578860i | ||||
\(383\) | −9.00000 | − | 9.00000i | −0.459879 | − | 0.459879i | 0.438737 | − | 0.898616i | \(-0.355426\pi\) |
−0.898616 | + | 0.438737i | \(0.855426\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.36396 | − | 0.878680i | 0.375302 | − | 0.0447817i | ||||
\(386\) | 10.0000 | 0.508987 | ||||||||
\(387\) | −16.9706 | − | 16.9706i | −0.862662 | − | 0.862662i | ||||
\(388\) | 6.00000 | + | 6.00000i | 0.304604 | + | 0.304604i | ||||
\(389\) | − | 30.0000i | − | 1.52106i | −0.649303 | − | 0.760530i | \(-0.724939\pi\) | ||
0.649303 | − | 0.760530i | \(-0.275061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.707107 | + | 0.707107i | 0.0357143 | + | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.0000i | 0.604551i | ||||||||
\(395\) | 8.48528 | − | 4.24264i | 0.426941 | − | 0.213470i | ||||
\(396\) | −9.00000 | + | 4.24264i | −0.452267 | + | 0.213201i | ||||
\(397\) | −9.00000 | + | 9.00000i | −0.451697 | + | 0.451697i | −0.895918 | − | 0.444220i | \(-0.853481\pi\) |
0.444220 | + | 0.895918i | \(0.353481\pi\) | |||||||
\(398\) | 15.5563 | − | 15.5563i | 0.779769 | − | 0.779769i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | + | 4.00000i | −0.150000 | + | 0.200000i | ||||
\(401\) | 22.0000 | 1.09863 | 0.549314 | − | 0.835616i | \(-0.314889\pi\) | ||||
0.549314 | + | 0.835616i | \(0.314889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.65685 | 0.281439 | ||||||||
\(405\) | 18.0000 | − | 9.00000i | 0.894427 | − | 0.447214i | ||||
\(406\) | − | 7.07107i | − | 0.350931i | ||||||
\(407\) | −9.51472 | + | 26.4853i | −0.471627 | + | 1.31283i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.89949 | 0.489499 | 0.244749 | − | 0.969586i | \(-0.421294\pi\) | ||||
0.244749 | + | 0.969586i | \(0.421294\pi\) | |||||||
\(410\) | 1.00000 | − | 3.00000i | 0.0493865 | − | 0.148159i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.00000 | + | 3.00000i | −0.147799 | + | 0.147799i | ||||
\(413\) | −2.82843 | + | 2.82843i | −0.139178 | + | 0.139178i | ||||
\(414\) | 8.48528 | 0.417029 | ||||||||
\(415\) | −8.48528 | + | 25.4558i | −0.416526 | + | 1.24958i | ||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13.2426 | + | 4.75736i | 0.647719 | + | 0.232690i | ||||
\(419\) | 8.00000i | 0.390826i | 0.980721 | + | 0.195413i | \(0.0626047\pi\) | ||||
−0.980721 | + | 0.195413i | \(0.937395\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.00000 | 0.292422 | 0.146211 | − | 0.989253i | \(-0.453292\pi\) | ||||
0.146211 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(422\) | 4.00000 | − | 4.00000i | 0.194717 | − | 0.194717i | ||||
\(423\) | −21.0000 | − | 21.0000i | −1.02105 | − | 1.02105i | ||||
\(424\) | −5.65685 | −0.274721 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.00000 | − | 2.00000i | 0.0967868 | − | 0.0967868i | ||||
\(428\) | −8.48528 | + | 8.48528i | −0.410152 | + | 0.410152i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.0000 | − | 8.00000i | 0.771589 | − | 0.385794i | ||||
\(431\) | 9.89949i | 0.476842i | 0.971162 | + | 0.238421i | \(0.0766298\pi\) | ||||
−0.971162 | + | 0.238421i | \(0.923370\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.0000 | + | 20.0000i | 0.961139 | + | 0.961139i | 0.999273 | − | 0.0381340i | \(-0.0121414\pi\) |
−0.0381340 | + | 0.999273i | \(0.512141\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 12.7279i | − | 0.609557i | ||||||
\(437\) | −8.48528 | − | 8.48528i | −0.405906 | − | 0.405906i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.1127 | 1.48493 | 0.742464 | − | 0.669886i | \(-0.233657\pi\) | ||||
0.742464 | + | 0.669886i | \(0.233657\pi\) | |||||||
\(440\) | −0.878680 | − | 7.36396i | −0.0418894 | − | 0.351063i | ||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.0000 | − | 15.0000i | −0.712672 | − | 0.712672i | 0.254422 | − | 0.967093i | \(-0.418115\pi\) |
−0.967093 | + | 0.254422i | \(0.918115\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.0000 | − | 28.0000i | −0.663664 | − | 1.32733i | ||||
\(446\) | 9.89949i | 0.468755i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.707107 | − | 0.707107i | 0.0334077 | − | 0.0334077i | ||||
\(449\) | 24.0000i | 1.13263i | 0.824189 | + | 0.566315i | \(0.191631\pi\) | ||||
−0.824189 | + | 0.566315i | \(0.808369\pi\) | |||||||
\(450\) | 2.12132 | + | 14.8492i | 0.100000 | + | 0.700000i | ||||
\(451\) | 2.00000 | + | 4.24264i | 0.0941763 | + | 0.199778i | ||||
\(452\) | 9.00000 | − | 9.00000i | 0.423324 | − | 0.423324i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 22.0000i | − | 1.03251i | ||||||
\(455\) | −4.00000 | + | 2.00000i | −0.187523 | + | 0.0937614i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.41421 | + | 1.41421i | 0.0661541 | + | 0.0661541i | 0.739410 | − | 0.673256i | \(-0.235105\pi\) |
