Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [810,3,Mod(269,810)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("810.269");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.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: | \(22.0709014132\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 270) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 539.3 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 810.539 |
Dual form | 810.3.j.e.269.3 |
$q$-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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).
\(n\) | \(487\) | \(731\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 1.22474i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | + | 1.73205i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.29410 | − | 4.82963i | −0.258819 | − | 0.965926i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.33013 | + | 2.50000i | −0.618590 | + | 0.357143i | −0.776320 | − | 0.630339i | \(-0.782916\pi\) |
0.157730 | + | 0.987482i | \(0.449582\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.00000 | − | 5.00000i | 0.500000 | − | 0.500000i | ||||
\(11\) | −1.22474 | + | 0.707107i | −0.111340 | + | 0.0642824i | −0.554636 | − | 0.832093i | \(-0.687143\pi\) |
0.443296 | + | 0.896375i | \(0.353809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.79423 | + | 4.50000i | 0.599556 | + | 0.346154i | 0.768867 | − | 0.639409i | \(-0.220821\pi\) |
−0.169311 | + | 0.985563i | \(0.554154\pi\) | |||||||
\(14\) | −6.12372 | − | 3.53553i | −0.437409 | − | 0.252538i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | 11.3137 | 0.665512 | 0.332756 | − | 0.943013i | \(-0.392021\pi\) | ||||
0.332756 | + | 0.943013i | \(0.392021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 21.0000 | 1.10526 | 0.552632 | − | 0.833426i | \(-0.313624\pi\) | ||||
0.552632 | + | 0.833426i | \(0.313624\pi\) | |||||||
\(20\) | 9.65926 | + | 2.58819i | 0.482963 | + | 0.129410i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.73205 | − | 1.00000i | −0.0787296 | − | 0.0454545i | ||||
\(23\) | −0.707107 | + | 1.22474i | −0.0307438 | + | 0.0532498i | −0.880988 | − | 0.473139i | \(-0.843121\pi\) |
0.850244 | + | 0.526389i | \(0.176454\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −21.6506 | + | 12.5000i | −0.866025 | + | 0.500000i | ||||
\(26\) | 12.7279i | 0.489535i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 10.0000i | − | 0.357143i | ||||||
\(29\) | −33.0681 | + | 19.0919i | −1.14028 | + | 0.658341i | −0.946500 | − | 0.322704i | \(-0.895408\pi\) |
−0.193780 | + | 0.981045i | \(0.562075\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −20.0000 | + | 34.6410i | −0.645161 | + | 1.11745i | 0.339103 | + | 0.940749i | \(0.389876\pi\) |
−0.984264 | + | 0.176703i | \(0.943457\pi\) | |||||||
\(32\) | 2.82843 | − | 4.89898i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.00000 | + | 13.8564i | 0.235294 | + | 0.407541i | ||||
\(35\) | 17.6777 | + | 17.6777i | 0.505076 | + | 0.505076i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 25.0000i | 0.675676i | 0.941204 | + | 0.337838i | \(0.109696\pi\) | ||||
−0.941204 | + | 0.337838i | \(0.890304\pi\) | |||||||
\(38\) | 14.8492 | + | 25.7196i | 0.390770 | + | 0.676833i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.66025 | + | 13.6603i | 0.0915064 | + | 0.341506i | ||||
\(41\) | 45.3156 | + | 26.1630i | 1.10526 | + | 0.638121i | 0.937597 | − | 0.347724i | \(-0.113045\pi\) |
0.167661 | + | 0.985845i | \(0.446379\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −55.4256 | + | 32.0000i | −1.28897 | + | 0.744186i | −0.978470 | − | 0.206388i | \(-0.933829\pi\) |
−0.310498 | + | 0.950574i | \(0.600496\pi\) | |||||||
\(44\) | − | 2.82843i | − | 0.0642824i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | −0.0434783 | ||||||||
\(47\) | −11.3137 | − | 19.5959i | −0.240717 | − | 0.416934i | 0.720202 | − | 0.693765i | \(-0.244049\pi\) |
−0.960919 | + | 0.276830i | \(0.910716\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12.0000 | + | 20.7846i | −0.244898 | + | 0.424176i | ||||
\(50\) | −30.6186 | − | 17.6777i | −0.612372 | − | 0.353553i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −15.5885 | + | 9.00000i | −0.299778 | + | 0.173077i | ||||
\(53\) | 72.1249 | 1.36085 | 0.680424 | − | 0.732819i | \(-0.261796\pi\) | ||||
0.680424 | + | 0.732819i | \(0.261796\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00000 | + | 5.00000i | 0.0909091 | + | 0.0909091i | ||||
\(56\) | 12.2474 | − | 7.07107i | 0.218704 | − | 0.126269i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −46.7654 | − | 27.0000i | −0.806300 | − | 0.465517i | ||||
\(59\) | 78.3837 | + | 45.2548i | 1.32854 | + | 0.767031i | 0.985073 | − | 0.172135i | \(-0.0550665\pi\) |
0.343463 | + | 0.939166i | \(0.388400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 48.5000 | + | 84.0045i | 0.795082 | + | 1.37712i | 0.922787 | + | 0.385310i | \(0.125906\pi\) |
−0.127705 | + | 0.991812i | \(0.540761\pi\) | |||||||
\(62\) | −56.5685 | −0.912396 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 11.6469 | − | 43.4667i | 0.179182 | − | 0.668718i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −113.449 | − | 65.5000i | −1.69327 | − | 0.977612i | −0.951845 | − | 0.306580i | \(-0.900815\pi\) |
−0.741429 | − | 0.671032i | \(-0.765851\pi\) | |||||||
\(68\) | −11.3137 | + | 19.5959i | −0.166378 | + | 0.288175i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.15064 | + | 34.1506i | −0.130723 | + | 0.487866i | ||||
\(71\) | 89.0955i | 1.25487i | 0.778671 | + | 0.627433i | \(0.215894\pi\) | ||||
−0.778671 | + | 0.627433i | \(0.784106\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 17.0000i | 0.232877i | 0.993198 | + | 0.116438i | \(0.0371477\pi\) | ||||
−0.993198 | + | 0.116438i | \(0.962852\pi\) | |||||||
\(74\) | −30.6186 | + | 17.6777i | −0.413765 | + | 0.238887i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −21.0000 | + | 36.3731i | −0.276316 | + | 0.478593i | ||||
\(77\) | 3.53553 | − | 6.12372i | 0.0459160 | − | 0.0795289i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 58.5000 | + | 101.325i | 0.740506 | + | 1.28259i | 0.952265 | + | 0.305273i | \(0.0987476\pi\) |
−0.211759 | + | 0.977322i | \(0.567919\pi\) | |||||||
\(80\) | −14.1421 | + | 14.1421i | −0.176777 | + | 0.176777i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 74.0000i | 0.902439i | ||||||||
\(83\) | 28.9914 | + | 50.2145i | 0.349294 | + | 0.604994i | 0.986124 | − | 0.166009i | \(-0.0530882\pi\) |
−0.636830 | + | 0.771004i | \(0.719755\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.6410 | − | 54.6410i | −0.172247 | − | 0.642835i | ||||
\(86\) | −78.3837 | − | 45.2548i | −0.911438 | − | 0.526219i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.46410 | − | 2.00000i | 0.0393648 | − | 0.0227273i | ||||
\(89\) | − | 147.078i | − | 1.65256i | −0.563257 | − | 0.826282i | \(-0.690452\pi\) | ||
0.563257 | − | 0.826282i | \(-0.309548\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −45.0000 | −0.494505 | ||||||||
\(92\) | −1.41421 | − | 2.44949i | −0.0153719 | − | 0.0266249i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 16.0000 | − | 27.7128i | 0.170213 | − | 0.294817i | ||||
\(95\) | −27.1760 | − | 101.422i | −0.286063 | − | 1.06760i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 35.5070 | − | 20.5000i | 0.366052 | − | 0.211340i | −0.305680 | − | 0.952134i | \(-0.598884\pi\) |
0.671732 | + | 0.740794i | \(0.265551\pi\) | |||||||
\(98\) | −33.9411 | −0.346338 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | − | 50.0000i | − | 0.500000i | ||||||
\(101\) | 78.3837 | − | 45.2548i | 0.776076 | − | 0.448068i | −0.0589618 | − | 0.998260i | \(-0.518779\pi\) |
0.835038 | + | 0.550193i | \(0.185446\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.2583 | − | 6.50000i | −0.109304 | − | 0.0631068i | 0.444351 | − | 0.895853i | \(-0.353434\pi\) |
−0.553655 | + | 0.832746i | \(0.686768\pi\) | |||||||
\(104\) | −22.0454 | − | 12.7279i | −0.211975 | − | 0.122384i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 51.0000 | + | 88.3346i | 0.481132 | + | 0.833345i | ||||
\(107\) | −123.037 | −1.14987 | −0.574937 | − | 0.818197i | \(-0.694974\pi\) | ||||
−0.574937 | + | 0.818197i | \(0.694974\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000 | 0.0733945 | 0.0366972 | − | 0.999326i | \(-0.488316\pi\) | ||||
0.0366972 | + | 0.999326i | \(0.488316\pi\) | |||||||
\(110\) | −2.58819 | + | 9.65926i | −0.0235290 | + | 0.0878114i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 17.3205 | + | 10.0000i | 0.154647 | + | 0.0892857i | ||||
\(113\) | 19.0919 | − | 33.0681i | 0.168955 | − | 0.292638i | −0.769098 | − | 0.639131i | \(-0.779294\pi\) |
