Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3120,2,Mod(1249,3120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3120.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3120.l (of order \(2\), degree \(1\), 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: | \(24.9133254306\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.57815240704.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 89x^{4} - 170x^{3} + 162x^{2} - 72x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1560) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.7 | ||
Root | \(0.353624 + 0.353624i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3120.1249 |
Dual form | 3120.2.l.n.1249.3 |
$q$-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 \(\left(\mathbb{Z}/3120\mathbb{Z}\right)^\times\).
\(n\) | \(1951\) | \(2081\) | \(2341\) | \(2497\) | \(2641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.353624 | − | 2.20793i | −0.158145 | − | 0.987416i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.09417i | − | 1.16949i | −0.811218 | − | 0.584744i | \(-0.801195\pi\) | ||
0.811218 | − | 0.584744i | \(-0.198805\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.51003 | −1.66134 | −0.830669 | − | 0.556767i | \(-0.812042\pi\) | ||||
−0.830669 | + | 0.556767i | \(0.812042\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.20793 | − | 0.353624i | 0.570085 | − | 0.0913053i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.21728i | 1.50791i | 0.656925 | + | 0.753956i | \(0.271857\pi\) | ||||
−0.656925 | + | 0.753956i | \(0.728143\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.09417 | 0.675204 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.21728i | − | 0.879364i | −0.898154 | − | 0.439682i | \(-0.855091\pi\) | ||
0.898154 | − | 0.439682i | \(-0.144909\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.74990 | + | 1.56155i | −0.949980 | + | 0.312311i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.70861 | 0.317281 | 0.158640 | − | 0.987336i | \(-0.449289\pi\) | ||||
0.158640 | + | 0.987336i | \(0.449289\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 5.51003i | − | 0.959173i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.83172 | + | 1.09417i | −1.15477 | + | 0.184949i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.02893i | 0.662352i | 0.943569 | + | 0.331176i | \(0.107445\pi\) | ||||
−0.943569 | + | 0.331176i | \(0.892555\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.198578 | 0.0310127 | 0.0155064 | − | 0.999880i | \(-0.495064\pi\) | ||||
0.0155064 | + | 0.999880i | \(0.495064\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.70861i | 0.870555i | 0.900296 | + | 0.435277i | \(0.143350\pi\) | ||||
−0.900296 | + | 0.435277i | \(0.856650\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.353624 | + | 2.20793i | 0.0527151 | + | 0.329139i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.41586i | − | 0.935849i | −0.883768 | − | 0.467925i | \(-0.845002\pi\) | ||
0.883768 | − | 0.467925i | \(-0.154998\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.57391 | −0.367702 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.21728 | −0.870593 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.02893i | 0.553416i | 0.960954 | + | 0.276708i | \(0.0892435\pi\) | ||||
−0.960954 | + | 0.276708i | \(0.910756\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.94848 | + | 12.1658i | 0.262733 | + | 1.64043i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.53896 | −0.981489 | −0.490745 | − | 0.871303i | \(-0.663275\pi\) | ||||
−0.490745 | + | 0.871303i | \(0.663275\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.9259 | 1.52695 | 0.763477 | − | 0.645835i | \(-0.223491\pi\) | ||||
0.763477 | + | 0.645835i | \(0.223491\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.09417i | 0.389829i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.20793 | − | 0.353624i | 0.273860 | − | 0.0438616i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.83172i | 0.590288i | 0.955453 | + | 0.295144i | \(0.0953676\pi\) | ||||
−0.955453 | + | 0.295144i | \(0.904632\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.21728 | 0.507701 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.98977 | −0.948211 | −0.474106 | − | 0.880468i | \(-0.657228\pi\) | ||||
−0.474106 | + | 0.880468i | \(0.657228\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.31145i | 1.08982i | 0.838494 | + | 0.544912i | \(0.183437\pi\) | ||||
−0.838494 | + | 0.544912i | \(0.816563\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.56155 | − | 4.74990i | −0.180313 | − | 0.548471i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17.0490i | 1.94291i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.51139 | 0.957607 | 0.478803 | − | 0.877922i | \(-0.341071\pi\) | ||||
0.478803 | + | 0.877922i | \(0.341071\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.7926i | 1.62369i | 0.583871 | + | 0.811847i | \(0.301538\pi\) | ||||
−0.583871 | + | 0.811847i | \(0.698462\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.7273 | − | 2.19858i | 1.48894 | − | 0.238469i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.70861i | 0.183182i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.40699 | 0.997139 | 0.498569 | − | 0.866850i | \(-0.333859\pi\) | ||||
0.498569 | + | 0.866850i | \(0.333859\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.09417 | 0.324358 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.3026i | − | 1.45221i | −0.687585 | − | 0.726104i | \(-0.741329\pi\) | ||
0.687585 | − | 0.726104i | \(-0.258671\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.51003 | 0.553779 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.72595 | −0.669257 | −0.334628 | − | 0.942350i | \(-0.608611\pi\) | ||||
−0.334628 | + | 0.942350i | \(0.608611\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.0779i | 1.68274i | 0.540461 | + | 0.841369i | \(0.318250\pi\) | ||||
−0.540461 | + | 0.841369i | \(0.681750\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.09417 | − | 6.83172i | −0.106780 | − | 0.666707i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.63450i | 0.738055i | 0.929418 | + | 0.369027i | \(0.120309\pi\) | ||||
−0.929418 | + | 0.369027i | \(0.879691\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.02006 | 0.480835 | 0.240417 | − | 0.970670i | \(-0.422716\pi\) | ||||
0.240417 | + | 0.970670i | \(0.422716\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.02893 | −0.382409 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.6229i | 1.56375i | 0.623434 | + | 0.781876i | \(0.285737\pi\) | ||||