−0.673256 | + | 0.739410i | \(0.735105\pi\) | |||||||
\(458\) | −1.41421 | + | 1.41421i | −0.0660819 | + | 0.0660819i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.00000 | + | 6.00000i | −0.0932505 | + | 0.279751i | ||||
\(461\) | 2.82843i | 0.131733i | 0.997828 | + | 0.0658665i | \(0.0209811\pi\) | ||||
−0.997828 | + | 0.0658665i | \(0.979019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0000 | − | 10.0000i | −0.464739 | − | 0.464739i | 0.435466 | − | 0.900205i | \(-0.356584\pi\) |
−0.900205 | + | 0.435466i | \(0.856584\pi\) | |||||||
\(464\) | −7.07107 | −0.328266 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 26.0000 | 1.20443 | ||||||||
\(467\) | −2.00000 | + | 2.00000i | −0.0925490 | + | 0.0925490i | −0.751865 | − | 0.659317i | \(-0.770846\pi\) |
0.659317 | + | 0.751865i | \(0.270846\pi\) | |||||||
\(468\) | 4.24264 | − | 4.24264i | 0.196116 | − | 0.196116i | ||||
\(469\) | −4.24264 | −0.195907 | ||||||||
\(470\) | 19.7990 | − | 9.89949i | 0.913259 | − | 0.456630i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.82843 | + | 2.82843i | 0.130189 | + | 0.130189i | ||||
\(473\) | −8.97056 | + | 24.9706i | −0.412467 | + | 1.14815i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.7279 | − | 16.9706i | 0.583997 | − | 0.778663i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.0000 | + | 12.0000i | −0.549442 | + | 0.549442i | ||||
\(478\) | −9.00000 | − | 9.00000i | −0.411650 | − | 0.411650i | ||||
\(479\) | 8.48528 | 0.387702 | 0.193851 | − | 0.981031i | \(-0.437902\pi\) | ||||
0.193851 | + | 0.981031i | \(0.437902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 16.9706i | − | 0.773791i | ||||||
\(482\) | −15.0000 | + | 15.0000i | −0.683231 | + | 0.683231i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.48528 | + | 7.00000i | 0.385695 | + | 0.318182i | ||||
\(485\) | −6.00000 | + | 18.0000i | −0.272446 | + | 0.817338i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(488\) | −2.00000 | − | 2.00000i | −0.0905357 | − | 0.0905357i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.707107 | + | 2.12132i | −0.0319438 | + | 0.0958315i | ||||
\(491\) | − | 2.82843i | − | 0.127645i | −0.997961 | − | 0.0638226i | \(-0.979671\pi\) | ||
0.997961 | − | 0.0638226i | \(-0.0203292\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −8.48528 | −0.381771 | ||||||||
\(495\) | −17.4853 | − | 13.7574i | −0.785905 | − | 0.618347i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.65685 | − | 5.65685i | −0.253745 | − | 0.253745i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 44.0000i | 1.96971i | 0.173379 | + | 0.984855i | \(0.444532\pi\) | ||||
−0.173379 | + | 0.984855i | \(0.555468\pi\) | |||||||
\(500\) | −11.0000 | − | 2.00000i | −0.491935 | − | 0.0894427i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.7990 | + | 19.7990i | −0.882793 | + | 0.882793i | −0.993818 | − | 0.111024i | \(-0.964587\pi\) |
0.111024 | + | 0.993818i | \(0.464587\pi\) | |||||||
\(504\) | − | 3.00000i | − | 0.133631i | ||||||
\(505\) | 5.65685 | + | 11.3137i | 0.251727 | + | 0.503453i | ||||
\(506\) | −4.00000 | − | 8.48528i | −0.177822 | − | 0.377217i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.89949 | − | 9.89949i | 0.439219 | − | 0.439219i | ||||
\(509\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | 0.265424 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.3137 | −0.499026 | ||||||||
\(515\) | −9.00000 | − | 3.00000i | −0.396587 | − | 0.132196i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.1005 | + | 30.8995i | −0.488200 | + | 1.35896i | ||||
\(518\) | −6.00000 | − | 6.00000i | −0.263625 | − | 0.263625i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.00000 | + | 4.00000i | 0.0877058 | + | 0.175412i | ||||
\(521\) | −30.0000 | −1.31432 | −0.657162 | − | 0.753749i | \(-0.728243\pi\) | ||||
−0.657162 | + | 0.753749i | \(0.728243\pi\) | |||||||
\(522\) | −15.0000 | + | 15.0000i | −0.656532 | + | 0.656532i | ||||
\(523\) | 9.89949 | − | 9.89949i | 0.432875 | − | 0.432875i | −0.456730 | − | 0.889605i | \(-0.650980\pi\) |
0.889605 | + | 0.456730i | \(0.150980\pi\) | |||||||
\(524\) | −1.41421 | −0.0617802 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.0000 | 0.610429 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 15.0000i | − | 0.652174i | ||||||
\(530\) | −5.65685 | − | 11.3137i | −0.245718 | − | 0.491436i | ||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | −3.00000 | + | 3.00000i | −0.130066 | + | 0.130066i | ||||
\(533\) | −2.00000 | − | 2.00000i | −0.0866296 | − | 0.0866296i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.4558 | − | 8.48528i | −1.10055 | − | 0.366851i | ||||
\(536\) | 4.24264i | 0.183254i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.7279 | + | 12.7279i | −0.548740 | + | 0.548740i | ||||