0.938053 | + | 0.346493i | \(0.112628\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.83013 | + | 1.83013i | 0.0593924 | + | 0.0159141i | ||||
\(116\) | − | 76.3675i | − | 0.658341i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 128.000i | 1.08475i | ||||||||
\(119\) | −48.9898 | + | 28.2843i | −0.411679 | + | 0.237683i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −59.5000 | + | 103.057i | −0.491736 | + | 0.851711i | ||||
\(122\) | −68.5894 | + | 118.800i | −0.562208 | + | 0.973773i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −40.0000 | − | 69.2820i | −0.322581 | − | 0.558726i | ||||
\(125\) | 88.3883 | + | 88.3883i | 0.707107 | + | 0.707107i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.00000i | − | 0.0629921i | −0.999504 | − | 0.0314961i | \(-0.989973\pi\) | ||
0.999504 | − | 0.0314961i | \(-0.0100272\pi\) | |||||||
\(128\) | 5.65685 | + | 9.79796i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 61.4711 | − | 16.4711i | 0.472855 | − | 0.126701i | ||||
\(131\) | −117.576 | − | 67.8823i | −0.897523 | − | 0.518185i | −0.0211272 | − | 0.999777i | \(-0.506726\pi\) |
−0.876396 | + | 0.481592i | \(0.840059\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −90.9327 | + | 52.5000i | −0.683704 | + | 0.394737i | ||||
\(134\) | − | 185.262i | − | 1.38255i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −32.0000 | −0.235294 | ||||||||
\(137\) | −133.643 | − | 231.477i | −0.975498 | − | 1.68961i | −0.678283 | − | 0.734801i | \(-0.737276\pi\) |
−0.297215 | − | 0.954811i | \(-0.596058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.5000 | − | 32.0429i | 0.133094 | − | 0.230525i | −0.791774 | − | 0.610814i | \(-0.790842\pi\) |
0.924868 | + | 0.380289i | \(0.124176\pi\) | |||||||
\(140\) | −48.2963 | + | 12.9410i | −0.344974 | + | 0.0924354i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −109.119 | + | 63.0000i | −0.768445 | + | 0.443662i | ||||
\(143\) | −12.7279 | −0.0890064 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 135.000 | + | 135.000i | 0.931034 | + | 0.931034i | ||||
\(146\) | −20.8207 | + | 12.0208i | −0.142607 | + | 0.0823344i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −43.3013 | − | 25.0000i | −0.292576 | − | 0.168919i | ||||
\(149\) | 225.353 | + | 130.108i | 1.51244 | + | 0.873206i | 0.999894 | + | 0.0145438i | \(0.00462959\pi\) |
0.512542 | + | 0.858662i | \(0.328704\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −54.5000 | − | 94.3968i | −0.360927 | − | 0.625144i | 0.627187 | − | 0.778869i | \(-0.284206\pi\) |
−0.988114 | + | 0.153725i | \(0.950873\pi\) | |||||||
\(152\) | −59.3970 | −0.390770 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.0000 | 0.0649351 | ||||||||
\(155\) | 193.185 | + | 51.7638i | 1.24636 | + | 0.333960i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 102.191 | + | 59.0000i | 0.650898 | + | 0.375796i | 0.788800 | − | 0.614650i | \(-0.210703\pi\) |
−0.137902 | + | 0.990446i | \(0.544036\pi\) | |||||||
\(158\) | −82.7315 | + | 143.295i | −0.523617 | + | 0.906931i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −27.3205 | − | 7.32051i | −0.170753 | − | 0.0457532i | ||||
\(161\) | − | 7.07107i | − | 0.0439197i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 203.000i | − | 1.24540i | −0.782461 | − | 0.622699i | \(-0.786036\pi\) | ||
0.782461 | − | 0.622699i | \(-0.213964\pi\) | |||||||
\(164\) | −90.6311 | + | 52.3259i | −0.552629 | + | 0.319060i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −41.0000 | + | 71.0141i | −0.246988 | + | 0.427796i | ||||
\(167\) | 50.9117 | − | 88.1816i | 0.304860 | − | 0.528034i | −0.672370 | − | 0.740215i | \(-0.734724\pi\) |
0.977230 | + | 0.212182i | \(0.0680569\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −44.0000 | − | 76.2102i | −0.260355 | − | 0.450948i | ||||
\(170\) | 56.5685 | − | 56.5685i | 0.332756 | − | 0.332756i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 128.000i | − | 0.744186i | ||||||
\(173\) | −5.65685 | − | 9.79796i | −0.0326986 | − | 0.0566356i | 0.849213 | − | 0.528050i | \(-0.177077\pi\) |
−0.881912 | + | 0.471415i | \(0.843743\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 62.5000 | − | 108.253i | 0.357143 | − | 0.618590i | ||||
\(176\) | 4.89898 | + | 2.82843i | 0.0278351 | + | 0.0160706i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 180.133 | − | 104.000i | 1.01198 | − | 0.584270i | ||||
\(179\) | 125.865i | 0.703156i | 0.936159 | + | 0.351578i | \(0.114355\pi\) | ||||
−0.936159 | + | 0.351578i | \(0.885645\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −127.000 | −0.701657 | −0.350829 | − | 0.936440i | \(-0.614100\pi\) | ||||
−0.350829 | + | 0.936440i | \(0.614100\pi\) | |||||||
\(182\) | −31.8198 | − | 55.1135i | −0.174834 | − | 0.302822i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.00000 | − | 3.46410i | 0.0108696 | − | 0.0188266i | ||||
\(185\) | 120.741 | − | 32.3524i | 0.652653 | − | 0.174878i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.8564 | + | 8.00000i | −0.0740984 | + | 0.0427807i | ||||
\(188\) | 45.2548 | 0.240717 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 105.000 | − | 105.000i | 0.552632 | − | 0.552632i | ||||
\(191\) | 88.1816 | − | 50.9117i | 0.461684 | − | 0.266553i | −0.251068 | − | 0.967969i | \(-0.580782\pi\) |
0.712752 | + | 0.701416i | \(0.247448\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 234.693 | + | 135.500i | 1.21603 | + | 0.702073i | 0.964065 | − | 0.265665i | \(-0.0855915\pi\) |
0.251960 | + | 0.967738i | \(0.418925\pi\) | |||||||
\(194\) | 50.2145 | + | 28.9914i | 0.258838 | + | 0.149440i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.0000 | − | 41.5692i | −0.122449 | − | 0.212088i | ||||
\(197\) | −316.784 | −1.60804 | −0.804020 | − | 0.594602i | \(-0.797309\pi\) | ||||
−0.804020 | + | 0.594602i | \(0.797309\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 147.000 | 0.738693 | 0.369347 | − | 0.929292i | \(-0.379581\pi\) | ||||
0.369347 | + | 0.929292i | \(0.379581\pi\) | |||||||
\(200\) | 61.2372 | − | 35.3553i | 0.306186 | − | 0.176777i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 110.851 | + | 64.0000i | 0.548769 | + | 0.316832i | ||||
\(203\) | 95.4594 | − | 165.341i | 0.470243 | − | 0.814486i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 67.7147 | − | 252.715i | 0.330316 | − | 1.23275i | ||||
\(206\) | − | 18.3848i | − | 0.0892465i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 36.0000i | − | 0.173077i | ||||||
\(209\) | −25.7196 | + | 14.8492i | −0.123060 | + | 0.0710490i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −70.5000 | + | 122.110i | −0.334123 | + | 0.578718i | −0.983316 | − | 0.181906i | \(-0.941774\pi\) |
0.649193 | + | 0.760624i | \(0.275107\pi\) | |||||||
\(212\) | −72.1249 | + | 124.924i | −0.340212 | + | 0.589264i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −87.0000 | − | 150.688i | −0.406542 | − | 0.704151i | ||||
\(215\) | 226.274 | + | 226.274i | 1.05244 | + | 1.05244i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 200.000i | − | 0.921659i | ||||||
\(218\) | 5.65685 | + | 9.79796i | 0.0259489 | + | 0.0449448i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −13.6603 | + | 3.66025i | −0.0620921 | + | 0.0166375i | ||||
\(221\) | 88.1816 | + | 50.9117i | 0.399012 | + | 0.230370i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.92820 | − | 4.00000i | 0.0310682 | − | 0.0179372i | −0.484385 | − | 0.874855i | \(-0.660957\pi\) |
0.515454 | + | 0.856917i | \(0.327623\pi\) | |||||||
\(224\) | 28.2843i | 0.126269i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 54.0000 | 0.238938 | ||||||||
\(227\) | 34.6482 | + | 60.0125i | 0.152635 | + | 0.264372i | 0.932196 | − | 0.361955i | \(-0.117891\pi\) |
−0.779560 | + | 0.626327i | \(0.784557\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.00000 | − | 6.92820i | 0.0174672 | − | 0.0302542i | −0.857160 | − | 0.515051i | \(-0.827773\pi\) |
0.874627 | + | 0.484797i | \(0.161106\pi\) | |||||||
\(230\) | 2.58819 | + | 9.65926i | 0.0112530 | + | 0.0419968i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 93.5307 | − | 54.0000i | 0.403150 | − | 0.232759i | ||||
\(233\) | 316.784 | 1.35959 | 0.679794 | − | 0.733403i | \(-0.262069\pi\) | ||||
0.679794 | + | 0.733403i | \(0.262069\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −80.0000 | + | 80.0000i | −0.340426 | + | 0.340426i | ||||
\(236\) | −156.767 | + | 90.5097i | −0.664268 | + | 0.383516i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −69.2820 | − | 40.0000i | −0.291101 | − | 0.168067i | ||||
\(239\) | −177.588 | − | 102.530i | −0.743046 | − | 0.428998i | 0.0801297 | − | 0.996784i | \(-0.474467\pi\) |
