Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(49,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.j (of order \(6\), degree \(2\), not 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.49 |
Dual form | 950.2.j.b.349.2 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | 0.228714 | − | 0.973494i | \(-0.426548\pi\) |
−0.728714 | + | 0.684819i | \(0.759881\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | − | 1.73205i | −0.333333 | − | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 5.19615 | − | 3.00000i | 1.44115 | − | 0.832050i | 0.443227 | − | 0.896410i | \(-0.353834\pi\) |
0.997927 | + | 0.0643593i | \(0.0205004\pi\) | |||||||
\(14\) | −1.00000 | + | 1.73205i | −0.267261 | + | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 6.06218 | + | 3.50000i | 1.47029 | + | 0.848875i | 0.999444 | − | 0.0333386i | \(-0.0106140\pi\) |
0.470850 | + | 0.882213i | \(0.343947\pi\) | |||||||
\(18\) | − | 2.00000i | − | 0.471405i | ||||||
\(19\) | −3.50000 | + | 2.59808i | −0.802955 | + | 0.596040i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | − | 1.73205i | 0.218218 | − | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.73205 | − | 1.00000i | 0.361158 | − | 0.208514i | −0.308431 | − | 0.951247i | \(-0.599804\pi\) |
0.669588 | + | 0.742732i | \(0.266471\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.00000 | 1.17670 | ||||||||
\(27\) | 5.00000i | 0.962250i | ||||||||
\(28\) | −1.73205 | + | 1.00000i | −0.327327 | + | 0.188982i | ||||
\(29\) | 5.00000 | + | 8.66025i | 0.928477 | + | 1.60817i | 0.785872 | + | 0.618389i | \(0.212214\pi\) |
0.142605 | + | 0.989780i | \(0.454452\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.50000 | + | 6.06218i | 0.600245 | + | 1.03965i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | − | 1.73205i | 0.166667 | − | 0.288675i | ||||
\(37\) | − | 4.00000i | − | 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | −4.33013 | + | 0.500000i | −0.702439 | + | 0.0811107i | ||||
\(39\) | −6.00000 | −0.960769 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | + | 1.73205i | −0.156174 | + | 0.270501i | −0.933486 | − | 0.358614i | \(-0.883249\pi\) |
0.777312 | + | 0.629115i | \(0.216583\pi\) | |||||||
\(42\) | 1.73205 | − | 1.00000i | 0.267261 | − | 0.154303i | ||||
\(43\) | 10.3923 | + | 6.00000i | 1.58481 | + | 0.914991i | 0.994142 | + | 0.108078i | \(0.0344695\pi\) |
0.590669 | + | 0.806914i | \(0.298864\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | 0.866025 | − | 0.500000i | 0.125000 | − | 0.0721688i | ||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.50000 | − | 6.06218i | −0.490098 | − | 0.848875i | ||||
\(52\) | 5.19615 | + | 3.00000i | 0.720577 | + | 0.416025i | ||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | −2.50000 | + | 4.33013i | −0.340207 | + | 0.589256i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | −0.267261 | ||||||||
\(57\) | 4.33013 | − | 0.500000i | 0.573539 | − | 0.0662266i | ||||
\(58\) | 10.0000i | 1.31306i | ||||||||
\(59\) | −0.500000 | + | 0.866025i | −0.0650945 | + | 0.112747i | −0.896736 | − | 0.442566i | \(-0.854068\pi\) |
0.831641 | + | 0.555313i | \(0.187402\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | −1.73205 | − | 1.00000i | −0.219971 | − | 0.127000i | ||||
\(63\) | 3.46410 | − | 2.00000i | 0.436436 | − | 0.251976i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.92820 | + | 4.00000i | −0.846415 | + | 0.488678i | −0.859440 | − | 0.511237i | \(-0.829187\pi\) |
0.0130248 | + | 0.999915i | \(0.495854\pi\) | |||||||
\(68\) | 7.00000i | 0.848875i | ||||||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | − | 10.3923i | 0.712069 | − | 1.23334i | −0.252010 | − | 0.967725i | \(-0.581092\pi\) |
0.964079 | − | 0.265615i | \(-0.0855750\pi\) | |||||||
\(72\) | 1.73205 | − | 1.00000i | 0.204124 | − | 0.117851i | ||||
\(73\) | 2.59808 | + | 1.50000i | 0.304082 | + | 0.175562i | 0.644275 | − | 0.764794i | \(-0.277159\pi\) |
−0.340193 | + | 0.940356i | \(0.610493\pi\) | |||||||
\(74\) | 2.00000 | − | 3.46410i | 0.232495 | − | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | − | 1.73205i | −0.458831 | − | 0.198680i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.19615 | − | 3.00000i | −0.588348 | − | 0.339683i | ||||
\(79\) | −2.00000 | + | 3.46410i | −0.225018 | + | 0.389742i | −0.956325 | − | 0.292306i | \(-0.905577\pi\) |
0.731307 | + | 0.682048i | \(0.238911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.73205 | + | 1.00000i | −0.191273 | + | 0.110432i | ||||
\(83\) | − | 13.0000i | − | 1.42694i | −0.700688 | − | 0.713468i | \(-0.747124\pi\) | ||
0.700688 | − | 0.713468i | \(-0.252876\pi\) | |||||||
\(84\) | 2.00000 | 0.218218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.00000 | + | 10.3923i | 0.646997 | + | 1.12063i | ||||
\(87\) | − | 10.0000i | − | 1.07211i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.50000 | − | 11.2583i | −0.688999 | − | 1.19338i | −0.972162 | − | 0.234309i | \(-0.924717\pi\) |
0.283164 | − | 0.959072i | \(-0.408616\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | + | 10.3923i | 0.628971 | + | 1.08941i | ||||
\(92\) | 1.73205 | + | 1.00000i | 0.180579 | + | 0.104257i | ||||
\(93\) | 1.73205 | + | 1.00000i | 0.179605 | + | 0.103695i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 12.9904 | + | 7.50000i | 1.31897 | + | 0.761510i | 0.983563 | − | 0.180563i | \(-0.0577919\pi\) |
0.335410 | + | 0.942072i | \(0.391125\pi\) | |||||||
\(98\) | 2.59808 | + | 1.50000i | 0.262445 | + | 0.151523i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.00000 | − | 1.73205i | −0.0995037 | − | 0.172345i | 0.811976 | − | 0.583691i | \(-0.198392\pi\) |
−0.911479 | + | 0.411346i | \(0.865059\pi\) | |||||||
\(102\) | − | 7.00000i | − | 0.693103i | ||||||
\(103\) | 12.0000i | 1.18240i | 0.806527 | + | 0.591198i | \(0.201345\pi\) | ||||
−0.806527 | + | 0.591198i | \(0.798655\pi\) | |||||||
\(104\) | 3.00000 | + | 5.19615i | 0.294174 | + | 0.509525i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 15.0000i | − | 1.45010i | −0.688694 | − | 0.725052i | \(-0.741816\pi\) | ||
0.688694 | − | 0.725052i | \(-0.258184\pi\) | |||||||
\(108\) | −4.33013 | + | 2.50000i | −0.416667 | + | 0.240563i | ||||
\(109\) | −1.00000 | + | 1.73205i | −0.0957826 | + | 0.165900i | −0.909935 | − | 0.414751i | \(-0.863869\pi\) |
0.814152 | + | 0.580651i | \(0.197202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | + | 3.46410i | −0.189832 | + | 0.328798i | ||||
\(112\) | −1.73205 | − | 1.00000i | −0.163663 | − | 0.0944911i | ||||
\(113\) | 1.00000i | 0.0940721i | 0.998893 | + | 0.0470360i | \(0.0149776\pi\) | ||||
−0.998893 | + | 0.0470360i | \(0.985022\pi\) | |||||||
\(114\) | 4.00000 | + | 1.73205i | 0.374634 | + | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.00000 | + | 8.66025i | −0.464238 | + | 0.804084i | ||||
\(117\) | −10.3923 | − | 6.00000i | −0.960769 | − | 0.554700i | ||||
\(118\) | −0.866025 | + | 0.500000i | −0.0797241 | + | 0.0460287i | ||||
\(119\) | −7.00000 | + | 12.1244i | −0.641689 | + | 1.11144i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | − | 8.00000i | − | 0.724286i | ||||||
\(123\) | 1.73205 | − | 1.00000i | 0.156174 | − | 0.0901670i | ||||
\(124\) | −1.00000 | − | 1.73205i | −0.0898027 | − | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.00000 | 0.356348 | ||||||||
\(127\) | −10.3923 | + | 6.00000i | −0.922168 | + | 0.532414i | −0.884326 | − | 0.466870i | \(-0.845382\pi\) |
−0.0378419 | + | 0.999284i | \(0.512048\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −6.00000 | − | 10.3923i | −0.528271 | − | 0.914991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.500000 | + | 0.866025i | −0.0436852 | + | 0.0756650i | −0.887041 | − | 0.461690i | \(-0.847243\pi\) |
0.843356 | + | 0.537355i | \(0.180577\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.19615 | − | 7.00000i | −0.450564 | − | 0.606977i | ||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.50000 | + | 6.06218i | −0.300123 | + | 0.519827i | ||||