\(539\) | −1.41421 | − | 3.00000i | −0.0609145 | − | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.0122i | 1.76325i | 0.471949 | + | 0.881626i | \(0.343551\pi\) | ||||
−0.471949 | + | 0.881626i | \(0.656449\pi\) | |||||||
\(542\) | 22.0000 | − | 22.0000i | 0.944981 | − | 0.944981i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25.4558 | − | 12.7279i | 1.09041 | − | 0.545204i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.82843 | − | 2.82843i | −0.120935 | − | 0.120935i | 0.644049 | − | 0.764984i | \(-0.277253\pi\) |
−0.764984 | + | 0.644049i | \(0.777253\pi\) | |||||||
\(548\) | 5.00000 | + | 5.00000i | 0.213589 | + | 0.213589i | ||||
\(549\) | −8.48528 | −0.362143 | ||||||||
\(550\) | 13.8492 | − | 9.12132i | 0.590534 | − | 0.388934i | ||||
\(551\) | 30.0000 | 1.27804 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.00000 | − | 3.00000i | −0.127573 | − | 0.127573i | ||||
\(554\) | − | 8.00000i | − | 0.339887i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.3848i | 0.779688i | ||||||||
\(557\) | 1.41421 | + | 1.41421i | 0.0599222 | + | 0.0599222i | 0.736433 | − | 0.676511i | \(-0.236509\pi\) |
−0.676511 | + | 0.736433i | \(0.736509\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 16.0000i | − | 0.676728i | ||||||
\(560\) | 2.12132 | + | 0.707107i | 0.0896421 | + | 0.0298807i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.0000 | + | 20.0000i | −0.843649 | + | 0.843649i | ||||
\(563\) | 14.1421 | − | 14.1421i | 0.596020 | − | 0.596020i | −0.343231 | − | 0.939251i | \(-0.611521\pi\) |
0.939251 | + | 0.343231i | \(0.111521\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.0000 | + | 9.00000i | 1.13590 | + | 0.378633i | ||||
\(566\) | −6.00000 | −0.252199 | ||||||||
\(567\) | −6.36396 | − | 6.36396i | −0.267261 | − | 0.267261i | ||||
\(568\) | −5.65685 | + | 5.65685i | −0.237356 | + | 0.237356i | ||||
\(569\) | 28.2843 | 1.18574 | 0.592869 | − | 0.805299i | \(-0.297995\pi\) | ||||
0.592869 | + | 0.805299i | \(0.297995\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 33.9411i | − | 1.42039i | −0.704004 | − | 0.710196i | \(-0.748606\pi\) | ||
0.704004 | − | 0.710196i | \(-0.251394\pi\) | |||||||
\(572\) | −6.24264 | − | 2.24264i | −0.261018 | − | 0.0937695i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.41421 | −0.0590281 | ||||||||
\(575\) | −14.0000 | + | 2.00000i | −0.583840 | + | 0.0834058i | ||||
\(576\) | −3.00000 | −0.125000 | ||||||||
\(577\) | 2.00000 | − | 2.00000i | 0.0832611 | − | 0.0832611i | −0.664250 | − | 0.747511i | \(-0.731249\pi\) |
0.747511 | + | 0.664250i | \(0.231249\pi\) | |||||||
\(578\) | −12.0208 | + | 12.0208i | −0.500000 | + | 0.500000i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.07107 | − | 14.1421i | −0.293610 | − | 0.587220i | ||||
\(581\) | 12.0000 | 0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.6569 | + | 6.34315i | 0.731272 | + | 0.262706i | ||||
\(584\) | − | 6.00000i | − | 0.248282i | ||||||
\(585\) | 12.7279 | + | 4.24264i | 0.526235 | + | 0.175412i | ||||
\(586\) | −30.0000 | −1.23929 | ||||||||
\(587\) | 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 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −2.82843 | + | 8.48528i | −0.116445 | + | 0.349334i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.00000 | + | 6.00000i | −0.246598 | + | 0.246598i | ||||
\(593\) | 24.0416 | − | 24.0416i | 0.987271 | − | 0.987271i | −0.0126486 | − | 0.999920i | \(-0.504026\pi\) |
0.999920 | + | 0.0126486i | \(0.00402627\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.89949i | 0.405499i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.00000 | + | 4.00000i | 0.163572 | + | 0.163572i | ||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.6985i | 1.21143i | 0.795683 | + | 0.605713i | \(0.207112\pi\) | ||||
−0.795683 | + | 0.605713i | \(0.792888\pi\) | |||||||
\(602\) | −5.65685 | − | 5.65685i | −0.230556 | − | 0.230556i | ||||
\(603\) | 9.00000 | + | 9.00000i | 0.366508 | + | 0.366508i | ||||
\(604\) | −18.3848 | −0.748066 | ||||||||
\(605\) | −5.51472 | + | 23.9706i | −0.224205 | + | 0.974542i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.65685 | − | 5.65685i | −0.229605 | − | 0.229605i | 0.582923 | − | 0.812527i | \(-0.301909\pi\) |
−0.812527 | + | 0.582923i | \(0.801909\pi\) | |||||||
\(608\) | 3.00000 | + | 3.00000i | 0.121666 | + | 0.121666i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.00000 | − | 6.00000i | 0.0809776 | − | 0.242933i | ||||
\(611\) | − | 19.7990i | − | 0.800981i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.07107 | + | 7.07107i | −0.285598 | + | 0.285598i | −0.835337 | − | 0.549739i | \(-0.814727\pi\) |
0.549739 | + | 0.835337i | \(0.314727\pi\) | |||||||
\(614\) | − | 26.0000i | − | 1.04927i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.00000 | + | 1.41421i | −0.120873 | + | 0.0569803i | ||||