−0.823176 | + | 0.567787i | \(0.807800\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −39.5000 | − | 68.4160i | −0.163900 | − | 0.283884i | 0.772364 | − | 0.635180i | \(-0.219074\pi\) |
−0.936264 | + | 0.351297i | \(0.885741\pi\) | |||||||
\(242\) | −168.291 | −0.695419 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −194.000 | −0.795082 | ||||||||
\(245\) | 115.911 | + | 31.0583i | 0.473107 | + | 0.126769i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 163.679 | + | 94.5000i | 0.662667 | + | 0.382591i | ||||
\(248\) | 56.5685 | − | 97.9796i | 0.228099 | − | 0.395079i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −45.7532 | + | 170.753i | −0.183013 | + | 0.683013i | ||||
\(251\) | 46.6690i | 0.185932i | 0.995669 | + | 0.0929662i | \(0.0296349\pi\) | ||||
−0.995669 | + | 0.0929662i | \(0.970365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.00000i | − | 0.00790514i | ||||||
\(254\) | 9.79796 | − | 5.65685i | 0.0385746 | − | 0.0222711i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −84.8528 | + | 146.969i | −0.330167 | + | 0.571865i | −0.982544 | − | 0.186029i | \(-0.940438\pi\) |
0.652378 | + | 0.757894i | \(0.273772\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −62.5000 | − | 108.253i | −0.241313 | − | 0.417966i | ||||
\(260\) | 63.6396 | + | 63.6396i | 0.244768 | + | 0.244768i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 192.000i | − | 0.732824i | ||||||
\(263\) | 141.421 | + | 244.949i | 0.537724 | + | 0.931365i | 0.999026 | + | 0.0441219i | \(0.0140490\pi\) |
−0.461302 | + | 0.887243i | \(0.652618\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −93.3365 | − | 348.336i | −0.352213 | − | 1.31448i | ||||
\(266\) | −128.598 | − | 74.2462i | −0.483452 | − | 0.279121i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 226.899 | − | 131.000i | 0.846637 | − | 0.488806i | ||||
\(269\) | 101.823i | 0.378526i | 0.981926 | + | 0.189263i | \(0.0606098\pi\) | ||||
−0.981926 | + | 0.189263i | \(0.939390\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −221.000 | −0.815498 | −0.407749 | − | 0.913094i | \(-0.633686\pi\) | ||||
−0.407749 | + | 0.913094i | \(0.633686\pi\) | |||||||
\(272\) | −22.6274 | − | 39.1918i | −0.0831890 | − | 0.144088i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 189.000 | − | 327.358i | 0.689781 | − | 1.19474i | ||||
\(275\) | 17.6777 | − | 30.6186i | 0.0642824 | − | 0.111340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 76.2102 | − | 44.0000i | 0.275127 | − | 0.158845i | −0.356088 | − | 0.934452i | \(-0.615890\pi\) |
0.631215 | + | 0.775608i | \(0.282556\pi\) | |||||||
\(278\) | 52.3259 | 0.188223 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −50.0000 | − | 50.0000i | −0.178571 | − | 0.178571i | ||||
\(281\) | −176.363 | + | 101.823i | −0.627627 | + | 0.362361i | −0.779833 | − | 0.625988i | \(-0.784696\pi\) |
0.152205 | + | 0.988349i | \(0.451362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.7128 | + | 16.0000i | 0.0979251 | + | 0.0565371i | 0.548163 | − | 0.836372i | \(-0.315327\pi\) |
−0.450238 | + | 0.892909i | \(0.648661\pi\) | |||||||
\(284\) | −154.318 | − | 89.0955i | −0.543373 | − | 0.313716i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.00000 | − | 15.5885i | −0.0314685 | − | 0.0545051i | ||||
\(287\) | −261.630 | −0.911601 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −161.000 | −0.557093 | ||||||||
\(290\) | −69.8811 | + | 260.800i | −0.240969 | + | 0.899310i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −29.4449 | − | 17.0000i | −0.100839 | − | 0.0582192i | ||||
\(293\) | 86.9741 | − | 150.644i | 0.296840 | − | 0.514142i | −0.678571 | − | 0.734535i | \(-0.737401\pi\) |
0.975411 | + | 0.220393i | \(0.0707338\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 117.128 | − | 437.128i | 0.397045 | − | 1.48179i | ||||
\(296\) | − | 70.7107i | − | 0.238887i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 368.000i | 1.23490i | ||||||||
\(299\) | −11.0227 | + | 6.36396i | −0.0368652 | + | 0.0212842i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 160.000 | − | 277.128i | 0.531561 | − | 0.920691i | ||||
\(302\) | 77.0746 | − | 133.497i | 0.255214 | − | 0.442044i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −42.0000 | − | 72.7461i | −0.138158 | − | 0.239296i | ||||
\(305\) | 342.947 | − | 342.947i | 1.12442 | − | 1.12442i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 486.000i | 1.58306i | 0.611129 | + | 0.791531i | \(0.290716\pi\) | ||||
−0.611129 | + | 0.791531i | \(0.709284\pi\) | |||||||
\(308\) | 7.07107 | + | 12.2474i | 0.0229580 | + | 0.0397644i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 73.2051 | + | 273.205i | 0.236145 | + | 0.881307i | ||||
\(311\) | 58.7878 | + | 33.9411i | 0.189028 | + | 0.109135i | 0.591528 | − | 0.806285i | \(-0.298525\pi\) |
−0.402499 | + | 0.915420i | \(0.631858\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 243.353 | − | 140.500i | 0.777486 | − | 0.448882i | −0.0580525 | − | 0.998314i | \(-0.518489\pi\) |
0.835539 | + | 0.549432i | \(0.185156\pi\) | |||||||
\(314\) | 166.877i | 0.531456i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −234.000 | −0.740506 | ||||||||
\(317\) | −260.215 | − | 450.706i | −0.820868 | − | 1.42179i | −0.905036 | − | 0.425334i | \(-0.860157\pi\) |
0.0841679 | − | 0.996452i | \(-0.473177\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.0000 | − | 46.7654i | 0.0846395 | − | 0.146600i | ||||
\(320\) | −10.3528 | − | 38.6370i | −0.0323524 | − | 0.120741i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.66025 | − | 5.00000i | 0.0268952 | − | 0.0155280i | ||||
\(323\) | 237.588 | 0.735566 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −225.000 | −0.692308 | ||||||||
\(326\) | 248.623 | − | 143.543i | 0.762648 | − | 0.440315i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −128.172 | − | 74.0000i | −0.390768 | − | 0.225610i | ||||
\(329\) | 97.9796 | + | 56.5685i | 0.297810 | + | 0.171941i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.5000 | + | 51.0955i | 0.0891239 | + | 0.154367i | 0.907141 | − | 0.420827i | \(-0.138260\pi\) |
−0.818017 | + | 0.575194i | \(0.804927\pi\) | |||||||
\(332\) | −115.966 | −0.349294 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 144.000 | 0.431138 | ||||||||
\(335\) | −169.526 | + | 632.681i | −0.506049 | + | 1.88860i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −47.6314 | − | 27.5000i | −0.141339 | − | 0.0816024i | 0.427663 | − | 0.903938i | \(-0.359337\pi\) |
−0.569002 | + | 0.822336i | \(0.692670\pi\) | |||||||
\(338\) | 62.2254 | − | 107.778i | 0.184099 | − | 0.318868i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 109.282 | + | 29.2820i | 0.321418 | + | 0.0861236i | ||||
\(341\) | − | 56.5685i | − | 0.165890i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 365.000i | − | 1.06414i | ||||||
\(344\) | 156.767 | − | 90.5097i | 0.455719 | − | 0.263109i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.00000 | − | 13.8564i | 0.0231214 | − | 0.0400474i | ||||
\(347\) | −299.106 | + | 518.067i | −0.861977 | + | 1.49299i | 0.00803996 | + | 0.999968i | \(0.497441\pi\) |
−0.870017 | + | 0.493021i | \(0.835893\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 219.500 | + | 380.185i | 0.628940 | + | 1.08936i | 0.987765 | + | 0.155951i | \(0.0498442\pi\) |
−0.358825 | + | 0.933405i | \(0.616823\pi\) | |||||||
\(350\) | 176.777 | 0.505076 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.00000i | 0.0227273i | ||||||||
\(353\) | −260.215 | − | 450.706i | −0.737154 | − | 1.27679i | −0.953772 | − | 0.300531i | \(-0.902836\pi\) |
0.216618 | − | 0.976256i | \(-0.430497\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 430.298 | − | 115.298i | 1.21211 | − | 0.324783i | ||||
\(356\) | 254.747 | + | 147.078i | 0.715581 | + | 0.413141i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −154.153 | + | 89.0000i | −0.430594 | + | 0.248603i | ||||
\(359\) | 55.1543i | 0.153633i | 0.997045 | + | 0.0768166i | \(0.0244756\pi\) | ||||
−0.997045 | + | 0.0768166i | \(0.975524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 80.0000 | 0.221607 | ||||||||
\(362\) | −89.8026 | − | 155.543i | −0.248073 | − | 0.429676i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 45.0000 | − | 77.9423i | 0.123626 | − | 0.214127i | ||||
\(365\) | 82.1037 | − | 21.9996i | 0.224942 | − | 0.0602729i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 510.089 | − | 294.500i | 1.38989 | − | 0.802452i | 0.396586 | − | 0.917998i | \(-0.370195\pi\) |
0.993302 | + | 0.115545i | \(0.0368615\pi\) | |||||||
\(368\) | 5.65685 | 0.0153719 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 125.000 | + | 125.000i | 0.337838 | + | 0.337838i | ||||
\(371\) | −312.310 | + | 180.312i | −0.841806 | + | 0.486017i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.79423 | + | 4.50000i | 0.0208961 | + | 0.0120643i | 0.510412 | − | 0.859930i | \(-0.329493\pi\) |