\(137\) | −12.9904 | + | 7.50000i | −1.10984 | + | 0.640768i | −0.938789 | − | 0.344493i | \(-0.888051\pi\) |
−0.171054 | + | 0.985262i | \(0.554717\pi\) | |||||||
\(138\) | −1.73205 | − | 1.00000i | −0.147442 | − | 0.0851257i | ||||
\(139\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.3923 | − | 6.00000i | 0.872103 | − | 0.503509i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.00000 | 0.166667 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.50000 | + | 2.59808i | 0.124141 | + | 0.215018i | ||||
\(147\) | −2.59808 | − | 1.50000i | −0.214286 | − | 0.123718i | ||||
\(148\) | 3.46410 | − | 2.00000i | 0.284747 | − | 0.164399i | ||||
\(149\) | 8.00000 | − | 13.8564i | 0.655386 | − | 1.13516i | −0.326411 | − | 0.945228i | \(-0.605840\pi\) |
0.981797 | − | 0.189933i | \(-0.0608272\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | −2.59808 | − | 3.50000i | −0.210732 | − | 0.283887i | ||||
\(153\) | − | 14.0000i | − | 1.13183i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.00000 | − | 5.19615i | −0.240192 | − | 0.416025i | ||||
\(157\) | 5.19615 | + | 3.00000i | 0.414698 | + | 0.239426i | 0.692806 | − | 0.721124i | \(-0.256374\pi\) |
−0.278108 | + | 0.960550i | \(0.589707\pi\) | |||||||
\(158\) | −3.46410 | + | 2.00000i | −0.275589 | + | 0.159111i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00000 | + | 3.46410i | 0.157622 | + | 0.273009i | ||||
\(162\) | −0.866025 | + | 0.500000i | −0.0680414 | + | 0.0392837i | ||||
\(163\) | − | 12.0000i | − | 0.939913i | −0.882690 | − | 0.469956i | \(-0.844270\pi\) | ||
0.882690 | − | 0.469956i | \(-0.155730\pi\) | |||||||
\(164\) | −2.00000 | −0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.50000 | − | 11.2583i | 0.504498 | − | 0.873816i | ||||
\(167\) | −8.66025 | + | 5.00000i | −0.670151 | + | 0.386912i | −0.796134 | − | 0.605121i | \(-0.793125\pi\) |
0.125983 | + | 0.992032i | \(0.459791\pi\) | |||||||
\(168\) | 1.73205 | + | 1.00000i | 0.133631 | + | 0.0771517i | ||||
\(169\) | 11.5000 | − | 19.9186i | 0.884615 | − | 1.53220i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.00000 | + | 3.46410i | 0.611775 | + | 0.264906i | ||||
\(172\) | 12.0000i | 0.914991i | ||||||||
\(173\) | −5.19615 | − | 3.00000i | −0.395056 | − | 0.228086i | 0.289292 | − | 0.957241i | \(-0.406580\pi\) |
−0.684349 | + | 0.729155i | \(0.739913\pi\) | |||||||
\(174\) | 5.00000 | − | 8.66025i | 0.379049 | − | 0.656532i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.866025 | − | 0.500000i | 0.0650945 | − | 0.0375823i | ||||
\(178\) | − | 13.0000i | − | 0.974391i | ||||||
\(179\) | 9.00000 | 0.672692 | 0.336346 | − | 0.941739i | \(-0.390809\pi\) | ||||
0.336346 | + | 0.941739i | \(0.390809\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | − | 17.3205i | −0.743294 | − | 1.28742i | −0.950988 | − | 0.309229i | \(-0.899929\pi\) |
0.207693 | − | 0.978194i | \(-0.433404\pi\) | |||||||
\(182\) | 12.0000i | 0.889499i | ||||||||
\(183\) | 8.00000i | 0.591377i | ||||||||
\(184\) | 1.00000 | + | 1.73205i | 0.0737210 | + | 0.127688i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.00000 | + | 1.73205i | 0.0733236 | + | 0.127000i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.0000 | −0.727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.0000 | −0.723575 | −0.361787 | − | 0.932261i | \(-0.617833\pi\) | ||||
−0.361787 | + | 0.932261i | \(0.617833\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | −9.52628 | − | 5.50000i | −0.685717 | − | 0.395899i | 0.116289 | − | 0.993215i | \(-0.462900\pi\) |
−0.802005 | + | 0.597317i | \(0.796234\pi\) | |||||||
\(194\) | 7.50000 | + | 12.9904i | 0.538469 | + | 0.932655i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.50000 | + | 2.59808i | 0.107143 | + | 0.185577i | ||||
\(197\) | − | 4.00000i | − | 0.284988i | −0.989796 | − | 0.142494i | \(-0.954488\pi\) | ||
0.989796 | − | 0.142494i | \(-0.0455122\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | − | 13.8564i | −0.567105 | − | 0.982255i | −0.996850 | − | 0.0793045i | \(-0.974730\pi\) |
0.429745 | − | 0.902950i | \(-0.358603\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | − | 2.00000i | − | 0.140720i | ||||||
\(203\) | −17.3205 | + | 10.0000i | −1.21566 | + | 0.701862i | ||||
\(204\) | 3.50000 | − | 6.06218i | 0.245049 | − | 0.424437i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.00000 | + | 10.3923i | −0.418040 | + | 0.724066i | ||||
\(207\) | −3.46410 | − | 2.00000i | −0.240772 | − | 0.139010i | ||||
\(208\) | 6.00000i | 0.416025i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.5000 | + | 19.9186i | −0.791693 | + | 1.37125i | 0.133226 | + | 0.991086i | \(0.457467\pi\) |
−0.924918 | + | 0.380166i | \(0.875867\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.3923 | + | 6.00000i | −0.712069 | + | 0.411113i | ||||
\(214\) | 7.50000 | − | 12.9904i | 0.512689 | − | 0.888004i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | − | 4.00000i | − | 0.271538i | ||||||
\(218\) | −1.73205 | + | 1.00000i | −0.117309 | + | 0.0677285i | ||||
\(219\) | −1.50000 | − | 2.59808i | −0.101361 | − | 0.175562i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 42.0000 | 2.82523 | ||||||||
\(222\) | −3.46410 | + | 2.00000i | −0.232495 | + | 0.134231i | ||||
\(223\) | 1.73205 | + | 1.00000i | 0.115987 | + | 0.0669650i | 0.556871 | − | 0.830599i | \(-0.312002\pi\) |
−0.440884 | + | 0.897564i | \(0.645335\pi\) | |||||||
\(224\) | −1.00000 | − | 1.73205i | −0.0668153 | − | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.500000 | + | 0.866025i | −0.0332595 | + | 0.0576072i | ||||
\(227\) | − | 13.0000i | − | 0.862840i | −0.902151 | − | 0.431420i | \(-0.858013\pi\) | ||
0.902151 | − | 0.431420i | \(-0.141987\pi\) | |||||||
\(228\) | 2.59808 | + | 3.50000i | 0.172062 | + | 0.231793i | ||||
\(229\) | 18.0000 | 1.18947 | 0.594737 | − | 0.803921i | \(-0.297256\pi\) | ||||
0.594737 | + | 0.803921i | \(0.297256\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.66025 | + | 5.00000i | −0.568574 | + | 0.328266i | ||||
\(233\) | −11.2583 | − | 6.50000i | −0.737558 | − | 0.425829i | 0.0836229 | − | 0.996497i | \(-0.473351\pi\) |
−0.821181 | + | 0.570668i | \(0.806684\pi\) | |||||||
\(234\) | −6.00000 | − | 10.3923i | −0.392232 | − | 0.679366i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | 3.46410 | − | 2.00000i | 0.225018 | − | 0.129914i | ||||
\(238\) | −12.1244 | + | 7.00000i | −0.785905 | + | 0.453743i | ||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.00000 | − | 12.1244i | −0.450910 | − | 0.780998i | 0.547533 | − | 0.836784i | \(-0.315567\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | −9.52628 | − | 5.50000i | −0.612372 | − | 0.353553i | ||||
\(243\) | 13.8564 | − | 8.00000i | 0.888889 | − | 0.513200i | ||||
\(244\) | 4.00000 | − | 6.92820i | 0.256074 | − | 0.443533i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.00000 | 0.127515 | ||||||||
\(247\) | −10.3923 | + | 24.0000i | −0.661247 | + | 1.52708i | ||||
\(248\) | − | 2.00000i | − | 0.127000i | ||||||
\(249\) | −6.50000 | + | 11.2583i | −0.411921 | + | 0.713468i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.0000 | + | 17.3205i | 0.631194 | + | 1.09326i | 0.987308 | + | 0.158818i | \(0.0507683\pi\) |
−0.356113 | + | 0.934443i | \(0.615898\pi\) | |||||||
\(252\) | 3.46410 | + | 2.00000i | 0.218218 | + | 0.125988i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −12.0000 | −0.752947 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 12.9904 | − | 7.50000i | 0.810318 | − | 0.467837i | −0.0367485 | − | 0.999325i | \(-0.511700\pi\) |
0.847066 | + | 0.531487i | \(0.178367\pi\) | |||||||
\(258\) | − | 12.0000i | − | 0.747087i | ||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.0000 | − | 17.3205i | 0.618984 | − | 1.07211i | ||||
\(262\) | −0.866025 | + | 0.500000i | −0.0535032 | + | 0.0308901i | ||||