\(617\) | −17.0000 | + | 17.0000i | −0.684394 | + | 0.684394i | −0.960987 | − | 0.276593i | \(-0.910795\pi\) |
0.276593 | + | 0.960987i | \(0.410795\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 12.0000i | − | 0.482321i | −0.970485 | − | 0.241160i | \(-0.922472\pi\) | ||
0.970485 | − | 0.241160i | \(-0.0775280\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.2132 | + | 21.2132i | 0.850572 | + | 0.850572i | ||||
\(623\) | −9.89949 | + | 9.89949i | −0.396615 | + | 0.396615i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 16.9706i | 0.678280i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.00000 | + | 7.00000i | 0.279330 | + | 0.279330i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 6.00000 | − | 3.00000i | 0.239046 | − | 0.119523i | ||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | −3.00000 | + | 3.00000i | −0.119334 | + | 0.119334i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.3137 | −0.449325 | ||||||||
\(635\) | 29.6985 | + | 9.89949i | 1.17855 | + | 0.392849i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.41421 | + | 1.41421i | 0.0560332 | + | 0.0560332i | ||||
\(638\) | 22.0711 | + | 7.92893i | 0.873802 | + | 0.313909i | ||||
\(639\) | 24.0000i | 0.949425i | ||||||||
\(640\) | 0.707107 | − | 2.12132i | 0.0279508 | − | 0.0838525i | ||||
\(641\) | 8.00000 | 0.315981 | 0.157991 | − | 0.987441i | \(-0.449498\pi\) | ||||
0.157991 | + | 0.987441i | \(0.449498\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.0000 | + | 28.0000i | 1.10421 | + | 1.10421i | 0.993897 | + | 0.110316i | \(0.0351862\pi\) |
0.110316 | + | 0.993897i | \(0.464814\pi\) | |||||||
\(644\) | 2.82843 | 0.111456 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.0000 | + | 19.0000i | −0.746967 | + | 0.746967i | −0.973908 | − | 0.226941i | \(-0.927127\pi\) |
0.226941 | + | 0.973908i | \(0.427127\pi\) | |||||||
\(648\) | −6.36396 | + | 6.36396i | −0.250000 | + | 0.250000i | ||||
\(649\) | −5.65685 | − | 12.0000i | −0.222051 | − | 0.471041i | ||||
\(650\) | −6.00000 | + | 8.00000i | −0.235339 | + | 0.313786i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.00000 | + | 1.00000i | −0.0391630 | + | 0.0391630i | ||||
\(653\) | 4.00000 | + | 4.00000i | 0.156532 | + | 0.156532i | 0.781028 | − | 0.624496i | \(-0.214696\pi\) |
−0.624496 | + | 0.781028i | \(0.714696\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.41421 | − | 2.82843i | −0.0552579 | − | 0.110516i | ||||
\(656\) | 1.41421i | 0.0552158i | ||||||||
\(657\) | −12.7279 | − | 12.7279i | −0.496564 | − | 0.496564i | ||||
\(658\) | −7.00000 | − | 7.00000i | −0.272888 | − | 0.272888i | ||||
\(659\) | 31.1127 | 1.21198 | 0.605989 | − | 0.795473i | \(-0.292777\pi\) | ||||
0.605989 | + | 0.795473i | \(0.292777\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.0000 | −0.855701 | −0.427850 | − | 0.903850i | \(-0.640729\pi\) | ||||
−0.427850 | + | 0.903850i | \(0.640729\pi\) | |||||||
\(662\) | −2.82843 | − | 2.82843i | −0.109930 | − | 0.109930i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 12.0000i | − | 0.465690i | ||||||
\(665\) | −9.00000 | − | 3.00000i | −0.349005 | − | 0.116335i | ||||
\(666\) | 25.4558i | 0.986394i | ||||||||
\(667\) | −14.1421 | − | 14.1421i | −0.547586 | − | 0.547586i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.48528 | + | 4.24264i | −0.327815 | + | 0.163908i | ||||
\(671\) | 4.00000 | + | 8.48528i | 0.154418 | + | 0.327571i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.5563 | + | 15.5563i | −0.599653 | + | 0.599653i | −0.940220 | − | 0.340567i | \(-0.889381\pi\) |
0.340567 | + | 0.940220i | \(0.389381\pi\) | |||||||
\(674\) | 22.0000i | 0.847408i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 18.3848 | + | 18.3848i | 0.706584 | + | 0.706584i | 0.965815 | − | 0.259231i | \(-0.0834691\pi\) |
−0.259231 | + | 0.965815i | \(0.583469\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.48528 | 0.325635 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.0000 | + | 33.0000i | 1.26271 | + | 1.26271i | 0.949774 | + | 0.312936i | \(0.101312\pi\) |
0.312936 | + | 0.949774i | \(0.398688\pi\) | |||||||
\(684\) | 12.7279 | 0.486664 | ||||||||
\(685\) | −5.00000 | + | 15.0000i | −0.191040 | + | 0.573121i | ||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.65685 | + | 5.65685i | −0.215666 | + | 0.215666i | ||||
\(689\) | −11.3137 | −0.431018 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.0000 | 0.456502 | 0.228251 | − | 0.973602i | \(-0.426699\pi\) | ||||
0.228251 | + | 0.973602i | \(0.426699\pi\) | |||||||
\(692\) | −12.7279 | − | 12.7279i | −0.483843 | − | 0.483843i | ||||
\(693\) | −3.36396 | + | 9.36396i | −0.127786 | + | 0.355707i | ||||
\(694\) | 4.00000i | 0.151838i | ||||||||