−0.489516 | + | 0.871995i | \(0.662826\pi\) | |||||||
\(374\) | −19.5959 | − | 11.3137i | −0.0523955 | − | 0.0302506i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 32.0000 | + | 55.4256i | 0.0851064 | + | 0.147409i | ||||
\(377\) | −343.654 | −0.911549 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 157.000 | 0.414248 | 0.207124 | − | 0.978315i | \(-0.433590\pi\) | ||||
0.207124 | + | 0.978315i | \(0.433590\pi\) | |||||||
\(380\) | 202.844 | + | 54.3520i | 0.533801 | + | 0.143032i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 124.708 | + | 72.0000i | 0.326460 | + | 0.188482i | ||||
\(383\) | −141.421 | + | 244.949i | −0.369246 | + | 0.639553i | −0.989448 | − | 0.144889i | \(-0.953717\pi\) |
0.620202 | + | 0.784443i | \(0.287051\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −34.1506 | − | 9.15064i | −0.0887029 | − | 0.0237679i | ||||
\(386\) | 383.252i | 0.992881i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 82.0000i | 0.211340i | ||||||||
\(389\) | 519.292 | − | 299.813i | 1.33494 | − | 0.770728i | 0.348888 | − | 0.937164i | \(-0.386559\pi\) |
0.986052 | + | 0.166436i | \(0.0532260\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | + | 13.8564i | −0.0204604 | + | 0.0354384i | ||||
\(392\) | 33.9411 | − | 58.7878i | 0.0865845 | − | 0.149969i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −224.000 | − | 387.979i | −0.568528 | − | 0.984719i | ||||
\(395\) | 413.657 | − | 413.657i | 1.04723 | − | 1.04723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 296.000i | − | 0.745592i | −0.927913 | − | 0.372796i | \(-0.878399\pi\) | ||
0.927913 | − | 0.372796i | \(-0.121601\pi\) | |||||||
\(398\) | 103.945 | + | 180.037i | 0.261168 | + | 0.452356i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 86.6025 | + | 50.0000i | 0.216506 | + | 0.125000i | ||||
\(401\) | 336.805 | + | 194.454i | 0.839912 | + | 0.484924i | 0.857234 | − | 0.514926i | \(-0.172181\pi\) |
−0.0173221 | + | 0.999850i | \(0.505514\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −311.769 | + | 180.000i | −0.773621 | + | 0.446650i | ||||
\(404\) | 181.019i | 0.448068i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 270.000 | 0.665025 | ||||||||
\(407\) | −17.6777 | − | 30.6186i | −0.0434341 | − | 0.0752300i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −72.5000 | + | 125.574i | −0.177262 | + | 0.307026i | −0.940942 | − | 0.338569i | \(-0.890057\pi\) |
0.763680 | + | 0.645595i | \(0.223391\pi\) | |||||||
\(410\) | 357.393 | − | 95.7630i | 0.871689 | − | 0.233568i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 22.5167 | − | 13.0000i | 0.0546521 | − | 0.0315534i | ||||
\(413\) | −452.548 | −1.09576 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 205.000 | − | 205.000i | 0.493976 | − | 0.493976i | ||||
\(416\) | 44.0908 | − | 25.4558i | 0.105988 | − | 0.0611919i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −36.3731 | − | 21.0000i | −0.0870169 | − | 0.0502392i | ||||
\(419\) | −607.473 | − | 350.725i | −1.44982 | − | 0.837052i | −0.451347 | − | 0.892348i | \(-0.649056\pi\) |
−0.998470 | + | 0.0552959i | \(0.982390\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −252.500 | − | 437.343i | −0.599762 | − | 1.03882i | −0.992856 | − | 0.119320i | \(-0.961928\pi\) |
0.393093 | − | 0.919499i | \(-0.371405\pi\) | |||||||
\(422\) | −199.404 | −0.472522 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −204.000 | −0.481132 | ||||||||
\(425\) | −244.949 | + | 141.421i | −0.576351 | + | 0.332756i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −420.022 | − | 242.500i | −0.983659 | − | 0.567916i | ||||
\(428\) | 123.037 | − | 213.106i | 0.287469 | − | 0.497910i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −117.128 | + | 437.128i | −0.272391 | + | 1.01658i | ||||
\(431\) | − | 43.8406i | − | 0.101718i | −0.998706 | − | 0.0508592i | \(-0.983804\pi\) | ||
0.998706 | − | 0.0508592i | \(-0.0161960\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.0000i | 0.0739030i | 0.999317 | + | 0.0369515i | \(0.0117647\pi\) | ||||
−0.999317 | + | 0.0369515i | \(0.988235\pi\) | |||||||
\(434\) | 244.949 | − | 141.421i | 0.564399 | − | 0.325856i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.00000 | + | 13.8564i | −0.0183486 | + | 0.0317807i | ||||
\(437\) | −14.8492 | + | 25.7196i | −0.0339800 | + | 0.0588550i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 252.000 | + | 436.477i | 0.574032 | + | 0.994252i | 0.996146 | + | 0.0877097i | \(0.0279548\pi\) |
−0.422114 | + | 0.906543i | \(0.638712\pi\) | |||||||
\(440\) | −14.1421 | − | 14.1421i | −0.0321412 | − | 0.0321412i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 144.000i | 0.325792i | ||||||||
\(443\) | 118.794 | + | 205.757i | 0.268158 | + | 0.464463i | 0.968386 | − | 0.249456i | \(-0.0802518\pi\) |
−0.700228 | + | 0.713919i | \(0.746918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −710.333 | + | 190.333i | −1.59625 | + | 0.427715i | ||||
\(446\) | 9.79796 | + | 5.65685i | 0.0219685 | + | 0.0126835i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −34.6410 | + | 20.0000i | −0.0773237 | + | 0.0446429i | ||||
\(449\) | 67.8823i | 0.151185i | 0.997139 | + | 0.0755927i | \(0.0240849\pi\) | ||||
−0.997139 | + | 0.0755927i | \(0.975915\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −74.0000 | −0.164080 | ||||||||
\(452\) | 38.1838 | + | 66.1362i | 0.0844774 | + | 0.146319i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −49.0000 | + | 84.8705i | −0.107930 | + | 0.186939i | ||||
\(455\) | 58.2343 | + | 217.333i | 0.127987 | + | 0.477656i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −651.251 | + | 376.000i | −1.42506 | + | 0.822757i | −0.996725 | − | 0.0808643i | \(-0.974232\pi\) |
−0.428332 | + | 0.903621i | \(0.640899\pi\) | |||||||
\(458\) | 11.3137 | 0.0247024 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.0000 | + | 10.0000i | −0.0217391 | + | 0.0217391i | ||||
\(461\) | 529.090 | − | 305.470i | 1.14770 | − | 0.662625i | 0.199374 | − | 0.979923i | \(-0.436109\pi\) |
0.948326 | + | 0.317298i | \(0.102776\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 517.017 | + | 298.500i | 1.11667 | + | 0.644708i | 0.940548 | − | 0.339660i | \(-0.110312\pi\) |
0.176120 | + | 0.984369i | \(0.443645\pi\) | |||||||
\(464\) | 132.272 | + | 76.3675i | 0.285070 | + | 0.164585i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 224.000 | + | 387.979i | 0.480687 | + | 0.832574i | ||||
\(467\) | −848.528 | −1.81698 | −0.908488 | − | 0.417910i | \(-0.862763\pi\) | ||||
−0.908488 | + | 0.417910i | \(0.862763\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 655.000 | 1.39659 | ||||||||
\(470\) | −154.548 | − | 41.4110i | −0.328826 | − | 0.0881086i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −221.703 | − | 128.000i | −0.469709 | − | 0.271186i | ||||
\(473\) | 45.2548 | − | 78.3837i | 0.0956762 | − | 0.165716i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −454.663 | + | 262.500i | −0.957186 | + | 0.552632i | ||||
\(476\) | − | 113.137i | − | 0.237683i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 290.000i | − | 0.606695i | ||||||
\(479\) | −145.745 | + | 84.1457i | −0.304269 | + | 0.175670i | −0.644359 | − | 0.764723i | \(-0.722876\pi\) |
0.340090 | + | 0.940393i | \(0.389542\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −112.500 | + | 194.856i | −0.233888 | + | 0.405105i | ||||
\(482\) | 55.8614 | − | 96.7548i | 0.115895 | − | 0.200736i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −119.000 | − | 206.114i | −0.245868 | − | 0.425855i | ||||
\(485\) | −144.957 | − | 144.957i | −0.298880 | − | 0.298880i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 507.000i | 1.04107i | 0.853841 | + | 0.520534i | \(0.174267\pi\) | ||||
−0.853841 | + | 0.520534i | \(0.825733\pi\) | |||||||
\(488\) | −137.179 | − | 237.601i | −0.281104 | − | 0.486886i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 43.9230 | + | 163.923i | 0.0896389 | + | 0.334537i | ||||
\(491\) | −371.098 | − | 214.253i | −0.755800 | − | 0.436361i | 0.0719859 | − | 0.997406i | \(-0.477066\pi\) |
−0.827786 | + | 0.561044i | \(0.810400\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −374.123 | + | 216.000i | −0.758870 | + | 0.438134i | ||||
\(494\) | 267.286i | 0.541066i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 160.000 | 0.322581 | ||||||||
\(497\) | −222.739 | − | 385.795i | −0.448166 | − | 0.776247i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −435.000 | + | 753.442i | −0.871743 | + | 1.50990i | −0.0115517 | + | 0.999933i | \(0.503677\pi\) |
−0.860192 | + | 0.509971i | \(0.829656\pi\) | |||||||