−0.623434 | + | 0.781876i | \(0.714263\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.31145 | + | 1.49133i | −0.868297 | + | 0.139067i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 1.00000i | − | 0.0924500i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.2373 | 1.76348 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.3604 | 1.76004 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.198578i | 0.0179052i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.12748 | + | 9.93524i | 0.458615 | + | 0.888635i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.87689i | − | 0.255283i | −0.991820 | − | 0.127642i | \(-0.959259\pi\) | ||
0.991820 | − | 0.127642i | \(-0.0407407\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.70861 | −0.502615 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.5199 | 1.44335 | 0.721674 | − | 0.692233i | \(-0.243373\pi\) | ||||
0.721674 | + | 0.692233i | \(0.243373\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.20793 | + | 0.353624i | −0.190028 | + | 0.0304351i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 12.8504i | − | 1.09789i | −0.835860 | − | 0.548943i | \(-0.815031\pi\) | ||
0.835860 | − | 0.548943i | \(-0.184969\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.0490 | −1.44608 | −0.723038 | − | 0.690808i | \(-0.757255\pi\) | ||||
−0.723038 | + | 0.690808i | \(0.757255\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.41586 | 0.540313 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 5.51003i | − | 0.460772i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.604205 | − | 3.77249i | −0.0501765 | − | 0.313288i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 2.57391i | − | 0.212293i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.5679 | −1.60306 | −0.801532 | − | 0.597952i | \(-0.795981\pi\) | ||||
−0.801532 | + | 0.597952i | \(0.795981\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.22887 | 0.751035 | 0.375518 | − | 0.926815i | \(-0.377465\pi\) | ||||
0.375518 | + | 0.926815i | \(0.377465\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.21728i | − | 0.502637i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.89423i | 0.310794i | 0.987852 | + | 0.155397i | \(0.0496656\pi\) | ||||
−0.987852 | + | 0.155397i | \(0.950334\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.02893 | −0.319515 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.0490 | −1.02840 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.237741i | 0.0186213i | 0.999957 | + | 0.00931067i | \(0.00296372\pi\) | ||||
−0.999957 | + | 0.00931067i | \(0.997036\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.1658 | + | 1.94848i | −0.947103 | + | 0.151689i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 11.8304i | − | 0.915460i | −0.889091 | − | 0.457730i | \(-0.848663\pi\) | ||
0.889091 | − | 0.457730i | \(-0.151337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.6634i | 0.886754i | 0.896335 | + | 0.443377i | \(0.146220\pi\) | ||||
−0.896335 | + | 0.443377i | \(0.853780\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.83172 | + | 14.6970i | 0.365243 | + | 1.11099i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 7.53896i | − | 0.566663i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.5403 | −0.937308 | −0.468654 | − | 0.883382i | \(-0.655261\pi\) | ||||
−0.468654 | + | 0.883382i | \(0.655261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.44343 | −0.404607 | −0.202303 | − | 0.979323i | \(-0.564843\pi\) | ||||
−0.202303 | + | 0.979323i | \(0.564843\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.9259i | 0.881587i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.89560 | − | 1.42473i | 0.654017 | − | 0.104748i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 34.2574i | − | 2.50515i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.09417 | −0.225068 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.22887 | −0.378348 | −0.189174 | − | 0.981944i | \(-0.560581\pi\) | ||||
−0.189174 | + | 0.981944i | \(0.560581\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.5287i | 1.26175i | 0.775886 | + | 0.630873i | \(0.217303\pi\) | ||||
−0.775886 | + | 0.630873i | \(0.782697\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.353624 | + | 2.20793i | 0.0253235 | + | 0.158113i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.4764i | 1.60138i | 0.599079 | + | 0.800690i | \(0.295534\pi\) | ||||
−0.599079 | + | 0.800690i | \(0.704466\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.9143 | −1.19902 | −0.599511 | − | 0.800366i | \(-0.704638\pi\) | ||||
−0.599511 | + | 0.800366i | \(0.704638\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.83172 | −0.340803 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 5.28674i | − | 0.371056i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0702221 | − | 0.438447i | −0.00490452 | − | 0.0306225i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.21728i | 0.293121i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.8391 | 0.815037 | 0.407518 | − | 0.913197i | \(-0.366394\pi\) | ||||
0.407518 | + | 0.913197i | \(0.366394\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 7.98977i | − | 0.547450i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.6042 | − | 2.01870i | 0.859600 | − | 0.137674i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.31145 | −0.629210 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.21728 | −0.418219 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.48246i | − | 0.300168i | −0.988673 | − | 0.150084i | \(-0.952046\pi\) | ||
0.988673 | − | 0.150084i | \(-0.0479544\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.74990 | − | 1.56155i | 0.316660 | − | 0.104104i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.35799i | − | 0.421995i | −0.977487 | − | 0.210997i | \(-0.932329\pi\) | ||
0.977487 | − | 0.210997i | \(-0.0676712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.45502 | −0.426560 | −0.213280 | − | 0.976991i | \(-0.568415\pi\) | ||||
−0.213280 | + | 0.976991i | \(0.568415\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.0490 | −1.12174 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6.40290i | − | 0.419468i | −0.977758 | − | 0.209734i | \(-0.932740\pi\) | ||
0.977758 | − | 0.209734i | \(-0.0672598\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.1658 | + | 2.26880i | −0.924072 | + | 0.148000i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.51139i | 0.552874i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.55793 | −0.100774 | −0.0503872 | − | 0.998730i | \(-0.516046\pi\) | ||||