\(695\) | −36.7696 | + | 18.3848i | −1.39475 | + | 0.697374i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 24.0000 | + | 24.0000i | 0.908413 | + | 0.908413i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.707107 | + | 4.94975i | 0.0267261 | + | 0.187083i | ||||
\(701\) | − | 38.1838i | − | 1.44218i | −0.692841 | − | 0.721090i | \(-0.743641\pi\) | ||
0.692841 | − | 0.721090i | \(-0.256359\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.4558 | − | 25.4558i | 0.960085 | − | 0.960085i | ||||
\(704\) | 1.41421 | + | 3.00000i | 0.0533002 | + | 0.113067i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.65685i | 0.212899i | ||||||||
\(707\) | 4.00000 | − | 4.00000i | 0.150435 | − | 0.150435i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.0000i | 0.375558i | 0.982211 | + | 0.187779i | \(0.0601289\pi\) | ||||
−0.982211 | + | 0.187779i | \(0.939871\pi\) | |||||||
\(710\) | −16.9706 | − | 5.65685i | −0.636894 | − | 0.212298i | ||||
\(711\) | 12.7279i | 0.477334i | ||||||||
\(712\) | 9.89949 | + | 9.89949i | 0.370999 | + | 0.370999i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.75736 | − | 14.7279i | −0.0657215 | − | 0.550793i | ||||
\(716\) | 2.00000 | 0.0747435 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.00000 | − | 7.00000i | −0.261238 | − | 0.261238i | ||||
\(719\) | 24.0000i | 0.895049i | 0.894272 | + | 0.447524i | \(0.147694\pi\) | ||||
−0.894272 | + | 0.447524i | \(0.852306\pi\) | |||||||
\(720\) | −3.00000 | − | 6.00000i | −0.111803 | − | 0.223607i | ||||
\(721\) | 4.24264i | 0.158004i | ||||||||
\(722\) | 0.707107 | + | 0.707107i | 0.0263158 | + | 0.0263158i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.00000i | 0.148659i | ||||||||
\(725\) | 21.2132 | − | 28.2843i | 0.787839 | − | 1.05045i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.0000 | + | 31.0000i | −1.14973 | + | 1.14973i | −0.163120 | + | 0.986606i | \(0.552156\pi\) |
−0.986606 | + | 0.163120i | \(0.947844\pi\) | |||||||
\(728\) | 1.41421 | − | 1.41421i | 0.0524142 | − | 0.0524142i | ||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 12.0000 | − | 6.00000i | 0.444140 | − | 0.222070i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.89949 | + | 9.89949i | −0.365646 | + | 0.365646i | −0.865887 | − | 0.500240i | \(-0.833245\pi\) |
0.500240 | + | 0.865887i | \(0.333245\pi\) | |||||||
\(734\) | −35.3553 | −1.30499 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 2.82843i | − | 0.104257i | ||||||
\(737\) | 4.75736 | − | 13.2426i | 0.175240 | − | 0.487799i | ||||
\(738\) | 3.00000 | + | 3.00000i | 0.110432 | + | 0.110432i | ||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | −18.0000 | − | 6.00000i | −0.661693 | − | 0.220564i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.00000 | + | 4.00000i | −0.146845 | + | 0.146845i | ||||
\(743\) | −1.41421 | + | 1.41421i | −0.0518825 | + | 0.0518825i | −0.732572 | − | 0.680690i | \(-0.761680\pi\) |
0.680690 | + | 0.732572i | \(0.261680\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.7990 | + | 9.89949i | −0.725379 | + | 0.362689i | ||||
\(746\) | 20.0000 | 0.732252 | ||||||||
\(747\) | −25.4558 | − | 25.4558i | −0.931381 | − | 0.931381i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.0000i | 0.438470i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.00000 | 0.145962 | 0.0729810 | − | 0.997333i | \(-0.476749\pi\) | ||||
0.0729810 | + | 0.997333i | \(0.476749\pi\) | |||||||
\(752\) | −7.00000 | + | 7.00000i | −0.255264 | + | 0.255264i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −14.1421 | −0.515026 | ||||||||
\(755\) | −18.3848 | − | 36.7696i | −0.669091 | − | 1.33818i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.0000 | + | 14.0000i | −0.508839 | + | 0.508839i | −0.914170 | − | 0.405331i | \(-0.867156\pi\) |
0.405331 | + | 0.914170i | \(0.367156\pi\) | |||||||
\(758\) | −21.2132 | + | 21.2132i | −0.770498 | + | 0.770498i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.00000 | + | 9.00000i | −0.108821 | + | 0.326464i | ||||
\(761\) | − | 9.89949i | − | 0.358856i | −0.983771 | − | 0.179428i | \(-0.942575\pi\) | ||
0.983771 | − | 0.179428i | \(-0.0574248\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.00000 | − | 9.00000i | −0.325822 | − | 0.325822i | ||||
\(764\) | − | 16.0000i | − | 0.578860i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.7279i | 0.459879i | ||||||||
\(767\) | 5.65685 | + | 5.65685i | 0.204257 | + | 0.204257i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.8406 | −1.58093 | −0.790467 | − | 0.612505i | \(-0.790162\pi\) | ||||
−0.790467 | + | 0.612505i | \(0.790162\pi\) | |||||||
\(770\) | −5.82843 | − | 4.58579i | −0.210042 | − | 0.165260i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.07107 | − | 7.07107i | −0.254493 | − | 0.254493i | ||||