\(500\) | −241.481 | + | 64.7048i | −0.482963 | + | 0.129410i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −57.1577 | + | 33.0000i | −0.113860 | + | 0.0657371i | ||||
\(503\) | 462.448 | 0.919379 | 0.459690 | − | 0.888080i | \(-0.347961\pi\) | ||||
0.459690 | + | 0.888080i | \(0.347961\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −320.000 | − | 320.000i | −0.633663 | − | 0.633663i | ||||
\(506\) | 2.44949 | − | 1.41421i | 0.00484089 | − | 0.00279489i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.8564 | + | 8.00000i | 0.0272764 | + | 0.0157480i | ||||
\(509\) | −709.127 | − | 409.415i | −1.39318 | − | 0.804351i | −0.399512 | − | 0.916728i | \(-0.630820\pi\) |
−0.993666 | + | 0.112377i | \(0.964154\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −42.5000 | − | 73.6122i | −0.0831703 | − | 0.144055i | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −240.000 | −0.466926 | ||||||||
\(515\) | −16.8232 | + | 62.7852i | −0.0326665 | + | 0.121913i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.7128 | + | 16.0000i | 0.0536031 | + | 0.0309478i | ||||
\(518\) | 88.3883 | − | 153.093i | 0.170634 | − | 0.295547i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −32.9423 | + | 122.942i | −0.0633506 | + | 0.236427i | ||||
\(521\) | − | 864.084i | − | 1.65851i | −0.558869 | − | 0.829256i | \(-0.688765\pi\) | ||
0.558869 | − | 0.829256i | \(-0.311235\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 163.000i | 0.311663i | 0.987784 | + | 0.155832i | \(0.0498058\pi\) | ||||
−0.987784 | + | 0.155832i | \(0.950194\pi\) | |||||||
\(524\) | 235.151 | − | 135.765i | 0.448761 | − | 0.259093i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −200.000 | + | 346.410i | −0.380228 | + | 0.658574i | ||||
\(527\) | −226.274 | + | 391.918i | −0.429363 | + | 0.743678i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 263.500 | + | 456.395i | 0.498110 | + | 0.862751i | ||||
\(530\) | 360.624 | − | 360.624i | 0.680424 | − | 0.680424i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 210.000i | − | 0.394737i | ||||||
\(533\) | 235.467 | + | 407.840i | 0.441776 | + | 0.765178i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 159.221 | + | 594.221i | 0.297609 | + | 1.11069i | ||||
\(536\) | 320.883 | + | 185.262i | 0.598663 | + | 0.345638i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −124.708 | + | 72.0000i | −0.231799 | + | 0.133829i | ||||
\(539\) | − | 33.9411i | − | 0.0629705i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 697.000 | 1.28835 | 0.644177 | − | 0.764876i | \(-0.277200\pi\) | ||||
0.644177 | + | 0.764876i | \(0.277200\pi\) | |||||||
\(542\) | −156.271 | − | 270.669i | −0.288322 | − | 0.499389i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 32.0000 | − | 55.4256i | 0.0588235 | − | 0.101885i | ||||
\(545\) | −10.3528 | − | 38.6370i | −0.0189959 | − | 0.0708936i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −336.884 | + | 194.500i | −0.615875 | + | 0.355576i | −0.775261 | − | 0.631640i | \(-0.782382\pi\) |
0.159386 | + | 0.987216i | \(0.449049\pi\) | |||||||
\(548\) | 534.573 | 0.975498 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 50.0000 | 0.0909091 | ||||||||
\(551\) | −694.430 | + | 400.930i | −1.26031 | + | 0.727640i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −506.625 | − | 292.500i | −0.916139 | − | 0.528933i | ||||
\(554\) | 107.778 | + | 62.2254i | 0.194544 | + | 0.112320i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 37.0000 | + | 64.0859i | 0.0665468 | + | 0.115262i | ||||
\(557\) | −1086.12 | −1.94994 | −0.974969 | − | 0.222339i | \(-0.928631\pi\) | ||||
−0.974969 | + | 0.222339i | \(0.928631\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −576.000 | −1.03041 | ||||||||
\(560\) | 25.8819 | − | 96.5926i | 0.0462177 | − | 0.172487i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −249.415 | − | 144.000i | −0.443799 | − | 0.256228i | ||||
\(563\) | −311.127 | + | 538.888i | −0.552623 | + | 0.957172i | 0.445461 | + | 0.895301i | \(0.353040\pi\) |
−0.998084 | + | 0.0618704i | \(0.980293\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −184.413 | − | 49.4134i | −0.326395 | − | 0.0874574i | ||||
\(566\) | 45.2548i | 0.0799555i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 252.000i | − | 0.443662i | ||||||
\(569\) | 401.716 | − | 231.931i | 0.706004 | − | 0.407612i | −0.103576 | − | 0.994622i | \(-0.533028\pi\) |
0.809580 | + | 0.587010i | \(0.199695\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 461.500 | − | 799.341i | 0.808231 | − | 1.39990i | −0.105857 | − | 0.994381i | \(-0.533758\pi\) |
0.914088 | − | 0.405516i | \(-0.132908\pi\) | |||||||
\(572\) | 12.7279 | − | 22.0454i | 0.0222516 | − | 0.0385409i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −185.000 | − | 320.429i | −0.322300 | − | 0.558239i | ||||
\(575\) | − | 35.3553i | − | 0.0614875i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 247.000i | 0.428076i | 0.976825 | + | 0.214038i | \(0.0686617\pi\) | ||||
−0.976825 | + | 0.214038i | \(0.931338\pi\) | |||||||
\(578\) | −113.844 | − | 197.184i | −0.196962 | − | 0.341149i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −368.827 | + | 98.8269i | −0.635908 | + | 0.170391i | ||||
\(581\) | −251.073 | − | 144.957i | −0.432139 | − | 0.249496i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −88.3346 | + | 51.0000i | −0.151517 | + | 0.0874786i | ||||
\(584\) | − | 48.0833i | − | 0.0823344i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 246.000 | 0.419795 | ||||||||
\(587\) | −226.981 | − | 393.143i | −0.386680 | − | 0.669750i | 0.605321 | − | 0.795982i | \(-0.293045\pi\) |
−0.992001 | + | 0.126232i | \(0.959712\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −420.000 | + | 727.461i | −0.713073 | + | 1.23508i | ||||
\(590\) | 618.193 | − | 165.644i | 1.04778 | − | 0.280753i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 86.6025 | − | 50.0000i | 0.146288 | − | 0.0844595i | ||||
\(593\) | 4.24264 | 0.00715454 | 0.00357727 | − | 0.999994i | \(-0.498861\pi\) | ||||
0.00357727 | + | 0.999994i | \(0.498861\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 200.000 | + | 200.000i | 0.336134 | + | 0.336134i | ||||
\(596\) | −450.706 | + | 260.215i | −0.756218 | + | 0.436603i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15.5885 | − | 9.00000i | −0.0260677 | − | 0.0150502i | ||||
\(599\) | −194.734 | − | 112.430i | −0.325099 | − | 0.187696i | 0.328564 | − | 0.944482i | \(-0.393435\pi\) |
−0.653663 | + | 0.756786i | \(0.726769\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 368.000 | + | 637.395i | 0.612313 | + | 1.06056i | 0.990850 | + | 0.134971i | \(0.0430940\pi\) |
−0.378537 | + | 0.925586i | \(0.623573\pi\) | |||||||
\(602\) | 452.548 | 0.751741 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 218.000 | 0.360927 | ||||||||
\(605\) | 574.726 | + | 153.997i | 0.949960 | + | 0.254541i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −378.453 | − | 218.500i | −0.623481 | − | 0.359967i | 0.154742 | − | 0.987955i | \(-0.450545\pi\) |
−0.778223 | + | 0.627988i | \(0.783879\pi\) | |||||||
\(608\) | 59.3970 | − | 102.879i | 0.0976924 | − | 0.169208i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 662.522 | + | 177.522i | 1.08610 | + | 0.291020i | ||||
\(611\) | − | 203.647i | − | 0.333301i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 335.000i | 0.546493i | 0.961944 | + | 0.273246i | \(0.0880974\pi\) | ||||
−0.961944 | + | 0.273246i | \(0.911903\pi\) | |||||||
\(614\) | −595.226 | + | 343.654i | −0.969423 | + | 0.559697i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.0000 | + | 17.3205i | −0.0162338 | + | 0.0281177i | ||||
\(617\) | 127.986 | − | 221.679i | 0.207433 | − | 0.359285i | −0.743472 | − | 0.668767i | \(-0.766822\pi\) |
0.950905 | + | 0.309482i | \(0.100156\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 482.500 | + | 835.715i | 0.779483 | + | 1.35010i | 0.932240 | + | 0.361840i | \(0.117851\pi\) |
−0.152757 | + | 0.988264i | \(0.548815\pi\) | |||||||
\(620\) | −282.843 | + | 282.843i | −0.456198 | + | 0.456198i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 96.0000i | 0.154341i | ||||||||
\(623\) | 367.696 | + | 636.867i | 0.590201 | + | 1.02226i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 312.500 | − | 541.266i | 0.500000 | − | 0.866025i | ||||
\(626\) | 344.153 | + | 198.697i | 0.549766 | + | 0.317407i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −204.382 | + | 118.000i | −0.325449 | + | 0.187898i | ||||
\(629\) | 282.843i | 0.449670i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 275.000 | 0.435816 | 0.217908 | − | 0.975969i | \(-0.430077\pi\) | ||||
0.217908 | + | 0.975969i | \(0.430077\pi\) | |||||||