−0.0503872 | + | 0.998730i | \(0.516046\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.1911 | −0.914127 | −0.457064 | − | 0.889434i | \(-0.651099\pi\) | ||||
−0.457064 | + | 0.889434i | \(0.651099\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.910196 | + | 5.68301i | 0.0581503 | + | 0.363074i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.7926 | −0.937440 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.7082 | −1.43333 | −0.716665 | − | 0.697418i | \(-0.754332\pi\) | ||||
−0.716665 | + | 0.697418i | \(0.754332\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.2373i | 1.46092i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.19858 | + | 13.7273i | 0.137680 | + | 0.859638i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.4172i | 1.33597i | 0.744175 | + | 0.667985i | \(0.232843\pi\) | ||||
−0.744175 | + | 0.667985i | \(0.767157\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.4662 | 0.774613 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.70861 | −0.105760 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.4951i | 1.63376i | 0.576807 | + | 0.816880i | \(0.304298\pi\) | ||||
−0.576807 | + | 0.816880i | \(0.695702\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.89560 | − | 1.42473i | 0.546452 | − | 0.0875203i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.40699i | 0.575698i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.7259 | −0.897857 | −0.448928 | − | 0.893568i | \(-0.648194\pi\) | ||||
−0.448928 | + | 0.893568i | \(0.648194\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.8491 | 1.57022 | 0.785109 | − | 0.619357i | \(-0.212607\pi\) | ||||
0.785109 | + | 0.619357i | \(0.212607\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.09417i | 0.187268i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 26.1721 | − | 8.60421i | 1.57824 | − | 0.518853i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 20.1227i | − | 1.20906i | −0.796584 | − | 0.604528i | \(-0.793362\pi\) | ||
0.796584 | − | 0.604528i | \(-0.206638\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.3954 | −0.978067 | −0.489034 | − | 0.872265i | \(-0.662650\pi\) | ||||
−0.489034 | + | 0.872265i | \(0.662650\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.5650i | 0.865802i | 0.901441 | + | 0.432901i | \(0.142510\pi\) | ||||
−0.901441 | + | 0.432901i | \(0.857490\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 0.614436i | − | 0.0362690i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −21.6546 | −1.27380 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.3026 | 0.838432 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 26.6995i | − | 1.55980i | −0.625904 | − | 0.779900i | \(-0.715270\pi\) | ||
0.625904 | − | 0.779900i | \(-0.284730\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.66596 | + | 16.6455i | 0.155218 | + | 0.969138i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.51003i | 0.319724i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.21728 | 0.243892 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.6634 | 1.01810 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 6.72595i | − | 0.386396i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.21728 | − | 26.3315i | −0.241481 | − | 1.50774i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.4230i | 0.651943i | 0.945380 | + | 0.325972i | \(0.105691\pi\) | ||||
−0.945380 | + | 0.325972i | \(0.894309\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.0779 | −0.971529 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.4546 | −1.10317 | −0.551585 | − | 0.834119i | \(-0.685977\pi\) | ||||
−0.551585 | + | 0.834119i | \(0.685977\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 32.5805i | − | 1.84156i | −0.390087 | − | 0.920778i | \(-0.627555\pi\) | ||
0.390087 | − | 0.920778i | \(-0.372445\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.83172 | − | 1.09417i | 0.384924 | − | 0.0616497i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 31.3781i | 1.76237i | 0.472774 | + | 0.881184i | \(0.343253\pi\) | ||||
−0.472774 | + | 0.881184i | \(0.656747\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.41450 | −0.527111 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.63450 | −0.426116 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.56155 | − | 4.74990i | −0.0866194 | − | 0.263477i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.02006i | 0.277610i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.8518 | −1.09446 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.4951 | 1.67616 | 0.838082 | − | 0.545544i | \(-0.183677\pi\) | ||||
0.838082 | + | 0.545544i | \(0.183677\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 4.02893i | − | 0.220784i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.6681 | − | 1.70861i | 0.582860 | − | 0.0933513i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.8765i | 0.864848i | 0.901670 | + | 0.432424i | \(0.142342\pi\) | ||||
−0.901670 | + | 0.432424i | \(0.857658\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.6229 | −0.902832 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.6951i | − | 0.739465i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.49133 | − | 9.31145i | −0.0802905 | − | 0.501312i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 21.1069i | − | 1.13308i | −0.824036 | − | 0.566538i | \(-0.808283\pi\) | ||
0.824036 | − | 0.566538i | \(-0.191717\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.82899 | −0.258490 | −0.129245 | − | 0.991613i | \(-0.541255\pi\) | ||||
−0.129245 | + | 0.991613i | \(0.541255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 19.4359i | − | 1.03447i | −0.855844 | − | 0.517235i | \(-0.826961\pi\) | ||
0.855844 | − | 0.517235i | \(-0.173039\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.82537 | + | 17.6408i | 0.149955 | + | 0.936279i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.2373i | 1.01815i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.2271 | −1.43699 | −0.718496 | − | 0.695531i | \(-0.755169\pi\) | ||||
−0.718496 | + | 0.695531i | \(0.755169\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.3604i | 1.01616i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.5590 | − | 3.29275i | 1.07611 | − | 0.172351i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.7008i | 0.819577i | 0.912181 | + | 0.409788i | \(0.134397\pi\) | ||||