\(773\) | 15.0000 | + | 15.0000i | 0.539513 | + | 0.539513i | 0.923386 | − | 0.383873i | \(-0.125410\pi\) |
−0.383873 | + | 0.923386i | \(0.625410\pi\) | |||||||
\(774\) | 24.0000i | 0.862662i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 8.48528i | − | 0.304604i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.2132 | + | 21.2132i | −0.760530 | + | 0.760530i | ||||
\(779\) | − | 6.00000i | − | 0.214972i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | − | 11.3137i | 0.858788 | − | 0.404836i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | −7.00000 | + | 21.0000i | −0.249841 | + | 0.749522i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.48528 | − | 8.48528i | −0.302468 | − | 0.302468i | 0.539511 | − | 0.841979i | \(-0.318609\pi\) |
−0.841979 | + | 0.539511i | \(0.818609\pi\) | |||||||
\(788\) | 8.48528 | − | 8.48528i | 0.302276 | − | 0.302276i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.00000 | − | 3.00000i | −0.320206 | − | 0.106735i | ||||
\(791\) | − | 12.7279i | − | 0.452553i | ||||||
\(792\) | 9.36396 | + | 3.36396i | 0.332734 | + | 0.119533i | ||||
\(793\) | −4.00000 | − | 4.00000i | −0.142044 | − | 0.142044i | ||||
\(794\) | 12.7279 | 0.451697 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.0000 | −0.779769 | ||||||||
\(797\) | −29.0000 | + | 29.0000i | −1.02723 | + | 1.02723i | −0.0276140 | + | 0.999619i | \(0.508791\pi\) |
−0.999619 | + | 0.0276140i | \(0.991209\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.94975 | − | 0.707107i | 0.175000 | − | 0.0250000i | ||||
\(801\) | 42.0000 | 1.48400 | ||||||||
\(802\) | −15.5563 | − | 15.5563i | −0.549314 | − | 0.549314i | ||||
\(803\) | −6.72792 | + | 18.7279i | −0.237423 | + | 0.660894i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.82843 | + | 5.65685i | 0.0996890 | + | 0.199378i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.00000 | − | 4.00000i | −0.140720 | − | 0.140720i | ||||
\(809\) | 45.2548 | 1.59108 | 0.795538 | − | 0.605904i | \(-0.207189\pi\) | ||||
0.795538 | + | 0.605904i | \(0.207189\pi\) | |||||||
\(810\) | −19.0919 | − | 6.36396i | −0.670820 | − | 0.223607i | ||||
\(811\) | 29.6985i | 1.04285i | 0.853296 | + | 0.521427i | \(0.174600\pi\) | ||||
−0.853296 | + | 0.521427i | \(0.825400\pi\) | |||||||
\(812\) | −5.00000 | + | 5.00000i | −0.175466 | + | 0.175466i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 25.4558 | − | 12.0000i | 0.892227 | − | 0.420600i | ||||
\(815\) | −3.00000 | − | 1.00000i | −0.105085 | − | 0.0350285i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.0000 | − | 24.0000i | 0.839654 | − | 0.839654i | ||||
\(818\) | −7.00000 | − | 7.00000i | −0.244749 | − | 0.244749i | ||||
\(819\) | − | 6.00000i | − | 0.209657i | ||||||
\(820\) | −2.82843 | + | 1.41421i | −0.0987730 | + | 0.0493865i | ||||
\(821\) | − | 46.6690i | − | 1.62876i | −0.580331 | − | 0.814380i | \(-0.697077\pi\) | ||
0.580331 | − | 0.814380i | \(-0.302923\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0000 | + | 16.0000i | 0.557725 | + | 0.557725i | 0.928659 | − | 0.370934i | \(-0.120962\pi\) |
−0.370934 | + | 0.928659i | \(0.620962\pi\) | |||||||
\(824\) | 4.24264 | 0.147799 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.00000 | 0.139178 | ||||||||
\(827\) | −16.9706 | − | 16.9706i | −0.590124 | − | 0.590124i | 0.347541 | − | 0.937665i | \(-0.387017\pi\) |
−0.937665 | + | 0.347541i | \(0.887017\pi\) | |||||||
\(828\) | −6.00000 | − | 6.00000i | −0.208514 | − | 0.208514i | ||||
\(829\) | 16.0000i | 0.555703i | 0.960624 | + | 0.277851i | \(0.0896223\pi\) | ||||
−0.960624 | + | 0.277851i | \(0.910378\pi\) | |||||||
\(830\) | 24.0000 | − | 12.0000i | 0.833052 | − | 0.416526i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.41421 | − | 1.41421i | −0.0490290 | − | 0.0490290i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.00000 | − | 12.7279i | −0.207514 | − | 0.440204i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.65685 | − | 5.65685i | 0.195413 | − | 0.195413i | ||||
\(839\) | − | 48.0000i | − | 1.65714i | −0.559883 | − | 0.828572i | \(-0.689154\pi\) | ||
0.559883 | − | 0.828572i | \(-0.310846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | −4.24264 | − | 4.24264i | −0.146211 | − | 0.146211i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.65685 | −0.194717 | ||||||||
\(845\) | −9.00000 | − | 18.0000i | −0.309609 | − | 0.619219i | ||||
\(846\) | 29.6985i | 1.02105i | ||||||||
\(847\) | 10.9497 | − | 1.05025i | 0.376238 | − | 0.0360871i | ||||
\(848\) | 4.00000 | + | 4.00000i | 0.137361 | + | 0.137361i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.0000 | −0.822709 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.89949 | + | 9.89949i | −0.338952 | + | 0.338952i | −0.855973 | − | 0.517021i | \(-0.827041\pi\) |
0.517021 | + | 0.855973i | \(0.327041\pi\) | |||||||