\(632\) | −165.463 | − | 286.590i | −0.261809 | − | 0.453466i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 368.000 | − | 637.395i | 0.580442 | − | 1.00535i | ||||
\(635\) | −38.6370 | + | 10.3528i | −0.0608457 | + | 0.0163036i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −187.061 | + | 108.000i | −0.293660 | + | 0.169545i | ||||
\(638\) | 76.3675 | 0.119698 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 40.0000 | − | 40.0000i | 0.0625000 | − | 0.0625000i | ||||
\(641\) | 421.312 | − | 243.245i | 0.657273 | − | 0.379477i | −0.133964 | − | 0.990986i | \(-0.542771\pi\) |
0.791237 | + | 0.611509i | \(0.209437\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −997.661 | − | 576.000i | −1.55157 | − | 0.895801i | −0.998014 | − | 0.0629907i | \(-0.979936\pi\) |
−0.553559 | − | 0.832810i | \(-0.686731\pi\) | |||||||
\(644\) | 12.2474 | + | 7.07107i | 0.0190178 | + | 0.0109799i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 168.000 | + | 290.985i | 0.260062 | + | 0.450440i | ||||
\(647\) | 691.550 | 1.06886 | 0.534428 | − | 0.845214i | \(-0.320527\pi\) | ||||
0.534428 | + | 0.845214i | \(0.320527\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −128.000 | −0.197227 | ||||||||
\(650\) | −159.099 | − | 275.568i | −0.244768 | − | 0.423950i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 351.606 | + | 203.000i | 0.539273 | + | 0.311350i | ||||
\(653\) | 175.362 | − | 303.737i | 0.268549 | − | 0.465140i | −0.699938 | − | 0.714203i | \(-0.746789\pi\) |
0.968487 | + | 0.249063i | \(0.0801226\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −175.692 | + | 655.692i | −0.268232 | + | 1.00106i | ||||
\(656\) | − | 209.304i | − | 0.319060i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 160.000i | 0.243161i | ||||||||
\(659\) | −431.110 | + | 248.902i | −0.654188 | + | 0.377696i | −0.790059 | − | 0.613031i | \(-0.789950\pi\) |
0.135871 | + | 0.990727i | \(0.456617\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 288.500 | − | 499.697i | 0.436460 | − | 0.755971i | −0.560954 | − | 0.827847i | \(-0.689565\pi\) |
0.997414 | + | 0.0718765i | \(0.0228987\pi\) | |||||||
\(662\) | −41.7193 | + | 72.2599i | −0.0630201 | + | 0.109154i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −82.0000 | − | 142.028i | −0.123494 | − | 0.213898i | ||||
\(665\) | 371.231 | + | 371.231i | 0.558242 | + | 0.558242i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 54.0000i | − | 0.0809595i | ||||||
\(668\) | 101.823 | + | 176.363i | 0.152430 | + | 0.264017i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −894.747 | + | 239.747i | −1.33544 | + | 0.357831i | ||||
\(671\) | −118.800 | − | 68.5894i | −0.177050 | − | 0.102220i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 423.486 | − | 244.500i | 0.629252 | − | 0.363299i | −0.151210 | − | 0.988502i | \(-0.548317\pi\) |
0.780462 | + | 0.625203i | \(0.214984\pi\) | |||||||
\(674\) | − | 77.7817i | − | 0.115403i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 176.000 | 0.260355 | ||||||||
\(677\) | 299.813 | + | 519.292i | 0.442856 | + | 0.767048i | 0.997900 | − | 0.0647722i | \(-0.0206321\pi\) |
−0.555044 | + | 0.831821i | \(0.687299\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −102.500 | + | 177.535i | −0.150957 | + | 0.261466i | ||||
\(680\) | 41.4110 | + | 154.548i | 0.0608986 | + | 0.227277i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 69.2820 | − | 40.0000i | 0.101587 | − | 0.0586510i | ||||
\(683\) | −236.174 | −0.345789 | −0.172894 | − | 0.984940i | \(-0.555312\pi\) | ||||
−0.172894 | + | 0.984940i | \(0.555312\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −945.000 | + | 945.000i | −1.37956 | + | 1.37956i | ||||
\(686\) | 447.032 | − | 258.094i | 0.651650 | − | 0.376230i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 221.703 | + | 128.000i | 0.322242 | + | 0.186047i | ||||
\(689\) | 562.158 | + | 324.562i | 0.815904 | + | 0.471062i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −320.000 | − | 554.256i | −0.463097 | − | 0.802107i | 0.536016 | − | 0.844208i | \(-0.319928\pi\) |
−0.999113 | + | 0.0421001i | \(0.986595\pi\) | |||||||
\(692\) | 22.6274 | 0.0326986 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −846.000 | −1.21902 | ||||||||
\(695\) | −178.696 | − | 47.8815i | −0.257117 | − | 0.0688943i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 512.687 | + | 296.000i | 0.735562 | + | 0.424677i | ||||
\(698\) | −310.420 | + | 537.663i | −0.444728 | + | 0.770291i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 125.000 | + | 216.506i | 0.178571 | + | 0.309295i | ||||
\(701\) | 1093.19i | 1.55947i | 0.626111 | + | 0.779734i | \(0.284646\pi\) | ||||
−0.626111 | + | 0.779734i | \(0.715354\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 525.000i | 0.746799i | ||||||||
\(704\) | −9.79796 | + | 5.65685i | −0.0139176 | + | 0.00803530i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 368.000 | − | 637.395i | 0.521246 | − | 0.902825i | ||||
\(707\) | −226.274 | + | 391.918i | −0.320048 | + | 0.554340i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 244.500 | + | 423.486i | 0.344852 | + | 0.597301i | 0.985327 | − | 0.170678i | \(-0.0545958\pi\) |
−0.640475 | + | 0.767979i | \(0.721262\pi\) | |||||||
\(710\) | 445.477 | + | 445.477i | 0.627433 | + | 0.627433i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 416.000i | 0.584270i | ||||||||
\(713\) | −28.2843 | − | 48.9898i | −0.0396694 | − | 0.0687094i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.4711 | + | 61.4711i | 0.0230366 | + | 0.0859736i | ||||
\(716\) | −218.005 | − | 125.865i | −0.304476 | − | 0.175789i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −67.5500 | + | 39.0000i | −0.0940808 | + | 0.0543175i | ||||
\(719\) | 620.840i | 0.863477i | 0.901999 | + | 0.431738i | \(0.142100\pi\) | ||||
−0.901999 | + | 0.431738i | \(0.857900\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 65.0000 | 0.0901526 | ||||||||
\(722\) | 56.5685 | + | 97.9796i | 0.0783498 | + | 0.135706i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 127.000 | − | 219.970i | 0.175414 | − | 0.303827i | ||||
\(725\) | 477.297 | − | 826.703i | 0.658341 | − | 1.14028i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 935.307 | − | 540.000i | 1.28653 | − | 0.742779i | 0.308496 | − | 0.951225i | \(-0.400174\pi\) |
0.978034 | + | 0.208447i | \(0.0668409\pi\) | |||||||
\(728\) | 127.279 | 0.174834 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 85.0000 | + | 85.0000i | 0.116438 | + | 0.116438i | ||||
\(731\) | −627.069 | + | 362.039i | −0.857824 | + | 0.495265i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 214.774 | + | 124.000i | 0.293007 | + | 0.169168i | 0.639297 | − | 0.768960i | \(-0.279225\pi\) |
−0.346290 | + | 0.938128i | \(0.612559\pi\) | |||||||
\(734\) | 721.375 | + | 416.486i | 0.982799 | + | 0.567419i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | + | 6.92820i | 0.00543478 | + | 0.00941332i | ||||
\(737\) | 185.262 | 0.251373 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 848.000 | 1.14750 | 0.573748 | − | 0.819032i | \(-0.305489\pi\) | ||||
0.573748 | + | 0.819032i | \(0.305489\pi\) | |||||||
\(740\) | −64.7048 | + | 241.481i | −0.0874389 | + | 0.326326i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −441.673 | − | 255.000i | −0.595247 | − | 0.343666i | ||||
\(743\) | 16.9706 | − | 29.3939i | 0.0228406 | − | 0.0395611i | −0.854379 | − | 0.519650i | \(-0.826062\pi\) |
0.877220 | + | 0.480089i | \(0.159396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 336.743 | − | 1256.74i | 0.452005 | − | 1.68690i | ||||
\(746\) | 12.7279i | 0.0170616i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 32.0000i | − | 0.0427807i | ||||||
\(749\) | 532.764 | − | 307.591i | 0.711300 | − | 0.410669i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 66.5000 | − | 115.181i | 0.0885486 | − | 0.153371i | −0.818349 | − | 0.574721i | \(-0.805110\pi\) |
0.906898 | + | 0.421351i | \(0.138444\pi\) | |||||||
\(752\) | −45.2548 | + | 78.3837i | −0.0601793 | + | 0.104234i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −243.000 | − | 420.888i | −0.322281 | − | 0.558207i | ||||
\(755\) | −385.373 | + | 385.373i | −0.510428 | + | 0.510428i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1271.00i | − | 1.67900i | −0.543363 | − | 0.839498i | \(-0.682849\pi\) | ||
0.543363 | − | 0.839498i | \(-0.317151\pi\) | |||||||
\(758\) | 111.016 | + | 192.285i | 0.146459 | + | 0.253674i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 76.8653 | + | 286.865i | 0.101139 | + | 0.377454i | ||||
\(761\) | −466.628 | − | 269.408i | −0.613177 | − | 0.354018i | 0.161031 | − | 0.986949i | \(-0.448518\pi\) |
−0.774208 | + | 0.632931i | \(0.781852\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.6410 | + | 20.0000i | −0.0454011 | + | 0.0262123i | ||||