\(263\) | −12.1244 | − | 7.00000i | −0.747620 | − | 0.431638i | 0.0772134 | − | 0.997015i | \(-0.475398\pi\) |
−0.824833 | + | 0.565376i | \(0.808731\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.00000 | − | 8.66025i | −0.0613139 | − | 0.530994i | ||||
\(267\) | 13.0000i | 0.795587i | ||||||||
\(268\) | −6.92820 | − | 4.00000i | −0.423207 | − | 0.244339i | ||||
\(269\) | 13.0000 | − | 22.5167i | 0.792624 | − | 1.37287i | −0.131713 | − | 0.991288i | \(-0.542048\pi\) |
0.924337 | − | 0.381577i | \(-0.124619\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.0000 | + | 22.5167i | −0.789694 | + | 1.36779i | 0.136461 | + | 0.990645i | \(0.456427\pi\) |
−0.926155 | + | 0.377144i | \(0.876906\pi\) | |||||||
\(272\) | −6.06218 | + | 3.50000i | −0.367574 | + | 0.212219i | ||||
\(273\) | − | 12.0000i | − | 0.726273i | ||||||
\(274\) | −15.0000 | −0.906183 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | − | 1.73205i | −0.0601929 | − | 0.104257i | ||||
\(277\) | 22.0000i | 1.32185i | 0.750451 | + | 0.660926i | \(0.229836\pi\) | ||||
−0.750451 | + | 0.660926i | \(0.770164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.00000 | + | 3.46410i | 0.119737 | + | 0.207390i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.50000 | − | 6.06218i | −0.208792 | − | 0.361639i | 0.742542 | − | 0.669800i | \(-0.233620\pi\) |
−0.951334 | + | 0.308160i | \(0.900287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.2487 | + | 14.0000i | 1.44144 | + | 0.832214i | 0.997946 | − | 0.0640654i | \(-0.0204066\pi\) |
0.443491 | + | 0.896279i | \(0.353740\pi\) | |||||||
\(284\) | 12.0000 | 0.712069 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.46410 | − | 2.00000i | −0.204479 | − | 0.118056i | ||||
\(288\) | 1.73205 | + | 1.00000i | 0.102062 | + | 0.0589256i | ||||
\(289\) | 16.0000 | + | 27.7128i | 0.941176 | + | 1.63017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.50000 | − | 12.9904i | −0.439658 | − | 0.761510i | ||||
\(292\) | 3.00000i | 0.175562i | ||||||||
\(293\) | 32.0000i | 1.86946i | 0.355359 | + | 0.934730i | \(0.384359\pi\) | ||||
−0.355359 | + | 0.934730i | \(0.615641\pi\) | |||||||
\(294\) | −1.50000 | − | 2.59808i | −0.0874818 | − | 0.151523i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.00000 | 0.232495 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.8564 | − | 8.00000i | 0.802680 | − | 0.463428i | ||||
\(299\) | 6.00000 | − | 10.3923i | 0.346989 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0000 | + | 20.7846i | −0.691669 | + | 1.19800i | ||||
\(302\) | −10.3923 | − | 6.00000i | −0.598010 | − | 0.345261i | ||||
\(303\) | 2.00000i | 0.114897i | ||||||||
\(304\) | −0.500000 | − | 4.33013i | −0.0286770 | − | 0.248350i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7.00000 | − | 12.1244i | 0.400163 | − | 0.693103i | ||||
\(307\) | −16.4545 | − | 9.50000i | −0.939107 | − | 0.542194i | −0.0494267 | − | 0.998778i | \(-0.515739\pi\) |
−0.889680 | + | 0.456584i | \(0.849073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.00000 | − | 10.3923i | 0.341328 | − | 0.591198i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.0000 | 1.70114 | 0.850572 | − | 0.525859i | \(-0.176256\pi\) | ||||
0.850572 | + | 0.525859i | \(0.176256\pi\) | |||||||
\(312\) | − | 6.00000i | − | 0.339683i | ||||||
\(313\) | 9.52628 | − | 5.50000i | 0.538457 | − | 0.310878i | −0.205996 | − | 0.978553i | \(-0.566043\pi\) |
0.744453 | + | 0.667674i | \(0.232710\pi\) | |||||||
\(314\) | 3.00000 | + | 5.19615i | 0.169300 | + | 0.293236i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | 20.7846 | − | 12.0000i | 1.16738 | − | 0.673987i | 0.214318 | − | 0.976764i | \(-0.431247\pi\) |
0.953062 | + | 0.302777i | \(0.0979136\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.50000 | + | 12.9904i | −0.418609 | + | 0.725052i | ||||
\(322\) | 4.00000i | 0.222911i | ||||||||
\(323\) | −30.3109 | + | 3.50000i | −1.68654 | + | 0.194745i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.00000 | − | 10.3923i | 0.332309 | − | 0.575577i | ||||
\(327\) | 1.73205 | − | 1.00000i | 0.0957826 | − | 0.0553001i | ||||
\(328\) | −1.73205 | − | 1.00000i | −0.0956365 | − | 0.0552158i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.0000 | −0.934405 | −0.467202 | − | 0.884150i | \(-0.654738\pi\) | ||||
−0.467202 | + | 0.884150i | \(0.654738\pi\) | |||||||
\(332\) | 11.2583 | − | 6.50000i | 0.617881 | − | 0.356734i | ||||
\(333\) | −6.92820 | + | 4.00000i | −0.379663 | + | 0.219199i | ||||
\(334\) | −10.0000 | −0.547176 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.00000 | + | 1.73205i | 0.0545545 | + | 0.0944911i | ||||
\(337\) | −19.0526 | − | 11.0000i | −1.03786 | − | 0.599208i | −0.118633 | − | 0.992938i | \(-0.537851\pi\) |
−0.919226 | + | 0.393730i | \(0.871184\pi\) | |||||||
\(338\) | 19.9186 | − | 11.5000i | 1.08343 | − | 0.625518i | ||||
\(339\) | 0.500000 | − | 0.866025i | 0.0271563 | − | 0.0470360i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 5.19615 | + | 7.00000i | 0.280976 | + | 0.378517i | ||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | −6.00000 | + | 10.3923i | −0.323498 | + | 0.560316i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.00000 | − | 5.19615i | −0.161281 | − | 0.279347i | ||||
\(347\) | −10.3923 | − | 6.00000i | −0.557888 | − | 0.322097i | 0.194409 | − | 0.980921i | \(-0.437721\pi\) |
−0.752297 | + | 0.658824i | \(0.771054\pi\) | |||||||
\(348\) | 8.66025 | − | 5.00000i | 0.464238 | − | 0.268028i | ||||
\(349\) | −16.0000 | −0.856460 | −0.428230 | − | 0.903670i | \(-0.640863\pi\) | ||||
−0.428230 | + | 0.903670i | \(0.640863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.0000 | + | 25.9808i | 0.800641 | + | 1.38675i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 3.00000i | − | 0.159674i | −0.996808 | − | 0.0798369i | \(-0.974560\pi\) | ||
0.996808 | − | 0.0798369i | \(-0.0254400\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.50000 | − | 11.2583i | 0.344499 | − | 0.596690i | ||||
\(357\) | 12.1244 | − | 7.00000i | 0.641689 | − | 0.370479i | ||||
\(358\) | 7.79423 | + | 4.50000i | 0.411938 | + | 0.237832i | ||||
\(359\) | −12.0000 | + | 20.7846i | −0.633336 | + | 1.09697i | 0.353529 | + | 0.935423i | \(0.384981\pi\) |
−0.986865 | + | 0.161546i | \(0.948352\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | − | 18.1865i | 0.289474 | − | 0.957186i | ||||
\(362\) | − | 20.0000i | − | 1.05118i | ||||||
\(363\) | 9.52628 | + | 5.50000i | 0.500000 | + | 0.288675i | ||||
\(364\) | −6.00000 | + | 10.3923i | −0.314485 | + | 0.544705i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.00000 | + | 6.92820i | −0.209083 | + | 0.362143i | ||||
\(367\) | 6.92820 | − | 4.00000i | 0.361649 | − | 0.208798i | −0.308155 | − | 0.951336i | \(-0.599711\pi\) |
0.669804 | + | 0.742538i | \(0.266378\pi\) | |||||||
\(368\) | 2.00000i | 0.104257i | ||||||||
\(369\) | 4.00000 | 0.208232 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.00000i | 0.103695i | ||||||||
\(373\) | − | 6.00000i | − | 0.310668i | −0.987862 | − | 0.155334i | \(-0.950355\pi\) | ||
0.987862 | − | 0.155334i | \(-0.0496454\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 51.9615 | + | 30.0000i | 2.67615 | + | 1.54508i | ||||
\(378\) | −8.66025 | − | 5.00000i | −0.445435 | − | 0.257172i | ||||
\(379\) | 1.00000 | 0.0513665 | 0.0256833 | − | 0.999670i | \(-0.491824\pi\) | ||||
0.0256833 | + | 0.999670i | \(0.491824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.0000 | 0.614779 | ||||||||
\(382\) | −8.66025 | − | 5.00000i | −0.443097 | − | 0.255822i | ||||
\(383\) | 10.3923 | + | 6.00000i | 0.531022 | + | 0.306586i | 0.741433 | − | 0.671027i | \(-0.234147\pi\) |
−0.210411 | + | 0.977613i | \(0.567480\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.50000 | − | 9.52628i | −0.279943 | − | 0.484875i | ||||
\(387\) | − | 24.0000i | − | 1.21999i | ||||||
\(388\) | 15.0000i | 0.761510i | ||||||||