−0.912181 | + | 0.409788i | \(0.865603\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.198578 | −0.0103376 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.4662 | 0.647214 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 3.86952i | − | 0.200356i | −0.994970 | − | 0.100178i | \(-0.968059\pi\) | ||
0.994970 | − | 0.100178i | \(-0.0319412\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.93524 | + | 5.12748i | −0.513054 | + | 0.264782i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.70861i | 0.0879979i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.30149 | −0.375052 | −0.187526 | − | 0.982260i | \(-0.560047\pi\) | ||||
−0.187526 | + | 0.982260i | \(0.560047\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.87689 | 0.147388 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 37.2094i | − | 1.90131i | −0.310250 | − | 0.950655i | \(-0.600413\pi\) | ||
0.310250 | − | 0.950655i | \(-0.399587\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 37.6430 | − | 6.02893i | 1.91846 | − | 0.307263i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 5.70861i | − | 0.290185i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.1227 | −1.52728 | −0.763641 | − | 0.645641i | \(-0.776590\pi\) | ||||
−0.763641 | + | 0.645641i | \(0.776590\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.2200 | 1.32600 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.5199i | 0.833317i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.00983 | − | 18.7926i | −0.151441 | − | 0.945556i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.25780i | − | 0.0631274i | −0.999502 | − | 0.0315637i | \(-0.989951\pi\) | ||
0.999502 | − | 0.0315637i | \(-0.0100487\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.6443 | 1.03093 | 0.515464 | − | 0.856911i | \(-0.327619\pi\) | ||||
0.515464 | + | 0.856911i | \(0.327619\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.353624 | − | 2.20793i | −0.0175717 | − | 0.109713i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 22.1995i | − | 1.10039i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.3820 | 1.55174 | 0.775870 | − | 0.630893i | \(-0.217311\pi\) | ||||
0.775870 | + | 0.630893i | \(0.217311\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.8504 | 0.633864 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23.3269i | 1.14784i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 32.6609 | − | 5.23100i | 1.60326 | − | 0.256780i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 17.0490i | − | 0.834893i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.5549 | −0.955321 | −0.477661 | − | 0.878544i | \(-0.658515\pi\) | ||||
−0.477661 | + | 0.878544i | \(0.658515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.07793 | −0.247483 | −0.123742 | − | 0.992314i | \(-0.539489\pi\) | ||||
−0.123742 | + | 0.992314i | \(0.539489\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.41586i | 0.311950i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.70861 | − | 29.5315i | −0.470937 | − | 1.43249i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 36.9008i | − | 1.78575i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.51003 | 0.266027 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.52900 | −0.362659 | −0.181330 | − | 0.983422i | \(-0.558040\pi\) | ||||
−0.181330 | + | 0.983422i | \(0.558040\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 37.4821i | − | 1.80127i | −0.434573 | − | 0.900637i | \(-0.643101\pi\) | ||
0.434573 | − | 0.900637i | \(-0.356899\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.77249 | − | 0.604205i | 0.180877 | − | 0.0289694i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.4836 | 0.643535 | 0.321767 | − | 0.946819i | \(-0.395723\pi\) | ||||
0.321767 | + | 0.946819i | \(0.395723\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.57391 | 0.122567 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.61171i | 0.314132i | 0.987588 | + | 0.157066i | \(0.0502035\pi\) | ||||
−0.987588 | + | 0.157066i | \(0.949796\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.32654 | − | 20.7700i | −0.157693 | − | 0.984591i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 19.5679i | − | 0.925530i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.24183 | −0.247377 | −0.123689 | − | 0.992321i | \(-0.539472\pi\) | ||||
−0.123689 | + | 0.992321i | \(0.539472\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.09417 | −0.0515226 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.22887i | 0.433610i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.09417 | − | 6.83172i | −0.0512957 | − | 0.320276i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.69702i | 0.406829i | 0.979093 | + | 0.203415i | \(0.0652039\pi\) | ||||
−0.979093 | + | 0.203415i | \(0.934796\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.21728 | 0.290198 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.11287 | −0.144981 | −0.0724905 | − | 0.997369i | \(-0.523095\pi\) | ||||
−0.0724905 | + | 0.997369i | \(0.523095\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.8328i | 1.57234i | 0.618008 | + | 0.786172i | \(0.287940\pi\) | ||||
−0.618008 | + | 0.786172i | \(0.712060\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.0112i | 1.29620i | 0.761554 | + | 0.648102i | \(0.224437\pi\) | ||||
−0.761554 | + | 0.648102i | \(0.775563\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.9502 | 0.690335 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.89423 | −0.179437 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 31.4546i | − | 1.44629i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 4.02893i | − | 0.184472i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.424328 | 0.0193880 | 0.00969401 | − | 0.999953i | \(-0.496914\pi\) | ||||
0.00969401 | + | 0.999953i | \(0.496914\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.02893 | −0.183703 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 13.0490i | − | 0.593750i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −31.5791 | + | 5.05774i | −1.43393 | + | 0.229660i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 32.5720i | − | 1.47598i | −0.674813 | − | 0.737989i | \(-0.735776\pi\) | ||
0.674813 | − | 0.737989i | \(-0.264224\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.237741 | −0.0107510 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.36659 | 0.0616734 | 0.0308367 | − | 0.999524i | \(-0.490183\pi\) | ||||