\(764\) | 203.647i | 0.266553i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −400.000 | −0.522193 | ||||||||
\(767\) | 407.294 | + | 705.453i | 0.531022 | + | 0.919756i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.5000 | − | 70.1481i | 0.0526658 | − | 0.0912198i | −0.838491 | − | 0.544916i | \(-0.816562\pi\) |
0.891156 | + | 0.453696i | \(0.149895\pi\) | |||||||
\(770\) | −12.9410 | − | 48.2963i | −0.0168064 | − | 0.0627225i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −469.386 | + | 271.000i | −0.608013 | + | 0.351036i | ||||
\(773\) | −445.477 | −0.576297 | −0.288148 | − | 0.957586i | \(-0.593040\pi\) | ||||
−0.288148 | + | 0.957586i | \(0.593040\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1000.00i | − | 1.29032i | ||||||
\(776\) | −100.429 | + | 57.9828i | −0.129419 | + | 0.0747200i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 734.390 | + | 424.000i | 0.943945 | + | 0.544987i | ||||
\(779\) | 951.627 | + | 549.422i | 1.22160 | + | 0.705291i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −63.0000 | − | 109.119i | −0.0806658 | − | 0.139717i | ||||
\(782\) | −22.6274 | −0.0289353 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 96.0000 | 0.122449 | ||||||||
\(785\) | 152.703 | − | 569.896i | 0.194526 | − | 0.725982i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 342.080 | + | 197.500i | 0.434663 | + | 0.250953i | 0.701331 | − | 0.712835i | \(-0.252589\pi\) |
−0.266668 | + | 0.963788i | \(0.585923\pi\) | |||||||
\(788\) | 316.784 | − | 548.686i | 0.402010 | − | 0.696302i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 799.125 | + | 214.125i | 1.01155 | + | 0.271044i | ||||
\(791\) | 190.919i | 0.241364i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 873.000i | 1.10088i | ||||||||
\(794\) | 362.524 | − | 209.304i | 0.456580 | − | 0.263607i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −147.000 | + | 254.611i | −0.184673 | + | 0.319864i | ||||
\(797\) | 537.401 | − | 930.806i | 0.674280 | − | 1.16789i | −0.302399 | − | 0.953181i | \(-0.597787\pi\) |
0.976679 | − | 0.214706i | \(-0.0688792\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −128.000 | − | 221.703i | −0.160200 | − | 0.277475i | ||||
\(800\) | 141.421i | 0.176777i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 550.000i | 0.685786i | ||||||||
\(803\) | −12.0208 | − | 20.8207i | −0.0149699 | − | 0.0259286i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −34.1506 | + | 9.15064i | −0.0424231 | + | 0.0113672i | ||||
\(806\) | −440.908 | − | 254.558i | −0.547032 | − | 0.315829i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −221.703 | + | 128.000i | −0.274384 | + | 0.158416i | ||||
\(809\) | − | 1255.82i | − | 1.55231i | −0.630540 | − | 0.776157i | \(-0.717167\pi\) | ||
0.630540 | − | 0.776157i | \(-0.282833\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −752.000 | −0.927250 | −0.463625 | − | 0.886031i | \(-0.653452\pi\) | ||||
−0.463625 | + | 0.886031i | \(0.653452\pi\) | |||||||
\(812\) | 190.919 | + | 330.681i | 0.235122 | + | 0.407243i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 25.0000 | − | 43.3013i | 0.0307125 | − | 0.0531957i | ||||
\(815\) | −980.415 | + | 262.701i | −1.20296 | + | 0.322333i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1163.94 | + | 672.000i | −1.42465 | + | 0.822521i | ||||
\(818\) | −205.061 | −0.250686 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 370.000 | + | 370.000i | 0.451220 | + | 0.451220i | ||||
\(821\) | 431.110 | − | 248.902i | 0.525104 | − | 0.303169i | −0.213917 | − | 0.976852i | \(-0.568622\pi\) |
0.739020 | + | 0.673683i | \(0.235289\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −459.859 | − | 265.500i | −0.558760 | − | 0.322600i | 0.193888 | − | 0.981024i | \(-0.437890\pi\) |
−0.752648 | + | 0.658423i | \(0.771224\pi\) | |||||||
\(824\) | 31.8434 | + | 18.3848i | 0.0386449 | + | 0.0223116i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −320.000 | − | 554.256i | −0.387409 | − | 0.671012i | ||||
\(827\) | 350.725 | 0.424093 | 0.212047 | − | 0.977260i | \(-0.431987\pi\) | ||||
0.212047 | + | 0.977260i | \(0.431987\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −705.000 | −0.850422 | −0.425211 | − | 0.905094i | \(-0.639800\pi\) | ||||
−0.425211 | + | 0.905094i | \(0.639800\pi\) | |||||||
\(830\) | 396.030 | + | 106.116i | 0.477144 | + | 0.127850i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 62.3538 | + | 36.0000i | 0.0749445 | + | 0.0432692i | ||||
\(833\) | −135.765 | + | 235.151i | −0.162983 | + | 0.282294i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −491.769 | − | 131.769i | −0.588945 | − | 0.157807i | ||||
\(836\) | − | 59.3970i | − | 0.0710490i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 992.000i | − | 1.18377i | ||||||
\(839\) | −1401.11 | + | 808.930i | −1.66997 | + | 0.964160i | −0.702326 | + | 0.711855i | \(0.747855\pi\) |
−0.967648 | + | 0.252304i | \(0.918812\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 308.500 | − | 534.338i | 0.366825 | − | 0.635360i | ||||
\(842\) | 357.089 | − | 618.496i | 0.424096 | − | 0.734556i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −141.000 | − | 244.219i | −0.167062 | − | 0.289359i | ||||
\(845\) | −311.127 | + | 311.127i | −0.368198 | + | 0.368198i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 595.000i | − | 0.702479i | ||||||
\(848\) | −144.250 | − | 249.848i | −0.170106 | − | 0.294632i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −346.410 | − | 200.000i | −0.407541 | − | 0.235294i | ||||
\(851\) | −30.6186 | − | 17.6777i | −0.0359796 | − | 0.0207728i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1419.42 | − | 819.500i | 1.66403 | − | 0.960727i | 0.693266 | − | 0.720682i | \(-0.256171\pi\) |
0.970762 | − | 0.240045i | \(-0.0771622\pi\) | |||||||
\(854\) | − | 685.894i | − | 0.803154i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 348.000 | 0.406542 | ||||||||
\(857\) | −494.268 | − | 856.097i | −0.576742 | − | 0.998946i | −0.995850 | − | 0.0910097i | \(-0.970991\pi\) |
0.419108 | − | 0.907936i | \(-0.362343\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −177.500 | + | 307.439i | −0.206636 | + | 0.357903i | −0.950653 | − | 0.310257i | \(-0.899585\pi\) |
0.744017 | + | 0.668161i | \(0.232918\pi\) | |||||||
\(860\) | −618.193 | + | 165.644i | −0.718829 | + | 0.192610i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 53.6936 | − | 31.0000i | 0.0622895 | − | 0.0359629i | ||||
\(863\) | 1459.47 | 1.69116 | 0.845578 | − | 0.533851i | \(-0.179256\pi\) | ||||
0.845578 | + | 0.533851i | \(0.179256\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40.0000 | + | 40.0000i | −0.0462428 | + | 0.0462428i | ||||
\(866\) | −39.1918 | + | 22.6274i | −0.0452562 | + | 0.0261287i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 346.410 | + | 200.000i | 0.399090 | + | 0.230415i | ||||
\(869\) | −143.295 | − | 82.7315i | −0.164897 | − | 0.0952031i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −589.500 | − | 1021.04i | −0.676808 | − | 1.17227i | ||||
\(872\) | −22.6274 | −0.0259489 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −42.0000 | −0.0480549 | ||||||||
\(875\) | −603.704 | − | 161.762i | −0.689947 | − | 0.184871i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 977.743 | + | 564.500i | 1.11487 | + | 0.643672i | 0.940087 | − | 0.340935i | \(-0.110744\pi\) |
0.174785 | + | 0.984607i | \(0.444077\pi\) | |||||||
\(878\) | −356.382 | + | 617.271i | −0.405902 | + | 0.703043i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.32051 | − | 27.3205i | 0.00831876 | − | 0.0310460i | ||||
\(881\) | 165.463i | 0.187813i | 0.995581 | + | 0.0939063i | \(0.0299354\pi\) | ||||
−0.995581 | + | 0.0939063i | \(0.970065\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1227.00i | − | 1.38958i | −0.719212 | − | 0.694790i | \(-0.755497\pi\) | ||
0.719212 | − | 0.694790i | \(-0.244503\pi\) | |||||||
\(884\) | −176.363 | + | 101.823i | −0.199506 | + | 0.115185i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −168.000 | + | 290.985i | −0.189616 | + | 0.328425i | ||||
\(887\) | 118.794 | − | 205.757i | 0.133928 | − | 0.231970i | −0.791260 | − | 0.611480i | \(-0.790574\pi\) |
0.925187 | + | 0.379511i | \(0.123908\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | + | 34.6410i | 0.0224972 | + | 0.0389663i | ||||
\(890\) | −735.391 | − | 735.391i | −0.826282 | − | 0.826282i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.0000i | 0.0179372i | ||||||||
\(893\) | −237.588 | − | 411.514i | −0.266056 | − | 0.460822i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 607.881 | − | 162.881i | 0.679197 | − | 0.181990i | ||||