\(389\) | 9.00000 | + | 15.5885i | 0.456318 | + | 0.790366i | 0.998763 | − | 0.0497253i | \(-0.0158346\pi\) |
−0.542445 | + | 0.840091i | \(0.682501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.0000 | 0.708010 | ||||||||
\(392\) | 3.00000i | 0.151523i | ||||||||
\(393\) | 0.866025 | − | 0.500000i | 0.0436852 | − | 0.0252217i | ||||
\(394\) | 2.00000 | − | 3.46410i | 0.100759 | − | 0.174519i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.1244 | + | 7.00000i | 0.608504 | + | 0.351320i | 0.772380 | − | 0.635161i | \(-0.219066\pi\) |
−0.163876 | + | 0.986481i | \(0.552400\pi\) | |||||||
\(398\) | − | 16.0000i | − | 0.802008i | ||||||
\(399\) | 1.00000 | + | 8.66025i | 0.0500626 | + | 0.433555i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00000 | − | 5.19615i | 0.149813 | − | 0.259483i | −0.781345 | − | 0.624099i | \(-0.785466\pi\) |
0.931158 | + | 0.364615i | \(0.118800\pi\) | |||||||
\(402\) | 6.92820 | + | 4.00000i | 0.345547 | + | 0.199502i | ||||
\(403\) | −10.3923 | + | 6.00000i | −0.517678 | + | 0.298881i | ||||
\(404\) | 1.00000 | − | 1.73205i | 0.0497519 | − | 0.0861727i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.0000 | −0.992583 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 6.06218 | − | 3.50000i | 0.300123 | − | 0.173276i | ||||
\(409\) | 1.00000 | + | 1.73205i | 0.0494468 | + | 0.0856444i | 0.889689 | − | 0.456566i | \(-0.150921\pi\) |
−0.840243 | + | 0.542211i | \(0.817588\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.0000 | 0.739895 | ||||||||
\(412\) | −10.3923 | + | 6.00000i | −0.511992 | + | 0.295599i | ||||
\(413\) | −1.73205 | − | 1.00000i | −0.0852286 | − | 0.0492068i | ||||
\(414\) | −2.00000 | − | 3.46410i | −0.0982946 | − | 0.170251i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.00000 | + | 5.19615i | −0.147087 | + | 0.254762i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.0000 | −0.635092 | −0.317546 | − | 0.948243i | \(-0.602859\pi\) | ||||
−0.317546 | + | 0.948243i | \(0.602859\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0000 | + | 29.4449i | −0.828529 | + | 1.43505i | 0.0706626 | + | 0.997500i | \(0.477489\pi\) |
−0.899192 | + | 0.437555i | \(0.855845\pi\) | |||||||
\(422\) | −19.9186 | + | 11.5000i | −0.969622 | + | 0.559811i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.0000 | −0.581402 | ||||||||
\(427\) | 13.8564 | − | 8.00000i | 0.670559 | − | 0.387147i | ||||
\(428\) | 12.9904 | − | 7.50000i | 0.627914 | − | 0.362526i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.0000 | − | 25.9808i | −0.722525 | − | 1.25145i | −0.959985 | − | 0.280052i | \(-0.909648\pi\) |
0.237460 | − | 0.971397i | \(-0.423685\pi\) | |||||||
\(432\) | −4.33013 | − | 2.50000i | −0.208333 | − | 0.120281i | ||||
\(433\) | −18.1865 | + | 10.5000i | −0.873989 | + | 0.504598i | −0.868672 | − | 0.495388i | \(-0.835026\pi\) |
−0.00531724 | + | 0.999986i | \(0.501693\pi\) | |||||||
\(434\) | 2.00000 | − | 3.46410i | 0.0960031 | − | 0.166282i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.00000 | −0.0957826 | ||||||||
\(437\) | −3.46410 | + | 8.00000i | −0.165710 | + | 0.382692i | ||||
\(438\) | − | 3.00000i | − | 0.143346i | ||||||
\(439\) | −4.00000 | + | 6.92820i | −0.190910 | + | 0.330665i | −0.945552 | − | 0.325471i | \(-0.894477\pi\) |
0.754642 | + | 0.656136i | \(0.227810\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | − | 5.19615i | −0.142857 | − | 0.247436i | ||||
\(442\) | 36.3731 | + | 21.0000i | 1.73009 | + | 0.998868i | ||||
\(443\) | 31.1769 | − | 18.0000i | 1.48126 | − | 0.855206i | 0.481486 | − | 0.876454i | \(-0.340097\pi\) |
0.999774 | + | 0.0212481i | \(0.00676401\pi\) | |||||||
\(444\) | −4.00000 | −0.189832 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.00000 | + | 1.73205i | 0.0473514 | + | 0.0820150i | ||||
\(447\) | −13.8564 | + | 8.00000i | −0.655386 | + | 0.378387i | ||||
\(448\) | − | 2.00000i | − | 0.0944911i | ||||||
\(449\) | −41.0000 | −1.93491 | −0.967455 | − | 0.253044i | \(-0.918568\pi\) | ||||
−0.967455 | + | 0.253044i | \(0.918568\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.866025 | + | 0.500000i | −0.0407344 | + | 0.0235180i | ||||
\(453\) | 10.3923 | + | 6.00000i | 0.488273 | + | 0.281905i | ||||
\(454\) | 6.50000 | − | 11.2583i | 0.305060 | − | 0.528380i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.500000 | + | 4.33013i | 0.0234146 | + | 0.202777i | ||||
\(457\) | − | 11.0000i | − | 0.514558i | −0.966337 | − | 0.257279i | \(-0.917174\pi\) | ||
0.966337 | − | 0.257279i | \(-0.0828260\pi\) | |||||||
\(458\) | 15.5885 | + | 9.00000i | 0.728401 | + | 0.420542i | ||||
\(459\) | −17.5000 | + | 30.3109i | −0.816830 | + | 1.41479i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.00000 | + | 1.73205i | −0.0465746 | + | 0.0806696i | −0.888373 | − | 0.459123i | \(-0.848164\pi\) |
0.841798 | + | 0.539792i | \(0.181497\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.0000i | − | 1.02243i | −0.859454 | − | 0.511213i | \(-0.829196\pi\) | ||
0.859454 | − | 0.511213i | \(-0.170804\pi\) | |||||||
\(464\) | −10.0000 | −0.464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.50000 | − | 11.2583i | −0.301107 | − | 0.521532i | ||||
\(467\) | − | 23.0000i | − | 1.06431i | −0.846646 | − | 0.532157i | \(-0.821382\pi\) | ||
0.846646 | − | 0.532157i | \(-0.178618\pi\) | |||||||
\(468\) | − | 12.0000i | − | 0.554700i | ||||||
\(469\) | −8.00000 | − | 13.8564i | −0.369406 | − | 0.639829i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.00000 | − | 5.19615i | −0.138233 | − | 0.239426i | ||||
\(472\) | −0.866025 | − | 0.500000i | −0.0398621 | − | 0.0230144i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4.00000 | 0.183726 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14.0000 | −0.641689 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.19615 | + | 3.00000i | 0.237666 | + | 0.137217i | ||||
\(479\) | 12.0000 | + | 20.7846i | 0.548294 | + | 0.949673i | 0.998392 | + | 0.0566937i | \(0.0180558\pi\) |
−0.450098 | + | 0.892979i | \(0.648611\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | − | 20.7846i | −0.547153 | − | 0.947697i | ||||
\(482\) | − | 14.0000i | − | 0.637683i | ||||||
\(483\) | − | 4.00000i | − | 0.182006i | ||||||
\(484\) | −5.50000 | − | 9.52628i | −0.250000 | − | 0.433013i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 16.0000 | 0.725775 | ||||||||
\(487\) | − | 20.0000i | − | 0.906287i | −0.891438 | − | 0.453143i | \(-0.850303\pi\) | ||
0.891438 | − | 0.453143i | \(-0.149697\pi\) | |||||||
\(488\) | 6.92820 | − | 4.00000i | 0.313625 | − | 0.181071i | ||||
\(489\) | −6.00000 | + | 10.3923i | −0.271329 | + | 0.469956i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.00000 | + | 6.92820i | −0.180517 | + | 0.312665i | −0.942057 | − | 0.335453i | \(-0.891111\pi\) |
0.761539 | + | 0.648119i | \(0.224444\pi\) | |||||||
\(492\) | 1.73205 | + | 1.00000i | 0.0780869 | + | 0.0450835i | ||||
\(493\) | 70.0000i | 3.15264i | ||||||||
\(494\) | −21.0000 | + | 15.5885i | −0.944835 | + | 0.701358i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00000 | − | 1.73205i | 0.0449013 | − | 0.0777714i | ||||
\(497\) | 20.7846 | + | 12.0000i | 0.932317 | + | 0.538274i | ||||
\(498\) | −11.2583 | + | 6.50000i | −0.504498 | + | 0.291272i | ||||
\(499\) | −16.5000 | + | 28.5788i | −0.738641 | + | 1.27936i | 0.214466 | + | 0.976732i | \(0.431199\pi\) |
−0.953107 | + | 0.302633i | \(0.902134\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.0000 | 0.446767 | ||||||||
\(502\) | 20.0000i | 0.892644i | ||||||||
\(503\) | 6.92820 | − | 4.00000i | 0.308913 | − | 0.178351i | −0.337527 | − | 0.941316i | \(-0.609590\pi\) |
0.646440 | + | 0.762965i | \(0.276257\pi\) | |||||||
\(504\) | 2.00000 | + | 3.46410i | 0.0890871 | + | 0.154303i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.9186 | + | 11.5000i | −0.884615 | + | 0.510733i | ||||
\(508\) | −10.3923 | − | 6.00000i | −0.461084 | − | 0.266207i | ||||