0.0308367 | + | 0.999524i | \(0.490183\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.6229i | 0.478432i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.94848 | − | 12.1658i | −0.0875776 | − | 0.546810i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.7217i | 1.10892i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.6430 | 0.789808 | 0.394904 | − | 0.918722i | \(-0.370778\pi\) | ||||
0.394904 | + | 0.918722i | \(0.370778\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.8304 | 0.528541 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 24.6202i | − | 1.09776i | −0.835901 | − | 0.548880i | \(-0.815054\pi\) | ||
0.835901 | − | 0.548880i | \(-0.184946\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.37846 | + | 14.8504i | 0.105840 | + | 0.660835i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.00000i | − | 0.0444116i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.41204 | −0.0625876 | −0.0312938 | − | 0.999510i | \(-0.509963\pi\) | ||||
−0.0312938 | + | 0.999510i | \(0.509963\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.8113 | 1.27453 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 37.7068 | − | 6.03916i | 1.66156 | − | 0.266117i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.3516i | 1.55476i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.6634 | −0.511968 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.5298 | 1.68802 | 0.844011 | − | 0.536326i | \(-0.180188\pi\) | ||||
0.844011 | + | 0.536326i | \(0.180188\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.23353i | 0.0976653i | 0.998807 | + | 0.0488326i | \(0.0155501\pi\) | ||||
−0.998807 | + | 0.0488326i | \(0.984450\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14.6970 | + | 4.83172i | −0.641430 | + | 0.210873i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.21455 | 0.226720 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.53896 | 0.327163 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.198578i | 0.00860139i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.8564 | − | 2.69974i | 0.728767 | − | 0.116720i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 12.5403i | − | 0.541155i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.1823 | 0.610876 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.8892 | −1.62898 | −0.814492 | − | 0.580175i | \(-0.802984\pi\) | ||||
−0.814492 | + | 0.580175i | \(0.802984\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 5.44343i | − | 0.233600i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.77521 | − | 11.0839i | −0.0760418 | − | 0.474784i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.8645i | 1.87551i | 0.347299 | + | 0.937755i | \(0.387099\pi\) | ||||
−0.347299 | + | 0.937755i | \(0.612901\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.9259 | −0.508985 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 26.3357i | − | 1.11991i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.42473 | + | 8.89560i | 0.0604763 | + | 0.377597i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.4537i | 0.570050i | 0.958520 | + | 0.285025i | \(0.0920019\pi\) | ||||
−0.958520 | + | 0.285025i | \(0.907998\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.70861 | −0.241448 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 34.2574 | 1.44635 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.6140i | 1.33237i | 0.745785 | + | 0.666186i | \(0.232074\pi\) | ||||
−0.745785 | + | 0.666186i | \(0.767926\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 36.7022 | − | 5.87826i | 1.54407 | − | 0.247300i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 3.09417i | − | 0.129943i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.3562 | 0.937222 | 0.468611 | − | 0.883405i | \(-0.344755\pi\) | ||||
0.468611 | + | 0.883405i | \(0.344755\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.6596 | 0.529788 | 0.264894 | − | 0.964277i | \(-0.414663\pi\) | ||||
0.264894 | + | 0.964277i | \(0.414663\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 5.22887i | − | 0.218439i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.58550 | + | 20.0317i | 0.274635 | + | 0.835378i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.48861i | 0.311755i | 0.987776 | + | 0.155877i | \(0.0498205\pi\) | ||||
−0.987776 | + | 0.155877i | \(0.950180\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.5287 | −0.728469 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 45.7707 | 1.89889 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 22.1995i | − | 0.919411i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.20793 | + | 0.353624i | −0.0912866 | + | 0.0146205i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 4.41858i | − | 0.182374i | −0.995834 | − | 0.0911872i | \(-0.970934\pi\) | ||
0.995834 | − | 0.0911872i | \(-0.0290662\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.4764 | −0.924557 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.5810i | 0.516641i | 0.966059 | + | 0.258320i | \(0.0831690\pi\) | ||||
−0.966059 | + | 0.258320i | \(0.916831\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.80278 | − | 42.4747i | −0.278887 | − | 1.74129i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 16.9143i | − | 0.692256i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.64337 | −0.108005 | −0.0540025 | − | 0.998541i | \(-0.517198\pi\) | ||||
−0.0540025 | + | 0.998541i | \(0.517198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.4740 | −0.427243 | −0.213622 | − | 0.976916i | \(-0.568526\pi\) | ||||
−0.213622 | + | 0.976916i | \(0.568526\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 4.83172i | − | 0.196763i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.84632 | − | 42.7465i | −0.278342 | − | 1.73789i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.0197i | 0.487863i | 0.969792 | + | 0.243932i | \(0.0784372\pi\) | ||||
−0.969792 | + | 0.243932i | \(0.921563\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.28674 | 0.214229 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.41586 | 0.259558 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.7676i | 1.40425i | 0.712054 | + | 0.702124i | \(0.247765\pi\) | ||||
−0.712054 | + | 0.702124i | \(0.752235\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.438447 | − | 0.0702221i | 0.0176799 | − | 0.00283163i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 31.6644i | − | 1.27476i | −0.770549 | − | 0.637380i | \(-0.780018\pi\) | ||
0.770549 | − | 0.637380i | \(-0.219982\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.6024 | 0.908469 | 0.454234 | − | 0.890882i | \(-0.349913\pi\) | ||||