\(896\) | −48.9898 | − | 28.2843i | −0.0546761 | − | 0.0315673i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −83.1384 | + | 48.0000i | −0.0925818 | + | 0.0534521i | ||||
\(899\) | − | 1527.35i | − | 1.69894i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 816.000 | 0.905660 | ||||||||
\(902\) | −52.3259 | − | 90.6311i | −0.0580110 | − | 0.100478i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −54.0000 | + | 93.5307i | −0.0597345 | + | 0.103463i | ||||
\(905\) | 164.350 | + | 613.363i | 0.181602 | + | 0.677749i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 870.356 | − | 502.500i | 0.959598 | − | 0.554024i | 0.0635488 | − | 0.997979i | \(-0.479758\pi\) |
0.896049 | + | 0.443954i | \(0.146425\pi\) | |||||||
\(908\) | −138.593 | −0.152635 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −225.000 | + | 225.000i | −0.247253 | + | 0.247253i | ||||
\(911\) | 676.059 | − | 390.323i | 0.742107 | − | 0.428455i | −0.0807281 | − | 0.996736i | \(-0.525725\pi\) |
0.822835 | + | 0.568281i | \(0.192391\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −71.0141 | − | 41.0000i | −0.0777810 | − | 0.0449069i | ||||
\(914\) | −921.008 | − | 531.744i | −1.00767 | − | 0.581777i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.00000 | + | 13.8564i | 0.00873362 | + | 0.0151271i | ||||
\(917\) | 678.823 | 0.740264 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 600.000 | 0.652884 | 0.326442 | − | 0.945217i | \(-0.394150\pi\) | ||||
0.326442 | + | 0.945217i | \(0.394150\pi\) | |||||||
\(920\) | −19.3185 | − | 5.17638i | −0.0209984 | − | 0.00562650i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 748.246 | + | 432.000i | 0.811547 | + | 0.468547i | ||||
\(923\) | −400.930 | + | 694.430i | −0.434377 | + | 0.752362i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −312.500 | − | 541.266i | −0.337838 | − | 0.585152i | ||||
\(926\) | 844.285i | 0.911755i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 216.000i | 0.232759i | ||||||||
\(929\) | −1091.25 | + | 630.032i | −1.17465 | + | 0.678183i | −0.954770 | − | 0.297344i | \(-0.903899\pi\) |
−0.219877 | + | 0.975528i | \(0.570566\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −252.000 | + | 436.477i | −0.270677 | + | 0.468826i | ||||
\(932\) | −316.784 | + | 548.686i | −0.339897 | + | 0.588719i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −600.000 | − | 1039.23i | −0.642398 | − | 1.11267i | ||||
\(935\) | 56.5685 | + | 56.5685i | 0.0605011 | + | 0.0605011i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1465.00i | − | 1.56350i | −0.623592 | − | 0.781750i | \(-0.714327\pi\) | ||
0.623592 | − | 0.781750i | \(-0.285673\pi\) | |||||||
\(938\) | 463.155 | + | 802.208i | 0.493769 | + | 0.855232i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −58.5641 | − | 218.564i | −0.0623022 | − | 0.232515i | ||||
\(941\) | 221.679 | + | 127.986i | 0.235578 | + | 0.136011i | 0.613143 | − | 0.789972i | \(-0.289905\pi\) |
−0.377565 | + | 0.925983i | \(0.623238\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −64.0859 | + | 37.0000i | −0.0679596 | + | 0.0392365i | ||||
\(944\) | − | 362.039i | − | 0.383516i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 128.000 | 0.135307 | ||||||||
\(947\) | 203.647 | + | 352.727i | 0.215044 | + | 0.372467i | 0.953286 | − | 0.302069i | \(-0.0976771\pi\) |
−0.738242 | + | 0.674536i | \(0.764344\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −76.5000 | + | 132.502i | −0.0806112 | + | 0.139623i | ||||
\(950\) | −642.991 | − | 371.231i | −0.676833 | − | 0.390770i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 138.564 | − | 80.0000i | 0.145550 | − | 0.0840336i | ||||
\(953\) | −497.803 | −0.522354 | −0.261177 | − | 0.965291i | \(-0.584111\pi\) | ||||
−0.261177 | + | 0.965291i | \(0.584111\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −360.000 | − | 360.000i | −0.376963 | − | 0.376963i | ||||
\(956\) | 355.176 | − | 205.061i | 0.371523 | − | 0.214499i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −206.114 | − | 119.000i | −0.215150 | − | 0.124217i | ||||
\(959\) | 1157.38 | + | 668.216i | 1.20687 | + | 0.696784i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −319.500 | − | 553.390i | −0.332466 | − | 0.575848i | ||||
\(962\) | −318.198 | −0.330767 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 158.000 | 0.163900 | ||||||||
\(965\) | 350.700 | − | 1308.83i | 0.363419 | − | 1.35630i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −425.218 | − | 245.500i | −0.439730 | − | 0.253878i | 0.263753 | − | 0.964590i | \(-0.415039\pi\) |
−0.703483 | + | 0.710712i | \(0.748373\pi\) | |||||||
\(968\) | 168.291 | − | 291.489i | 0.173855 | − | 0.301125i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 75.0352 | − | 280.035i | 0.0773559 | − | 0.288696i | ||||
\(971\) | − | 509.117i | − | 0.524322i | −0.965024 | − | 0.262161i | \(-0.915565\pi\) | ||
0.965024 | − | 0.262161i | \(-0.0844352\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 185.000i | 0.190134i | ||||||||
\(974\) | −620.946 | + | 358.503i | −0.637521 | + | 0.368073i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 194.000 | − | 336.018i | 0.198770 | − | 0.344281i | ||||
\(977\) | −235.467 | + | 407.840i | −0.241010 | + | 0.417441i | −0.961002 | − | 0.276541i | \(-0.910812\pi\) |
0.719992 | + | 0.693982i | \(0.244145\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 104.000 | + | 180.133i | 0.106231 | + | 0.183997i | ||||
\(980\) | −169.706 | + | 169.706i | −0.173169 | + | 0.173169i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 606.000i | − | 0.617108i | ||||||
\(983\) | −300.520 | − | 520.517i | −0.305718 | − | 0.529518i | 0.671703 | − | 0.740820i | \(-0.265563\pi\) |
−0.977421 | + | 0.211302i | \(0.932230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 409.948 | + | 1529.95i | 0.416191 | + | 1.55325i | ||||
\(986\) | −529.090 | − | 305.470i | −0.536602 | − | 0.309807i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −327.358 | + | 189.000i | −0.331334 | + | 0.191296i | ||||
\(989\) | − | 90.5097i | − | 0.0915163i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −755.000 | −0.761857 | −0.380928 | − | 0.924605i | \(-0.624396\pi\) | ||||
−0.380928 | + | 0.924605i | \(0.624396\pi\) | |||||||
\(992\) | 113.137 | + | 195.959i | 0.114049 | + | 0.197539i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 315.000 | − | 545.596i | 0.316901 | − | 0.548889i | ||||
\(995\) | −190.232 | − | 709.955i | −0.191188 | − | 0.713523i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.7846 | + | 12.0000i | −0.0208472 | + | 0.0120361i | −0.510387 | − | 0.859945i | \(-0.670498\pi\) |
0.489540 | + | 0.871981i | \(0.337165\pi\) | |||||||
\(998\) | −1230.37 | −1.23283 | ||||||||
\(999\) | 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 | 810.3.j.e.539.3 | 8 | ||
3.2 | odd | 2 | inner | 810.3.j.e.539.2 | 8 | ||
5.4 | even | 2 | inner | 810.3.j.e.539.1 | 8 | ||
9.2 | odd | 6 | inner | 810.3.j.e.269.1 | 8 | ||
9.4 | even | 3 | 270.3.b.c.269.2 | yes | 4 | ||
9.5 | odd | 6 | 270.3.b.c.269.3 | yes | 4 | ||
9.7 | even | 3 | inner | 810.3.j.e.269.4 | 8 | ||
15.14 | odd | 2 | inner | 810.3.j.e.539.4 | 8 | ||
36.23 | even | 6 | 2160.3.c.i.1889.3 | 4 | |||
36.31 | odd | 6 | 2160.3.c.i.1889.2 | 4 | |||
45.4 | even | 6 | 270.3.b.c.269.4 | yes | 4 | ||
45.13 | odd | 12 | 1350.3.d.f.701.2 | 2 | |||
45.14 | odd | 6 | 270.3.b.c.269.1 | ✓ | 4 | ||
45.22 | odd | 12 | 1350.3.d.g.701.1 | 2 | |||
45.23 | even | 12 | 1350.3.d.f.701.1 | 2 | |||
45.29 | odd | 6 | inner | 810.3.j.e.269.3 | 8 | ||
45.32 | even | 12 | 1350.3.d.g.701.2 | 2 | |||
45.34 | even | 6 | inner | 810.3.j.e.269.2 | 8 | ||
180.59 | even | 6 | 2160.3.c.i.1889.1 | 4 | |||
180.139 | odd | 6 | 2160.3.c.i.1889.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.3.b.c.269.1 | ✓ | 4 | 45.14 | odd | 6 | ||
270.3.b.c.269.2 | yes | 4 | 9.4 | even | 3 | ||
270.3.b.c.269.3 | yes | 4 | 9.5 | odd | 6 | ||
270.3.b.c.269.4 | yes | 4 | 45.4 | even | 6 | ||
810.3.j.e.269.1 | 8 | 9.2 | odd | 6 | inner | ||
810.3.j.e.269.2 | 8 | 45.34 | even | 6 | inner | ||
810.3.j.e.269.3 | 8 | 45.29 | odd | 6 | inner | ||
810.3.j.e.269.4 | 8 | 9.7 | even | 3 | inner | ||
810.3.j.e.539.1 | 8 | 5.4 | even | 2 | inner | ||
810.3.j.e.539.2 | 8 | 3.2 | odd | 2 | inner | ||
810.3.j.e.539.3 | 8 | 1.1 | even | 1 | trivial | ||
810.3.j.e.539.4 | 8 | 15.14 | odd | 2 | inner | ||
1350.3.d.f.701.1 | 2 | 45.23 | even | 12 | |||
1350.3.d.f.701.2 | 2 | 45.13 | odd | 12 | |||
1350.3.d.g.701.1 | 2 | 45.22 | odd | 12 | |||
1350.3.d.g.701.2 | 2 | 45.32 | even | 12 | |||
2160.3.c.i.1889.1 | 4 | 180.59 | even | 6 | |||
2160.3.c.i.1889.2 | 4 | 36.31 | odd | 6 | |||
2160.3.c.i.1889.3 | 4 | 36.23 | even | 6 | |||
2160.3.c.i.1889.4 | 4 | 180.139 | odd | 6 |