\(509\) | 3.00000 | + | 5.19615i | 0.132973 | + | 0.230315i | 0.924821 | − | 0.380402i | \(-0.124214\pi\) |
−0.791849 | + | 0.610718i | \(0.790881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.00000 | + | 5.19615i | −0.132712 | + | 0.229864i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −12.9904 | − | 17.5000i | −0.573539 | − | 0.772644i | ||||
\(514\) | 15.0000 | 0.661622 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.00000 | − | 10.3923i | 0.264135 | − | 0.457496i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.92820 | + | 4.00000i | 0.304408 | + | 0.175750i | ||||
\(519\) | 3.00000 | + | 5.19615i | 0.131685 | + | 0.228086i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | −0.262865 | −0.131432 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | 17.3205 | − | 10.0000i | 0.758098 | − | 0.437688i | ||||
\(523\) | −25.1147 | + | 14.5000i | −1.09819 | + | 0.634041i | −0.935745 | − | 0.352677i | \(-0.885272\pi\) |
−0.162446 | + | 0.986718i | \(0.551938\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.00000 | − | 12.1244i | −0.305215 | − | 0.528647i | ||||
\(527\) | −12.1244 | − | 7.00000i | −0.528145 | − | 0.304925i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.50000 | + | 16.4545i | −0.413043 | + | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.00000 | 0.0867926 | ||||||||
\(532\) | 3.46410 | − | 8.00000i | 0.150188 | − | 0.346844i | ||||
\(533\) | 12.0000i | 0.519778i | ||||||||
\(534\) | −6.50000 | + | 11.2583i | −0.281283 | + | 0.487196i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.00000 | − | 6.92820i | −0.172774 | − | 0.299253i | ||||
\(537\) | −7.79423 | − | 4.50000i | −0.336346 | − | 0.194189i | ||||
\(538\) | 22.5167 | − | 13.0000i | 0.970762 | − | 0.560470i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | + | 8.66025i | 0.214967 | + | 0.372333i | 0.953262 | − | 0.302144i | \(-0.0977023\pi\) |
−0.738296 | + | 0.674477i | \(0.764369\pi\) | |||||||
\(542\) | −22.5167 | + | 13.0000i | −0.967173 | + | 0.558398i | ||||
\(543\) | 20.0000i | 0.858282i | ||||||||
\(544\) | −7.00000 | −0.300123 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.00000 | − | 10.3923i | 0.256776 | − | 0.444750i | ||||
\(547\) | 0.866025 | − | 0.500000i | 0.0370286 | − | 0.0213785i | −0.481371 | − | 0.876517i | \(-0.659861\pi\) |
0.518400 | + | 0.855138i | \(0.326528\pi\) | |||||||
\(548\) | −12.9904 | − | 7.50000i | −0.554922 | − | 0.320384i | ||||
\(549\) | −8.00000 | + | 13.8564i | −0.341432 | + | 0.591377i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.0000 | − | 17.3205i | −1.70406 | − | 0.737878i | ||||
\(552\) | − | 2.00000i | − | 0.0851257i | ||||||
\(553\) | −6.92820 | − | 4.00000i | −0.294617 | − | 0.170097i | ||||
\(554\) | −11.0000 | + | 19.0526i | −0.467345 | + | 0.809466i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.73205 | − | 1.00000i | 0.0733893 | − | 0.0423714i | −0.462856 | − | 0.886433i | \(-0.653175\pi\) |
0.536246 | + | 0.844062i | \(0.319842\pi\) | |||||||
\(558\) | 4.00000i | 0.169334i | ||||||||
\(559\) | 72.0000 | 3.04528 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 7.00000i | − | 0.295277i | ||||||
\(563\) | − | 43.0000i | − | 1.81223i | −0.423027 | − | 0.906117i | \(-0.639033\pi\) | ||
0.423027 | − | 0.906117i | \(-0.360967\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.0000 | + | 24.2487i | 0.588464 | + | 1.01925i | ||||
\(567\) | −1.73205 | − | 1.00000i | −0.0727393 | − | 0.0419961i | ||||
\(568\) | 10.3923 | + | 6.00000i | 0.436051 | + | 0.251754i | ||||
\(569\) | −1.00000 | −0.0419222 | −0.0209611 | − | 0.999780i | \(-0.506673\pi\) | ||||
−0.0209611 | + | 0.999780i | \(0.506673\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.00000 | 0.0418487 | 0.0209243 | − | 0.999781i | \(-0.493339\pi\) | ||||
0.0209243 | + | 0.999781i | \(0.493339\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.66025 | + | 5.00000i | 0.361787 | + | 0.208878i | ||||
\(574\) | −2.00000 | − | 3.46410i | −0.0834784 | − | 0.144589i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | + | 1.73205i | 0.0416667 | + | 0.0721688i | ||||
\(577\) | 34.0000i | 1.41544i | 0.706494 | + | 0.707719i | \(0.250276\pi\) | ||||
−0.706494 | + | 0.707719i | \(0.749724\pi\) | |||||||
\(578\) | 32.0000i | 1.33102i | ||||||||
\(579\) | 5.50000 | + | 9.52628i | 0.228572 | + | 0.395899i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.0000 | 1.07866 | ||||||||
\(582\) | − | 15.0000i | − | 0.621770i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.50000 | + | 2.59808i | −0.0620704 | + | 0.107509i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.0000 | + | 27.7128i | −0.660954 | + | 1.14481i | ||||
\(587\) | 38.9711 | + | 22.5000i | 1.60851 | + | 0.928674i | 0.989704 | + | 0.143132i | \(0.0457173\pi\) |
0.618808 | + | 0.785543i | \(0.287616\pi\) | |||||||
\(588\) | − | 3.00000i | − | 0.123718i | ||||||
\(589\) | 7.00000 | − | 5.19615i | 0.288430 | − | 0.214104i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.00000 | + | 3.46410i | −0.0822690 | + | 0.142494i | ||||
\(592\) | 3.46410 | + | 2.00000i | 0.142374 | + | 0.0821995i | ||||
\(593\) | −12.1244 | + | 7.00000i | −0.497888 | + | 0.287456i | −0.727841 | − | 0.685746i | \(-0.759476\pi\) |
0.229953 | + | 0.973202i | \(0.426143\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.0000 | 0.655386 | ||||||||
\(597\) | 16.0000i | 0.654836i | ||||||||
\(598\) | 10.3923 | − | 6.00000i | 0.424973 | − | 0.245358i | ||||
\(599\) | −6.00000 | − | 10.3923i | −0.245153 | − | 0.424618i | 0.717021 | − | 0.697051i | \(-0.245505\pi\) |
−0.962175 | + | 0.272433i | \(0.912172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.0000 | 1.42768 | 0.713840 | − | 0.700309i | \(-0.246954\pi\) | ||||
0.713840 | + | 0.700309i | \(0.246954\pi\) | |||||||
\(602\) | −20.7846 | + | 12.0000i | −0.847117 | + | 0.489083i | ||||
\(603\) | 13.8564 | + | 8.00000i | 0.564276 | + | 0.325785i | ||||
\(604\) | −6.00000 | − | 10.3923i | −0.244137 | − | 0.422857i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.00000 | + | 1.73205i | −0.0406222 | + | 0.0703598i | ||||
\(607\) | − | 14.0000i | − | 0.568242i | −0.958788 | − | 0.284121i | \(-0.908298\pi\) | ||
0.958788 | − | 0.284121i | \(-0.0917018\pi\) | |||||||
\(608\) | 1.73205 | − | 4.00000i | 0.0702439 | − | 0.162221i | ||||
\(609\) | 20.0000 | 0.810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 12.1244 | − | 7.00000i | 0.490098 | − | 0.282958i | ||||
\(613\) | 12.1244 | + | 7.00000i | 0.489698 | + | 0.282727i | 0.724449 | − | 0.689328i | \(-0.242094\pi\) |
−0.234751 | + | 0.972056i | \(0.575428\pi\) | |||||||
\(614\) | −9.50000 | − | 16.4545i | −0.383389 | − | 0.664049i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.06218 | − | 3.50000i | 0.244054 | − | 0.140905i | −0.372985 | − | 0.927838i | \(-0.621666\pi\) |
0.617039 | + | 0.786933i | \(0.288332\pi\) | |||||||
\(618\) | 10.3923 | − | 6.00000i | 0.418040 | − | 0.241355i | ||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.00000 | + | 8.66025i | 0.200643 | + | 0.347524i | ||||
\(622\) | 25.9808 | + | 15.0000i | 1.04173 | + | 0.601445i | ||||
\(623\) | 22.5167 | − | 13.0000i | 0.902111 | − | 0.520834i | ||||
\(624\) | 3.00000 | − | 5.19615i | 0.120096 | − | 0.208013i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11.0000 | 0.439648 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.00000i | 0.239426i | ||||||||
\(629\) | 14.0000 | − | 24.2487i | 0.558217 | − | 0.966859i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.0000 | − | 41.5692i | −0.955425 | − | 1.65484i | −0.733393 | − | 0.679805i | \(-0.762064\pi\) |
−0.222032 | − | 0.975039i | \(-0.571269\pi\) | |||||||
\(632\) | −3.46410 | − | 2.00000i | −0.137795 | − | 0.0795557i | ||||
\(633\) | 19.9186 | − | 11.5000i | 0.791693 | − | 0.457084i | ||||