0.454234 | + | 0.890882i | \(0.349913\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.21728 | −0.169234 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 29.1069i | − | 1.16614i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.1231 | − | 14.8344i | 0.804924 | − | 0.593378i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25.0490 | −0.998769 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.6229 | −0.741366 | −0.370683 | − | 0.928759i | \(-0.620876\pi\) | ||||
−0.370683 | + | 0.928759i | \(0.620876\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.8391i | 0.470562i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.35198 | + | 1.01734i | −0.252071 | + | 0.0403718i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.57391i | − | 0.101982i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.98977 | 0.316070 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.77658 | −0.346654 | −0.173327 | − | 0.984864i | \(-0.555452\pi\) | ||||
−0.173327 | + | 0.984864i | \(0.555452\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.6920i | 1.21037i | 0.796084 | + | 0.605186i | \(0.206901\pi\) | ||||
−0.796084 | + | 0.605186i | \(0.793099\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.01870 | + | 12.6042i | 0.0794863 | + | 0.496290i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.2023i | 1.42326i | 0.702555 | + | 0.711629i | \(0.252042\pi\) | ||||
−0.702555 | + | 0.711629i | \(0.747958\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41.5399 | 1.63058 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 42.8746i | − | 1.67781i | −0.544277 | − | 0.838906i | \(-0.683196\pi\) | ||
0.544277 | − | 0.838906i | \(-0.316804\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.84182 | − | 36.4747i | −0.228259 | − | 1.42518i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 9.31145i | − | 0.363274i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.72907 | −0.145264 | −0.0726320 | − | 0.997359i | \(-0.523140\pi\) | ||||
−0.0726320 | + | 0.997359i | \(0.523140\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.2057 | −0.513642 | −0.256821 | − | 0.966459i | \(-0.582675\pi\) | ||||
−0.256821 | + | 0.966459i | \(0.582675\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 6.21728i | − | 0.241459i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.20569i | − | 0.279005i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.48246 | 0.173302 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −65.7120 | −2.53678 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 0.901611i | − | 0.0347546i | −0.999849 | − | 0.0173773i | \(-0.994468\pi\) | ||
0.999849 | − | 0.0173773i | \(-0.00553164\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.56155 | + | 4.74990i | 0.0601042 | + | 0.182824i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.0057i | 0.384552i | 0.981341 | + | 0.192276i | \(0.0615869\pi\) | ||||
−0.981341 | + | 0.192276i | \(0.938413\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −44.2547 | −1.69834 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.35799 | 0.243639 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.9110i | 0.647082i | 0.946214 | + | 0.323541i | \(0.104873\pi\) | ||||
−0.946214 | + | 0.323541i | \(0.895127\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.3728 | + | 4.54421i | −1.08407 | + | 0.173626i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 6.45502i | − | 0.246274i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.02893 | −0.153490 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.1003 | −1.63961 | −0.819807 | − | 0.572640i | \(-0.805919\pi\) | ||||
−0.819807 | + | 0.572640i | \(0.805919\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 17.0490i | − | 0.647638i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.02893 | + | 37.6430i | 0.228690 | + | 1.42788i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.23462i | 0.0467645i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.40290 | 0.242180 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.9170 | 1.31880 | 0.659399 | − | 0.751793i | \(-0.270811\pi\) | ||||
0.659399 | + | 0.751793i | \(0.270811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.26880 | − | 14.1658i | −0.0854480 | − | 0.533513i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.8113i | 0.782688i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.8140 | −0.781685 | −0.390843 | − | 0.920457i | \(-0.627816\pi\) | ||||
−0.390843 | + | 0.920457i | \(0.627816\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.51139 | −0.319202 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.1658 | + | 1.94848i | −0.454974 | + | 0.0728690i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 1.55793i | − | 0.0581821i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.6024 | 0.395404 | 0.197702 | − | 0.980262i | \(-0.436652\pi\) | ||||
0.197702 | + | 0.980262i | \(0.436652\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 52.8421 | 1.96794 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 14.1911i | − | 0.527772i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.11573 | + | 2.66808i | −0.301411 | + | 0.0990902i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.06524i | − | 0.0395076i | −0.999805 | − | 0.0197538i | \(-0.993712\pi\) | ||
0.999805 | − | 0.0197538i | \(-0.00628824\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −35.4920 | −1.31272 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 29.1216i | − | 1.07563i | −0.843062 | − | 0.537816i | \(-0.819250\pi\) | ||
0.843062 | − | 0.537816i | \(-0.180750\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.68301 | + | 0.910196i | −0.209621 | + | 0.0335731i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 26.6229i | − | 0.980667i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.7966 | −1.53751 | −0.768757 | − | 0.639541i | \(-0.779125\pi\) | ||||
−0.768757 | + | 0.639541i | \(0.779125\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 32.8531i | − | 1.20526i | −0.798019 | − | 0.602632i | \(-0.794119\pi\) | ||
0.798019 | − | 0.602632i | \(-0.205881\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.91968 | + | 43.2045i | 0.253517 | + | 1.58289i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 14.7926i | − | 0.541231i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.6225 | 0.863146 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.2956 | 0.740597 | 0.370299 | − | 0.928913i | \(-0.379255\pi\) | ||||