\(854\) | −2.82843 | −0.0967868 | ||||||||
\(855\) | 12.7279 | + | 25.4558i | 0.435286 | + | 0.870572i | ||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | 26.8701 | + | 26.8701i | 0.917864 | + | 0.917864i | 0.996874 | − | 0.0790101i | \(-0.0251759\pi\) |
−0.0790101 | + | 0.996874i | \(0.525176\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000i | 0.682391i | 0.939992 | + | 0.341196i | \(0.110832\pi\) | ||||
−0.939992 | + | 0.341196i | \(0.889168\pi\) | |||||||
\(860\) | −16.9706 | − | 5.65685i | −0.578691 | − | 0.192897i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.00000 | − | 7.00000i | 0.238421 | − | 0.238421i | ||||
\(863\) | 32.0000 | + | 32.0000i | 1.08929 | + | 1.08929i | 0.995601 | + | 0.0936914i | \(0.0298667\pi\) |
0.0936914 | + | 0.995601i | \(0.470133\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.7279 | − | 38.1838i | 0.432762 | − | 1.29829i | ||||
\(866\) | − | 28.2843i | − | 0.961139i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.7279 | − | 6.00000i | 0.431765 | − | 0.203536i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.48528i | 0.287513i | ||||||||
\(872\) | −9.00000 | + | 9.00000i | −0.304778 | + | 0.304778i | ||||
\(873\) | −18.0000 | − | 18.0000i | −0.609208 | − | 0.609208i | ||||
\(874\) | 12.0000i | 0.405906i | ||||||||
\(875\) | −9.19239 | + | 6.36396i | −0.310759 | + | 0.215141i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.6274 | − | 22.6274i | −0.764074 | − | 0.764074i | 0.212982 | − | 0.977056i | \(-0.431682\pi\) |
−0.977056 | + | 0.212982i | \(0.931682\pi\) | |||||||
\(878\) | −22.0000 | − | 22.0000i | −0.742464 | − | 0.742464i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.58579 | + | 5.82843i | −0.154587 | + | 0.196476i | ||||
\(881\) | 22.0000 | 0.741199 | 0.370599 | − | 0.928793i | \(-0.379152\pi\) | ||||
0.370599 | + | 0.928793i | \(0.379152\pi\) | |||||||
\(882\) | −2.12132 | − | 2.12132i | −0.0714286 | − | 0.0714286i | ||||
\(883\) | −3.00000 | − | 3.00000i | −0.100958 | − | 0.100958i | 0.654824 | − | 0.755782i | \(-0.272743\pi\) |
−0.755782 | + | 0.654824i | \(0.772743\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.2132i | 0.712672i | ||||||||
\(887\) | −25.4558 | − | 25.4558i | −0.854724 | − | 0.854724i | 0.135987 | − | 0.990711i | \(-0.456579\pi\) |
−0.990711 | + | 0.135987i | \(0.956579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 14.0000i | − | 0.469545i | ||||||
\(890\) | −9.89949 | + | 29.6985i | −0.331832 | + | 0.995495i | ||||
\(891\) | 27.0000 | − | 12.7279i | 0.904534 | − | 0.426401i | ||||
\(892\) | 7.00000 | − | 7.00000i | 0.234377 | − | 0.234377i | ||||
\(893\) | 29.6985 | − | 29.6985i | 0.993822 | − | 0.993822i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.00000 | + | 4.00000i | 0.0668526 | + | 0.133705i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.9706 | − | 16.9706i | 0.566315 | − | 0.566315i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 9.00000 | − | 12.0000i | 0.300000 | − | 0.400000i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 1.58579 | − | 4.41421i | 0.0528009 | − | 0.146977i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.7279 | −0.423324 | ||||||||
\(905\) | −8.00000 | + | 4.00000i | −0.265929 | + | 0.132964i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.0000 | + | 35.0000i | −1.16216 | + | 1.16216i | −0.178153 | + | 0.984003i | \(0.557012\pi\) |
−0.984003 | + | 0.178153i | \(0.942988\pi\) | |||||||
\(908\) | −15.5563 | + | 15.5563i | −0.516256 | + | 0.516256i | ||||
\(909\) | −16.9706 | −0.562878 | ||||||||
\(910\) | 4.24264 | + | 1.41421i | 0.140642 | + | 0.0468807i | ||||
\(911\) | −20.0000 | −0.662630 | −0.331315 | − | 0.943520i | \(-0.607492\pi\) | ||||
−0.331315 | + | 0.943520i | \(0.607492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.4558 | + | 37.4558i | −0.445323 | + | 1.23961i | ||||
\(914\) | − | 2.00000i | − | 0.0661541i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.00000 | 0.0660819 | ||||||||
\(917\) | −1.00000 | + | 1.00000i | −0.0330229 | + | 0.0330229i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.1838 | 1.25957 | 0.629783 | − | 0.776771i | \(-0.283144\pi\) | ||||
0.629783 | + | 0.776771i | \(0.283144\pi\) | |||||||
\(920\) | 5.65685 | − | 2.82843i | 0.186501 | − | 0.0932505i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.00000 | − | 2.00000i | 0.0658665 | − | 0.0658665i | ||||
\(923\) | −11.3137 | + | 11.3137i | −0.372395 | + | 0.372395i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.00000 | − | 42.0000i | −0.197279 | − | 1.38095i | ||||
\(926\) | 14.1421i | 0.464739i | ||||||||
\(927\) | 9.00000 | − | 9.00000i | 0.295599 | − | 0.295599i | ||||
\(928\) | 5.00000 | + | 5.00000i | 0.164133 | + | 0.164133i | ||||
\(929\) | 6.00000i | 0.196854i | 0.995144 | + | 0.0984268i | \(0.0313810\pi\) | ||||