\(634\) | 24.0000 | 0.953162 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.5885 | − | 9.00000i | 0.617637 | − | 0.356593i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.0000 | −0.949425 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.5000 | − | 33.7750i | 0.770204 | − | 1.33403i | −0.167247 | − | 0.985915i | \(-0.553488\pi\) |
0.937451 | − | 0.348117i | \(-0.113179\pi\) | |||||||
\(642\) | −12.9904 | + | 7.50000i | −0.512689 | + | 0.296001i | ||||
\(643\) | 21.6506 | + | 12.5000i | 0.853818 | + | 0.492952i | 0.861937 | − | 0.507015i | \(-0.169251\pi\) |
−0.00811944 | + | 0.999967i | \(0.502585\pi\) | |||||||
\(644\) | −2.00000 | + | 3.46410i | −0.0788110 | + | 0.136505i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −28.0000 | − | 12.1244i | −1.10165 | − | 0.477026i | ||||
\(647\) | 12.0000i | 0.471769i | 0.971781 | + | 0.235884i | \(0.0757987\pi\) | ||||
−0.971781 | + | 0.235884i | \(0.924201\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.00000 | + | 3.46410i | −0.0783862 | + | 0.135769i | ||||
\(652\) | 10.3923 | − | 6.00000i | 0.406994 | − | 0.234978i | ||||
\(653\) | − | 12.0000i | − | 0.469596i | −0.972044 | − | 0.234798i | \(-0.924557\pi\) | ||
0.972044 | − | 0.234798i | \(-0.0754429\pi\) | |||||||
\(654\) | 2.00000 | 0.0782062 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.00000 | − | 1.73205i | −0.0390434 | − | 0.0676252i | ||||
\(657\) | − | 6.00000i | − | 0.234082i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.50000 | + | 2.59808i | 0.0584317 | + | 0.101207i | 0.893762 | − | 0.448542i | \(-0.148057\pi\) |
−0.835330 | + | 0.549749i | \(0.814723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.00000 | + | 3.46410i | 0.0777910 | + | 0.134738i | 0.902297 | − | 0.431116i | \(-0.141880\pi\) |
−0.824506 | + | 0.565854i | \(0.808547\pi\) | |||||||
\(662\) | −14.7224 | − | 8.50000i | −0.572204 | − | 0.330362i | ||||
\(663\) | −36.3731 | − | 21.0000i | −1.41261 | − | 0.815572i | ||||
\(664\) | 13.0000 | 0.504498 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.00000 | −0.309994 | ||||||||
\(667\) | 17.3205 | + | 10.0000i | 0.670653 | + | 0.387202i | ||||
\(668\) | −8.66025 | − | 5.00000i | −0.335075 | − | 0.193456i | ||||
\(669\) | −1.00000 | − | 1.73205i | −0.0386622 | − | 0.0669650i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.00000i | 0.0771517i | ||||||||
\(673\) | − | 26.0000i | − | 1.00223i | −0.865382 | − | 0.501113i | \(-0.832924\pi\) | ||
0.865382 | − | 0.501113i | \(-0.167076\pi\) | |||||||
\(674\) | −11.0000 | − | 19.0526i | −0.423704 | − | 0.733877i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | − | 26.0000i | − | 0.999261i | −0.866239 | − | 0.499631i | \(-0.833469\pi\) | ||
0.866239 | − | 0.499631i | \(-0.166531\pi\) | |||||||
\(678\) | 0.866025 | − | 0.500000i | 0.0332595 | − | 0.0192024i | ||||
\(679\) | −15.0000 | + | 25.9808i | −0.575647 | + | 0.997050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.50000 | + | 11.2583i | −0.249081 | + | 0.431420i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.0000i | 0.573959i | 0.957937 | + | 0.286980i | \(0.0926512\pi\) | ||||
−0.957937 | + | 0.286980i | \(0.907349\pi\) | |||||||
\(684\) | 1.00000 | + | 8.66025i | 0.0382360 | + | 0.331133i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.0000 | + | 17.3205i | −0.381802 | + | 0.661300i | ||||
\(687\) | −15.5885 | − | 9.00000i | −0.594737 | − | 0.343371i | ||||
\(688\) | −10.3923 | + | 6.00000i | −0.396203 | + | 0.228748i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.0000 | 1.40755 | 0.703773 | − | 0.710425i | \(-0.251497\pi\) | ||||
0.703773 | + | 0.710425i | \(0.251497\pi\) | |||||||
\(692\) | − | 6.00000i | − | 0.228086i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.00000 | − | 10.3923i | −0.227757 | − | 0.394486i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 10.0000 | 0.379049 | ||||||||
\(697\) | −12.1244 | + | 7.00000i | −0.459243 | + | 0.265144i | ||||
\(698\) | −13.8564 | − | 8.00000i | −0.524473 | − | 0.302804i | ||||
\(699\) | 6.50000 | + | 11.2583i | 0.245853 | + | 0.425829i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.0000 | − | 20.7846i | 0.453234 | − | 0.785024i | −0.545351 | − | 0.838208i | \(-0.683604\pi\) |
0.998585 | + | 0.0531839i | \(0.0169370\pi\) | |||||||
\(702\) | 30.0000i | 1.13228i | ||||||||
\(703\) | 10.3923 | + | 14.0000i | 0.391953 | + | 0.528020i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.50000 | − | 2.59808i | 0.0564532 | − | 0.0977799i | ||||
\(707\) | 3.46410 | − | 2.00000i | 0.130281 | − | 0.0752177i | ||||
\(708\) | 0.866025 | + | 0.500000i | 0.0325472 | + | 0.0187912i | ||||
\(709\) | −14.0000 | − | 24.2487i | −0.525781 | − | 0.910679i | −0.999549 | − | 0.0300298i | \(-0.990440\pi\) |
0.473768 | − | 0.880650i | \(-0.342894\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000 | 0.300023 | ||||||||
\(712\) | 11.2583 | − | 6.50000i | 0.421924 | − | 0.243598i | ||||
\(713\) | −3.46410 | + | 2.00000i | −0.129732 | + | 0.0749006i | ||||
\(714\) | 14.0000 | 0.523937 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.50000 | + | 7.79423i | 0.168173 | + | 0.291284i | ||||
\(717\) | −5.19615 | − | 3.00000i | −0.194054 | − | 0.112037i | ||||
\(718\) | −20.7846 | + | 12.0000i | −0.775675 | + | 0.447836i | ||||
\(719\) | 16.0000 | − | 27.7128i | 0.596699 | − | 1.03351i | −0.396605 | − | 0.917989i | \(-0.629812\pi\) |
0.993305 | − | 0.115524i | \(-0.0368548\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | −0.893807 | ||||||||
\(722\) | 13.8564 | − | 13.0000i | 0.515682 | − | 0.483810i | ||||
\(723\) | 14.0000i | 0.520666i | ||||||||
\(724\) | 10.0000 | − | 17.3205i | 0.371647 | − | 0.643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.50000 | + | 9.52628i | 0.204124 | + | 0.353553i | ||||
\(727\) | −12.1244 | − | 7.00000i | −0.449667 | − | 0.259616i | 0.258022 | − | 0.966139i | \(-0.416929\pi\) |
−0.707690 | + | 0.706523i | \(0.750263\pi\) | |||||||
\(728\) | −10.3923 | + | 6.00000i | −0.385164 | + | 0.222375i | ||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 42.0000 | + | 72.7461i | 1.55343 | + | 2.69061i | ||||
\(732\) | −6.92820 | + | 4.00000i | −0.256074 | + | 0.147844i | ||||
\(733\) | − | 6.00000i | − | 0.221615i | −0.993842 | − | 0.110808i | \(-0.964656\pi\) | ||
0.993842 | − | 0.110808i | \(-0.0353437\pi\) | |||||||
\(734\) | 8.00000 | 0.295285 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | + | 1.73205i | −0.0368605 | + | 0.0638442i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 3.46410 | + | 2.00000i | 0.127515 | + | 0.0736210i | ||||
\(739\) | 23.5000 | − | 40.7032i | 0.864461 | − | 1.49729i | −0.00311943 | − | 0.999995i | \(-0.500993\pi\) |
0.867581 | − | 0.497296i | \(-0.165674\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.0000 | − | 15.5885i | 0.771454 | − | 0.572656i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.5167 | − | 13.0000i | −0.826056 | − | 0.476924i | 0.0264443 | − | 0.999650i | \(-0.491582\pi\) |
−0.852500 | + | 0.522727i | \(0.824915\pi\) | |||||||
\(744\) | −1.00000 | + | 1.73205i | −0.0366618 | + | 0.0635001i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.00000 | − | 5.19615i | 0.109838 | − | 0.190245i | ||||
\(747\) | −22.5167 | + | 13.0000i | −0.823842 | + | 0.475645i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.0000 | 1.09618 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0000 | + | 22.5167i | 0.474377 | + | 0.821645i | 0.999570 | − | 0.0293387i | \(-0.00934013\pi\) |
−0.525193 | + | 0.850983i | \(0.676007\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 20.0000i | − | 0.728841i | ||||||
\(754\) | 30.0000 | + | 51.9615i | 1.09254 | + | 1.89233i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.00000 | − | 8.66025i | −0.181848 | − | 0.314970i | ||||
\(757\) | 27.7128 | + | 16.0000i | 1.00724 | + | 0.581530i | 0.910382 | − | 0.413768i | \(-0.135788\pi\) |
0.0968571 | + | 0.995298i | \(0.469121\pi\) | |||||||
\(758\) | 0.866025 | + | 0.500000i | 0.0314555 | + | 0.0181608i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | −0.217500 | −0.108750 | − | 0.994069i | \(-0.534685\pi\) | ||||