0.370299 | + | 0.928913i | \(0.379255\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 22.7082i | − | 0.827533i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.26355 | − | 20.3767i | −0.118773 | − | 0.741584i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.62331i | 0.0590000i | 0.999565 | + | 0.0295000i | \(0.00939151\pi\) | ||||
−0.999565 | + | 0.0295000i | \(0.990608\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −23.2373 | −0.843462 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −50.4410 | −1.82848 | −0.914242 | − | 0.405169i | \(-0.867213\pi\) | ||||
−0.914242 | + | 0.405169i | \(0.867213\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 15.5329i | − | 0.562330i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.7273 | + | 2.19858i | −0.496312 | + | 0.0794898i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 7.53896i | − | 0.272216i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.75339 | 0.243533 | 0.121767 | − | 0.992559i | \(-0.461144\pi\) | ||||
0.121767 | + | 0.992559i | \(0.461144\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.4172 | −0.771322 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.5660i | 1.31519i | 0.753373 | + | 0.657594i | \(0.228426\pi\) | ||||
−0.753373 | + | 0.657594i | \(0.771574\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.4662i | 0.447223i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.0239 | 1.57530 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.70861i | − | 0.0610607i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.59819 | − | 1.37709i | 0.306883 | − | 0.0491506i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.21426i | 0.221514i | 0.993847 | + | 0.110757i | \(0.0353276\pi\) | ||||
−0.993847 | + | 0.110757i | \(0.964672\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −26.4951 | −0.943252 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 51.4342 | 1.82879 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.9259i | 0.423501i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.42473 | + | 8.89560i | 0.0505298 | + | 0.315494i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 39.5788i | − | 1.40195i | −0.713184 | − | 0.700977i | \(-0.752748\pi\) | ||
0.713184 | − | 0.700977i | \(-0.247252\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.8892 | 1.41118 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.40699 | −0.332380 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 51.3064i | − | 1.81056i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.61444 | + | 28.8113i | 0.162638 | + | 1.01546i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 14.7259i | − | 0.518378i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.47236 | 0.122082 | 0.0610408 | − | 0.998135i | \(-0.480558\pi\) | ||||
0.0610408 | + | 0.998135i | \(0.480558\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.2404 | 1.02677 | 0.513384 | − | 0.858159i | \(-0.328392\pi\) | ||||
0.513384 | + | 0.858159i | \(0.328392\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.8491i | 0.906566i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.524916 | − | 0.0840710i | 0.0183870 | − | 0.00294488i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.09417 | −0.108119 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.3417 | 1.68714 | 0.843569 | − | 0.537020i | \(-0.180450\pi\) | ||||
0.843569 | + | 0.537020i | \(0.180450\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.33889i | 0.325533i | 0.986665 | + | 0.162767i | \(0.0520418\pi\) | ||||
−0.986665 | + | 0.162767i | \(0.947958\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.60421 | + | 26.1721i | 0.299560 | + | 0.911196i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 45.8175i | − | 1.59323i | −0.604486 | − | 0.796616i | \(-0.706621\pi\) | ||
0.604486 | − | 0.796616i | \(-0.293379\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.8819 | 1.31569 | 0.657847 | − | 0.753151i | \(-0.271467\pi\) | ||||
0.657847 | + | 0.753151i | \(0.271467\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.1227 | 0.698049 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 16.0027i | − | 0.554462i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.1206 | + | 4.18350i | −0.903940 | + | 0.144776i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.6678 | −1.12782 | −0.563909 | − | 0.825837i | \(-0.690703\pi\) | ||||
−0.563909 | + | 0.825837i | \(0.690703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0807 | −0.899333 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 16.3954i | − | 0.564687i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.353624 | + | 2.20793i | 0.0121650 | + | 0.0759551i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 59.9046i | − | 2.05835i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.5650 | −0.499871 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.9911 | 0.582448 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.4867i | 0.906887i | 0.891285 | + | 0.453443i | \(0.149805\pi\) | ||||
−0.891285 | + | 0.453443i | \(0.850195\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 43.1292i | − | 1.47327i | −0.676292 | − | 0.736634i | \(-0.736414\pi\) | ||
0.676292 | − | 0.736634i | \(-0.263586\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.1690 | −1.40467 | −0.702334 | − | 0.711848i | \(-0.747859\pi\) | ||||
−0.702334 | + | 0.711848i | \(0.747859\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.614436 | 0.0209399 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 7.88822i | − | 0.268518i | −0.990946 | − | 0.134259i | \(-0.957135\pi\) | ||
0.990946 | − | 0.134259i | \(-0.0428654\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.7520 | − | 4.12447i | 0.875595 | − | 0.140236i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 21.6546i | − | 0.735428i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −46.8980 | −1.59091 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.83172 | −0.163716 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.3026i | 0.484069i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30.7414 | − | 15.8653i | 1.03925 | − | 0.536345i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.03740i | 0.203869i | 0.994791 | + | 0.101934i | \(0.0325031\pi\) | ||||
−0.994791 | + | 0.101934i | \(0.967497\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.6995 | 0.900551 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.4546 | −1.39664 | −0.698321 | − | 0.715785i | \(-0.746069\pi\) | ||||
−0.698321 | + | 0.715785i | \(0.746069\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 35.0575i | − | 1.17978i | −0.807484 | − | 0.589889i | \(-0.799172\pi\) | ||