−0.995144 | + | 0.0984268i | \(0.968619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.24264i | 0.139047i | ||||||||
\(932\) | −18.3848 | − | 18.3848i | −0.602213 | − | 0.602213i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.82843 | 0.0925490 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.00000 | −0.196116 | ||||||||
\(937\) | 31.1127 | + | 31.1127i | 1.01641 | + | 1.01641i | 0.999863 | + | 0.0165444i | \(0.00526649\pi\) |
0.0165444 | + | 0.999863i | \(0.494734\pi\) | |||||||
\(938\) | 3.00000 | + | 3.00000i | 0.0979535 | + | 0.0979535i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −21.0000 | − | 7.00000i | −0.684944 | − | 0.228315i | ||||
\(941\) | 39.5980i | 1.29086i | 0.763821 | + | 0.645429i | \(0.223321\pi\) | ||||
−0.763821 | + | 0.645429i | \(0.776679\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.82843 | + | 2.82843i | −0.0921063 | + | 0.0921063i | ||||
\(944\) | − | 4.00000i | − | 0.130189i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.0000 | − | 11.3137i | 0.780307 | − | 0.367840i | ||||
\(947\) | 39.0000 | − | 39.0000i | 1.26733 | − | 1.26733i | 0.319867 | − | 0.947462i | \(-0.396362\pi\) |
0.947462 | − | 0.319867i | \(-0.103638\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 12.0000i | − | 0.389536i | ||||||
\(950\) | −21.0000 | + | 3.00000i | −0.681330 | + | 0.0973329i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.89949 | + | 9.89949i | −0.320676 | + | 0.320676i | −0.849026 | − | 0.528350i | \(-0.822811\pi\) |
0.528350 | + | 0.849026i | \(0.322811\pi\) | |||||||
\(954\) | 16.9706 | 0.549442 | ||||||||
\(955\) | 32.0000 | − | 16.0000i | 1.03550 | − | 0.517748i | ||||
\(956\) | 12.7279i | 0.411650i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.00000 | − | 6.00000i | −0.193851 | − | 0.193851i | ||||
\(959\) | 7.07107 | 0.228337 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −12.0000 | + | 12.0000i | −0.386896 | + | 0.386896i | ||||
\(963\) | 25.4558 | − | 25.4558i | 0.820303 | − | 0.820303i | ||||
\(964\) | 21.2132 | 0.683231 | ||||||||
\(965\) | 7.07107 | − | 21.2132i | 0.227626 | − | 0.682877i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.7279 | − | 12.7279i | −0.409302 | − | 0.409302i | 0.472193 | − | 0.881495i | \(-0.343463\pi\) |
−0.881495 | + | 0.472193i | \(0.843463\pi\) | |||||||
\(968\) | −1.05025 | − | 10.9497i | −0.0337564 | − | 0.351938i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.9706 | − | 8.48528i | 0.544892 | − | 0.272446i | ||||
\(971\) | −12.0000 | −0.385098 | −0.192549 | − | 0.981287i | \(-0.561675\pi\) | ||||
−0.192549 | + | 0.981287i | \(0.561675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.0000 | + | 13.0000i | 0.416761 | + | 0.416761i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.82843i | 0.0905357i | ||||||||
\(977\) | −15.0000 | + | 15.0000i | −0.479893 | + | 0.479893i | −0.905097 | − | 0.425205i | \(-0.860202\pi\) |
0.425205 | + | 0.905097i | \(0.360202\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.7990 | − | 42.0000i | −0.632778 | − | 1.34233i | ||||
\(980\) | 2.00000 | − | 1.00000i | 0.0638877 | − | 0.0319438i | ||||
\(981\) | 38.1838i | 1.21911i | ||||||||
\(982\) | −2.00000 | + | 2.00000i | −0.0638226 | + | 0.0638226i | ||||
\(983\) | −23.0000 | − | 23.0000i | −0.733586 | − | 0.733586i | 0.237742 | − | 0.971328i | \(-0.423593\pi\) |
−0.971328 | + | 0.237742i | \(0.923593\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.4558 | + | 8.48528i | 0.811091 | + | 0.270364i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.00000 | + | 6.00000i | 0.190885 | + | 0.190885i | ||||
\(989\) | −22.6274 | −0.719510 | ||||||||
\(990\) | 2.63604 | + | 22.0919i | 0.0837788 | + | 0.702126i | ||||
\(991\) | −28.0000 | −0.889449 | −0.444725 | − | 0.895667i | \(-0.646698\pi\) | ||||
−0.444725 | + | 0.895667i | \(0.646698\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.00000i | 0.253745i | ||||||||
\(995\) | −22.0000 | − | 44.0000i | −0.697447 | − | 1.39489i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.07107 | − | 7.07107i | −0.223943 | − | 0.223943i | 0.586214 | − | 0.810157i | \(-0.300618\pi\) |
−0.810157 | + | 0.586214i | \(0.800618\pi\) | |||||||
\(998\) | 31.1127 | − | 31.1127i | 0.984855 | − | 0.984855i | ||||
\(999\) | 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 | 770.2.m.a.43.1 | ✓ | 4 | |
5.2 | odd | 4 | inner | 770.2.m.a.197.2 | yes | 4 | |
11.10 | odd | 2 | inner | 770.2.m.a.43.2 | yes | 4 | |
55.32 | even | 4 | inner | 770.2.m.a.197.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.m.a.43.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
770.2.m.a.43.2 | yes | 4 | 11.10 | odd | 2 | inner | |
770.2.m.a.197.1 | yes | 4 | 55.32 | even | 4 | inner | |
770.2.m.a.197.2 | yes | 4 | 5.2 | odd | 4 | inner |