−0.108750 | + | 0.994069i | \(0.534685\pi\) | |||||||
\(762\) | 10.3923 | + | 6.00000i | 0.376473 | + | 0.217357i | ||||
\(763\) | −3.46410 | − | 2.00000i | −0.125409 | − | 0.0724049i | ||||
\(764\) | −5.00000 | − | 8.66025i | −0.180894 | − | 0.313317i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.00000 | + | 10.3923i | 0.216789 | + | 0.375489i | ||||
\(767\) | 6.00000i | 0.216647i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −11.5000 | − | 19.9186i | −0.414701 | − | 0.718283i | 0.580696 | − | 0.814120i | \(-0.302780\pi\) |
−0.995397 | + | 0.0958377i | \(0.969447\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.0000 | −0.540212 | ||||||||
\(772\) | − | 11.0000i | − | 0.395899i | ||||||
\(773\) | 5.19615 | − | 3.00000i | 0.186893 | − | 0.107903i | −0.403634 | − | 0.914920i | \(-0.632253\pi\) |
0.590527 | + | 0.807018i | \(0.298920\pi\) | |||||||
\(774\) | 12.0000 | − | 20.7846i | 0.431331 | − | 0.747087i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.50000 | + | 12.9904i | −0.269234 | + | 0.466328i | ||||
\(777\) | −6.92820 | − | 4.00000i | −0.248548 | − | 0.143499i | ||||
\(778\) | 18.0000i | 0.645331i | ||||||||
\(779\) | −1.00000 | − | 8.66025i | −0.0358287 | − | 0.310286i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 12.1244 | + | 7.00000i | 0.433566 | + | 0.250319i | ||||
\(783\) | −43.3013 | + | 25.0000i | −1.54746 | + | 0.893427i | ||||
\(784\) | −1.50000 | + | 2.59808i | −0.0535714 | + | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.00000 | 0.0356688 | ||||||||
\(787\) | 29.0000i | 1.03374i | 0.856064 | + | 0.516869i | \(0.172903\pi\) | ||||
−0.856064 | + | 0.516869i | \(0.827097\pi\) | |||||||
\(788\) | 3.46410 | − | 2.00000i | 0.123404 | − | 0.0712470i | ||||
\(789\) | 7.00000 | + | 12.1244i | 0.249207 | + | 0.431638i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.00000 | −0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.5692 | − | 24.0000i | −1.47617 | − | 0.852265i | ||||
\(794\) | 7.00000 | + | 12.1244i | 0.248421 | + | 0.430277i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.00000 | − | 13.8564i | 0.283552 | − | 0.491127i | ||||
\(797\) | 8.00000i | 0.283375i | 0.989911 | + | 0.141687i | \(0.0452527\pi\) | ||||
−0.989911 | + | 0.141687i | \(0.954747\pi\) | |||||||
\(798\) | −3.46410 | + | 8.00000i | −0.122628 | + | 0.283197i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.0000 | + | 22.5167i | −0.459332 | + | 0.795587i | ||||
\(802\) | 5.19615 | − | 3.00000i | 0.183483 | − | 0.105934i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 4.00000 | + | 6.92820i | 0.141069 | + | 0.244339i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.0000 | −0.422682 | ||||||||
\(807\) | −22.5167 | + | 13.0000i | −0.792624 | + | 0.457622i | ||||
\(808\) | 1.73205 | − | 1.00000i | 0.0609333 | − | 0.0351799i | ||||
\(809\) | −45.0000 | −1.58212 | −0.791058 | − | 0.611741i | \(-0.790469\pi\) | ||||
−0.791058 | + | 0.611741i | \(0.790469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.0000 | − | 38.1051i | −0.772524 | − | 1.33805i | −0.936175 | − | 0.351533i | \(-0.885660\pi\) |
0.163651 | − | 0.986518i | \(-0.447673\pi\) | |||||||
\(812\) | −17.3205 | − | 10.0000i | −0.607831 | − | 0.350931i | ||||
\(813\) | 22.5167 | − | 13.0000i | 0.789694 | − | 0.455930i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.00000 | 0.245049 | ||||||||
\(817\) | −51.9615 | + | 6.00000i | −1.81790 | + | 0.209913i | ||||
\(818\) | 2.00000i | 0.0699284i | ||||||||
\(819\) | 12.0000 | − | 20.7846i | 0.419314 | − | 0.726273i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.0000 | − | 39.8372i | −0.802706 | − | 1.39033i | −0.917829 | − | 0.396976i | \(-0.870060\pi\) |
0.115124 | − | 0.993351i | \(-0.463274\pi\) | |||||||
\(822\) | 12.9904 | + | 7.50000i | 0.453092 | + | 0.261593i | ||||
\(823\) | −6.92820 | + | 4.00000i | −0.241502 | + | 0.139431i | −0.615867 | − | 0.787850i | \(-0.711194\pi\) |
0.374365 | + | 0.927281i | \(0.377861\pi\) | |||||||
\(824\) | −12.0000 | −0.418040 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.00000 | − | 1.73205i | −0.0347945 | − | 0.0602658i | ||||
\(827\) | −31.1769 | + | 18.0000i | −1.08413 | + | 0.625921i | −0.932007 | − | 0.362441i | \(-0.881944\pi\) |
−0.152121 | + | 0.988362i | \(0.548610\pi\) | |||||||
\(828\) | − | 4.00000i | − | 0.139010i | ||||||
\(829\) | 30.0000 | 1.04194 | 0.520972 | − | 0.853574i | \(-0.325570\pi\) | ||||
0.520972 | + | 0.853574i | \(0.325570\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.0000 | − | 19.0526i | 0.381586 | − | 0.660926i | ||||
\(832\) | −5.19615 | + | 3.00000i | −0.180144 | + | 0.104006i | ||||
\(833\) | 18.1865 | + | 10.5000i | 0.630126 | + | 0.363803i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 10.0000i | − | 0.345651i | ||||||
\(838\) | −11.2583 | − | 6.50000i | −0.388913 | − | 0.224539i | ||||
\(839\) | 12.0000 | − | 20.7846i | 0.414286 | − | 0.717564i | −0.581067 | − | 0.813856i | \(-0.697365\pi\) |
0.995353 | + | 0.0962912i | \(0.0306980\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −35.5000 | + | 61.4878i | −1.22414 | + | 2.12027i | ||||
\(842\) | −29.4449 | + | 17.0000i | −1.01474 | + | 0.585859i | ||||
\(843\) | 7.00000i | 0.241093i | ||||||||
\(844\) | −23.0000 | −0.791693 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 22.0000i | − | 0.755929i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.0000 | − | 24.2487i | −0.480479 | − | 0.832214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.00000 | − | 6.92820i | −0.137118 | − | 0.237496i | ||||
\(852\) | −10.3923 | − | 6.00000i | −0.356034 | − | 0.205557i | ||||
\(853\) | 38.1051 | + | 22.0000i | 1.30469 | + | 0.753266i | 0.981205 | − | 0.192966i | \(-0.0618108\pi\) |
0.323489 | + | 0.946232i | \(0.395144\pi\) | |||||||
\(854\) | 16.0000 | 0.547509 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.0000 | 0.512689 | ||||||||
\(857\) | −15.5885 | − | 9.00000i | −0.532492 | − | 0.307434i | 0.209539 | − | 0.977800i | \(-0.432804\pi\) |
−0.742030 | + | 0.670366i | \(0.766137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.5000 | − | 21.6506i | −0.426494 | − | 0.738710i | 0.570064 | − | 0.821600i | \(-0.306918\pi\) |
−0.996559 | + | 0.0828900i | \(0.973585\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.00000 | + | 3.46410i | 0.0681598 | + | 0.118056i | ||||
\(862\) | − | 30.0000i | − | 1.02180i | ||||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | −2.50000 | − | 4.33013i | −0.0850517 | − | 0.147314i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −21.0000 | −0.713609 | ||||||||
\(867\) | − | 32.0000i | − | 1.08678i | ||||||
\(868\) | 3.46410 | − | 2.00000i | 0.117579 | − | 0.0678844i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0000 | + | 41.5692i | −0.813209 | + | 1.40852i | ||||
\(872\) | −1.73205 | − | 1.00000i | −0.0586546 | − | 0.0338643i | ||||
\(873\) | − | 30.0000i | − | 1.01535i | ||||||
\(874\) | −7.00000 | + | 5.19615i | −0.236779 | + | 0.175762i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.50000 | − | 2.59808i | 0.0506803 | − | 0.0877809i | ||||
\(877\) | −8.66025 | − | 5.00000i | −0.292436 | − | 0.168838i | 0.346604 | − | 0.938012i | \(-0.387335\pi\) |
−0.639040 | + | 0.769174i | \(0.720668\pi\) | |||||||
\(878\) | −6.92820 | + | 4.00000i | −0.233816 | + | 0.134993i | ||||
\(879\) | 16.0000 | − | 27.7128i | 0.539667 | − | 0.934730i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.0000 | −1.24656 | −0.623281 | − | 0.781998i | \(-0.714201\pi\) | ||||
−0.623281 | + | 0.781998i | \(0.714201\pi\) | |||||||
\(882\) | − | 6.00000i | − | 0.202031i | ||||||
\(883\) | 11.2583 | − | 6.50000i | 0.378873 | − | 0.218742i | −0.298455 | − | 0.954424i | \(-0.596471\pi\) |
0.677328 | + | 0.735681i | \(0.263138\pi\) | |||||||
\(884\) | 21.0000 | + | 36.3731i | 0.706306 | + | 1.22336i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.0000 | 1.20944 | ||||||||