0.807484 | − | 0.589889i | \(-0.200828\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.6455 | + | 2.66596i | −0.559532 | + | 0.0896152i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.8661i | 0.902075i | 0.892505 | + | 0.451038i | \(0.148946\pi\) | ||||
−0.892505 | + | 0.451038i | \(0.851054\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.90161 | −0.298550 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.51003 | −0.184593 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.43456 | + | 27.6881i | 0.148231 | + | 0.925513i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.21728i | 0.140811i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.0490 | −0.834503 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.6634i | 0.587802i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.92493 | + | 12.0187i | 0.0639867 | + | 0.399515i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 38.2137i | − | 1.26887i | −0.772978 | − | 0.634433i | \(-0.781234\pi\) | ||
0.772978 | − | 0.634433i | \(-0.218766\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.72595 | 0.223086 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.8919 | 1.65299 | 0.826496 | − | 0.562942i | \(-0.190331\pi\) | ||||
0.826496 | + | 0.562942i | \(0.190331\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 81.5074i | − | 2.69750i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26.3315 | − | 4.21728i | 0.870493 | − | 0.139419i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 51.1153i | − | 1.68798i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.41599 | 0.178657 | 0.0893284 | − | 0.996002i | \(-0.471528\pi\) | ||||
0.0893284 | + | 0.996002i | \(0.471528\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.4230 | −0.376400 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 7.98977i | − | 0.262986i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.29139 | − | 19.1370i | −0.206860 | − | 0.629221i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 17.0779i | − | 0.560913i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 58.7311 | 1.92691 | 0.963453 | − | 0.267878i | \(-0.0863224\pi\) | ||||
0.963453 | + | 0.267878i | \(0.0863224\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 19.4546i | − | 0.636916i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −75.6379 | + | 12.1142i | −2.47362 | + | 0.396178i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.01541i | 0.196515i | 0.995161 | + | 0.0982574i | \(0.0313269\pi\) | ||||
−0.995161 | + | 0.0982574i | \(0.968673\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.5805 | 1.06322 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.7389 | 1.32805 | 0.664025 | − | 0.747710i | \(-0.268847\pi\) | ||||
0.664025 | + | 0.747710i | \(0.268847\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 0.837461i | − | 0.0272715i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.09417 | + | 6.83172i | 0.0355935 | + | 0.222236i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.69715i | 0.120141i | 0.998194 | + | 0.0600705i | \(0.0191326\pi\) | ||||
−0.998194 | + | 0.0600705i | \(0.980867\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.31145 | −0.302263 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.3781 | −1.01750 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.12460i | − | 0.0364292i | −0.999834 | − | 0.0182146i | \(-0.994202\pi\) | ||
0.999834 | − | 0.0182146i | \(-0.00579822\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.84905 | + | 11.5450i | 0.0598340 | + | 0.373587i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 9.41450i | − | 0.304327i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −39.7614 | −1.28396 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 7.63450i | − | 0.246018i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 38.7022 | − | 6.19858i | 1.24587 | − | 0.199539i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 5.85956i | − | 0.188431i | −0.995552 | − | 0.0942153i | \(-0.969966\pi\) | ||
0.995552 | − | 0.0942153i | \(-0.0300342\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.0737 | −1.06138 | −0.530692 | − | 0.847565i | \(-0.678068\pi\) | ||||
−0.530692 | + | 0.847565i | \(0.678068\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 52.7526i | 1.69117i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.74990 | − | 1.56155i | 0.152119 | − | 0.0500097i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.1488i | 0.676610i | 0.941037 | + | 0.338305i | \(0.109853\pi\) | ||||
−0.941037 | + | 0.338305i | \(0.890147\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51.8328 | −1.65658 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.02006 | −0.160278 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.8960i | 1.04922i | 0.851343 | + | 0.524610i | \(0.175789\pi\) | ||||
−0.851343 | + | 0.524610i | \(0.824211\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 49.6264 | − | 7.94821i | 1.58123 | − | 0.253251i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 19.8518i | − | 0.631889i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0748 | 0.765534 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.6322 | 0.591871 | 0.295935 | − | 0.955208i | \(-0.404369\pi\) | ||||
0.295935 | + | 0.955208i | \(0.404369\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.4951i | 0.967734i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.98130 | + | 37.3456i | 0.189620 | + | 1.18393i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 3.08298i | − | 0.0976389i | −0.998808 | − | 0.0488195i | \(-0.984454\pi\) | ||
0.998808 | − | 0.0488195i | \(-0.0155459\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.02893 | 0.127470 |
(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 | 3120.2.l.n.1249.7 | 8 | ||
4.3 | odd | 2 | 1560.2.l.d.1249.3 | ✓ | 8 | ||
5.4 | even | 2 | inner | 3120.2.l.n.1249.3 | 8 | ||
12.11 | even | 2 | 4680.2.l.g.2809.4 | 8 | |||
20.3 | even | 4 | 7800.2.a.by.1.3 | 4 | |||
20.7 | even | 4 | 7800.2.a.bt.1.2 | 4 | |||
20.19 | odd | 2 | 1560.2.l.d.1249.7 | yes | 8 | ||
60.59 | even | 2 | 4680.2.l.g.2809.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.l.d.1249.3 | ✓ | 8 | 4.3 | odd | 2 | ||
1560.2.l.d.1249.7 | yes | 8 | 20.19 | odd | 2 | ||
3120.2.l.n.1249.3 | 8 | 5.4 | even | 2 | inner | ||
3120.2.l.n.1249.7 | 8 | 1.1 | even | 1 | trivial | ||
4680.2.l.g.2809.3 | 8 | 60.59 | even | 2 | |||
4680.2.l.g.2809.4 | 8 | 12.11 | even | 2 | |||
7800.2.a.bt.1.2 | 4 | 20.7 | even | 4 | |||
7800.2.a.by.1.3 | 4 | 20.3 | even | 4 |