\(887\) | 24.2487 | − | 14.0000i | 0.814192 | − | 0.470074i | −0.0342175 | − | 0.999414i | \(-0.510894\pi\) |
0.848410 | + | 0.529340i | \(0.177561\pi\) | |||||||
\(888\) | −3.46410 | − | 2.00000i | −0.116248 | − | 0.0671156i | ||||
\(889\) | −12.0000 | − | 20.7846i | −0.402467 | − | 0.697093i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.00000i | 0.0669650i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −16.0000 | −0.535120 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000 | − | 1.73205i | 0.0334077 | − | 0.0578638i | ||||
\(897\) | −10.3923 | + | 6.00000i | −0.346989 | + | 0.200334i | ||||
\(898\) | −35.5070 | − | 20.5000i | −1.18489 | − | 0.684094i | ||||
\(899\) | −10.0000 | − | 17.3205i | −0.333519 | − | 0.577671i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.7846 | − | 12.0000i | 0.691669 | − | 0.399335i | ||||
\(904\) | −1.00000 | −0.0332595 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.00000 | + | 10.3923i | 0.199337 | + | 0.345261i | ||||
\(907\) | −45.8993 | − | 26.5000i | −1.52406 | − | 0.879918i | −0.999594 | − | 0.0284883i | \(-0.990931\pi\) |
−0.524469 | − | 0.851430i | \(-0.675736\pi\) | |||||||
\(908\) | 11.2583 | − | 6.50000i | 0.373621 | − | 0.215710i | ||||
\(909\) | −2.00000 | + | 3.46410i | −0.0663358 | + | 0.114897i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.00000 | −0.265052 | −0.132526 | − | 0.991180i | \(-0.542309\pi\) | ||||
−0.132526 | + | 0.991180i | \(0.542309\pi\) | |||||||
\(912\) | −1.73205 | + | 4.00000i | −0.0573539 | + | 0.132453i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 5.50000 | − | 9.52628i | 0.181924 | − | 0.315101i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.00000 | + | 15.5885i | 0.297368 | + | 0.515057i | ||||
\(917\) | −1.73205 | − | 1.00000i | −0.0571974 | − | 0.0330229i | ||||
\(918\) | −30.3109 | + | 17.5000i | −1.00041 | + | 0.577586i | ||||
\(919\) | −56.0000 | −1.84727 | −0.923635 | − | 0.383274i | \(-0.874797\pi\) | ||||
−0.923635 | + | 0.383274i | \(0.874797\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.50000 | + | 16.4545i | 0.313036 | + | 0.542194i | ||||
\(922\) | −1.73205 | + | 1.00000i | −0.0570421 | + | 0.0329332i | ||||
\(923\) | − | 72.0000i | − | 2.36991i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.0000 | − | 19.0526i | 0.361482 | − | 0.626106i | ||||
\(927\) | 20.7846 | − | 12.0000i | 0.682656 | − | 0.394132i | ||||
\(928\) | −8.66025 | − | 5.00000i | −0.284287 | − | 0.164133i | ||||
\(929\) | −1.50000 | + | 2.59808i | −0.0492134 | + | 0.0852401i | −0.889583 | − | 0.456774i | \(-0.849005\pi\) |
0.840369 | + | 0.542014i | \(0.182338\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.5000 | + | 7.79423i | −0.344124 | + | 0.255446i | ||||
\(932\) | − | 13.0000i | − | 0.425829i | ||||||
\(933\) | −25.9808 | − | 15.0000i | −0.850572 | − | 0.491078i | ||||
\(934\) | 11.5000 | − | 19.9186i | 0.376291 | − | 0.651756i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.00000 | − | 10.3923i | 0.196116 | − | 0.339683i | ||||
\(937\) | −0.866025 | + | 0.500000i | −0.0282918 | + | 0.0163343i | −0.514079 | − | 0.857743i | \(-0.671866\pi\) |
0.485787 | + | 0.874077i | \(0.338533\pi\) | |||||||
\(938\) | − | 16.0000i | − | 0.522419i | ||||||
\(939\) | −11.0000 | −0.358971 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.0000 | − | 38.1051i | −0.717180 | − | 1.24219i | −0.962113 | − | 0.272651i | \(-0.912099\pi\) |
0.244933 | − | 0.969540i | \(-0.421234\pi\) | |||||||
\(942\) | − | 6.00000i | − | 0.195491i | ||||||
\(943\) | 4.00000i | 0.130258i | ||||||||
\(944\) | −0.500000 | − | 0.866025i | −0.0162736 | − | 0.0281867i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.0333 | + | 26.0000i | 1.46339 | + | 0.844886i | 0.999166 | − | 0.0408333i | \(-0.0130013\pi\) |
0.464220 | + | 0.885720i | \(0.346335\pi\) | |||||||
\(948\) | 3.46410 | + | 2.00000i | 0.112509 | + | 0.0649570i | ||||
\(949\) | 18.0000 | 0.584305 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.0000 | −0.778253 | ||||||||
\(952\) | −12.1244 | − | 7.00000i | −0.392953 | − | 0.226871i | ||||
\(953\) | 1.73205 | + | 1.00000i | 0.0561066 | + | 0.0323932i | 0.527791 | − | 0.849374i | \(-0.323020\pi\) |
−0.471684 | + | 0.881768i | \(0.656354\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.00000 | + | 5.19615i | 0.0970269 | + | 0.168056i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24.0000i | 0.775405i | ||||||||
\(959\) | −15.0000 | − | 25.9808i | −0.484375 | − | 0.838963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | − | 24.0000i | − | 0.773791i | ||||||
\(963\) | −25.9808 | + | 15.0000i | −0.837218 | + | 0.483368i | ||||
\(964\) | 7.00000 | − | 12.1244i | 0.225455 | − | 0.390499i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.00000 | − | 3.46410i | 0.0643489 | − | 0.111456i | ||||
\(967\) | 10.3923 | + | 6.00000i | 0.334194 | + | 0.192947i | 0.657702 | − | 0.753279i | \(-0.271529\pi\) |
−0.323508 | + | 0.946226i | \(0.604862\pi\) | |||||||
\(968\) | − | 11.0000i | − | 0.353553i | ||||||
\(969\) | 28.0000 | + | 12.1244i | 0.899490 | + | 0.389490i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.5000 | − | 38.9711i | 0.722059 | − | 1.25064i | −0.238114 | − | 0.971237i | \(-0.576529\pi\) |
0.960173 | − | 0.279406i | \(-0.0901376\pi\) | |||||||
\(972\) | 13.8564 | + | 8.00000i | 0.444444 | + | 0.256600i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 10.0000 | − | 17.3205i | 0.320421 | − | 0.554985i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.00000 | 0.256074 | ||||||||
\(977\) | 42.0000i | 1.34370i | 0.740688 | + | 0.671850i | \(0.234500\pi\) | ||||
−0.740688 | + | 0.671850i | \(0.765500\pi\) | |||||||
\(978\) | −10.3923 | + | 6.00000i | −0.332309 | + | 0.191859i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.00000 | 0.127710 | ||||||||
\(982\) | −6.92820 | + | 4.00000i | −0.221088 | + | 0.127645i | ||||
\(983\) | 20.7846 | + | 12.0000i | 0.662926 | + | 0.382741i | 0.793391 | − | 0.608712i | \(-0.208314\pi\) |
−0.130465 | + | 0.991453i | \(0.541647\pi\) | |||||||
\(984\) | 1.00000 | + | 1.73205i | 0.0318788 | + | 0.0552158i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −35.0000 | + | 60.6218i | −1.11463 | + | 1.93059i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25.9808 | + | 3.00000i | −0.826558 | + | 0.0954427i | ||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | − | 34.6410i | 0.635321 | − | 1.10041i | −0.351126 | − | 0.936328i | \(-0.614201\pi\) |
0.986447 | − | 0.164080i | \(-0.0524655\pi\) | |||||||
\(992\) | 1.73205 | − | 1.00000i | 0.0549927 | − | 0.0317500i | ||||
\(993\) | 14.7224 | + | 8.50000i | 0.467202 | + | 0.269739i | ||||
\(994\) | 12.0000 | + | 20.7846i | 0.380617 | + | 0.659248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.0000 | −0.411921 | ||||||||
\(997\) | −19.0526 | + | 11.0000i | −0.603401 | + | 0.348373i | −0.770378 | − | 0.637587i | \(-0.779933\pi\) |
0.166978 | + | 0.985961i | \(0.446599\pi\) | |||||||
\(998\) | −28.5788 | + | 16.5000i | −0.904647 | + | 0.522298i | ||||
\(999\) | 20.0000 | 0.632772 |
(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 | 950.2.j.b.49.2 | 4 | ||
5.2 | odd | 4 | 950.2.e.b.201.1 | ✓ | 2 | ||
5.3 | odd | 4 | 950.2.e.g.201.1 | yes | 2 | ||
5.4 | even | 2 | inner | 950.2.j.b.49.1 | 4 | ||
19.7 | even | 3 | inner | 950.2.j.b.349.1 | 4 | ||
95.7 | odd | 12 | 950.2.e.b.501.1 | yes | 2 | ||
95.64 | even | 6 | inner | 950.2.j.b.349.2 | 4 | ||
95.83 | odd | 12 | 950.2.e.g.501.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.e.b.201.1 | ✓ | 2 | 5.2 | odd | 4 | ||
950.2.e.b.501.1 | yes | 2 | 95.7 | odd | 12 | ||
950.2.e.g.201.1 | yes | 2 | 5.3 | odd | 4 | ||
950.2.e.g.501.1 | yes | 2 | 95.83 | odd | 12 | ||
950.2.j.b.49.1 | 4 | 5.4 | even | 2 | inner | ||
950.2.j.b.49.2 | 4 | 1.1 | even | 1 | trivial | ||
950.2.j.b.349.1 | 4 | 19.7 | even | 3 | inner | ||
950.2.j.b.349.2 | 4 | 95.64 | even | 6 | inner |