Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4830,2,Mod(1,4830)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4830, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4830.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4830.a (trivial) |
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: | yes |
Analytic conductor: | \(38.5677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4830.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 3.26180 | 0.983468 | 0.491734 | − | 0.870745i | \(-0.336363\pi\) | ||||
0.491734 | + | 0.870745i | \(0.336363\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.34017 | −1.20375 | −0.601874 | − | 0.798591i | \(-0.705579\pi\) | ||||
−0.601874 | + | 0.798591i | \(0.705579\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.75872 | 1.39670 | 0.698348 | − | 0.715759i | \(-0.253919\pi\) | ||||
0.698348 | + | 0.715759i | \(0.253919\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.07838 | −0.706228 | −0.353114 | − | 0.935580i | \(-0.614877\pi\) | ||||
−0.353114 | + | 0.935580i | \(0.614877\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 3.26180 | 0.695417 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.34017 | −0.851178 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 0.581449 | 0.107972 | 0.0539862 | − | 0.998542i | \(-0.482807\pi\) | ||||
0.0539862 | + | 0.998542i | \(0.482807\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 3.07838 | 0.552893 | 0.276446 | − | 0.961029i | \(-0.410843\pi\) | ||||
0.276446 | + | 0.961029i | \(0.410843\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.26180 | −0.567806 | ||||||||
\(34\) | 5.75872 | 0.987613 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | −3.07838 | −0.499379 | ||||||||
\(39\) | 4.34017 | 0.694984 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −8.83710 | −1.38012 | −0.690062 | − | 0.723751i | \(-0.742417\pi\) | ||||
−0.690062 | + | 0.723751i | \(0.742417\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 0.738205 | 0.112575 | 0.0562876 | − | 0.998415i | \(-0.482074\pi\) | ||||
0.0562876 | + | 0.998415i | \(0.482074\pi\) | |||||||
\(44\) | 3.26180 | 0.491734 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 3.07838 | 0.449028 | 0.224514 | − | 0.974471i | \(-0.427921\pi\) | ||||
0.224514 | + | 0.974471i | \(0.427921\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −5.75872 | −0.806383 | ||||||||
\(52\) | −4.34017 | −0.601874 | ||||||||
\(53\) | 8.83710 | 1.21387 | 0.606935 | − | 0.794752i | \(-0.292399\pi\) | ||||
0.606935 | + | 0.794752i | \(0.292399\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −3.26180 | −0.439820 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 3.07838 | 0.407741 | ||||||||
\(58\) | 0.581449 | 0.0763480 | ||||||||
\(59\) | 6.15676 | 0.801541 | 0.400771 | − | 0.916178i | \(-0.368742\pi\) | ||||
0.400771 | + | 0.916178i | \(0.368742\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 8.15676 | 1.04437 | 0.522183 | − | 0.852834i | \(-0.325118\pi\) | ||||
0.522183 | + | 0.852834i | \(0.325118\pi\) | |||||||
\(62\) | 3.07838 | 0.390954 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.34017 | 0.538332 | ||||||||
\(66\) | −3.26180 | −0.401499 | ||||||||
\(67\) | 0.738205 | 0.0901861 | 0.0450930 | − | 0.998983i | \(-0.485642\pi\) | ||||
0.0450930 | + | 0.998983i | \(0.485642\pi\) | |||||||
\(68\) | 5.75872 | 0.698348 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −5.41855 | −0.643064 | −0.321532 | − | 0.946899i | \(-0.604198\pi\) | ||||
−0.321532 | + | 0.946899i | \(0.604198\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −6.31351 | −0.738941 | −0.369470 | − | 0.929243i | \(-0.620461\pi\) | ||||
−0.369470 | + | 0.929243i | \(0.620461\pi\) | |||||||
\(74\) | 2.00000 | 0.232495 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −3.07838 | −0.353114 | ||||||||
\(77\) | 3.26180 | 0.371716 | ||||||||
\(78\) | 4.34017 | 0.491428 | ||||||||
\(79\) | −2.15676 | −0.242654 | −0.121327 | − | 0.992613i | \(-0.538715\pi\) | ||||
−0.121327 | + | 0.992613i | \(0.538715\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.83710 | −0.975895 | ||||||||
\(83\) | −9.60197 | −1.05395 | −0.526976 | − | 0.849880i | \(-0.676674\pi\) | ||||
−0.526976 | + | 0.849880i | \(0.676674\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −5.75872 | −0.624621 | ||||||||
\(86\) | 0.738205 | 0.0796027 | ||||||||
\(87\) | −0.581449 | −0.0623379 | ||||||||
\(88\) | 3.26180 | 0.347709 | ||||||||
\(89\) | 10.8638 | 1.15156 | 0.575778 | − | 0.817606i | \(-0.304699\pi\) | ||||
0.575778 | + | 0.817606i | \(0.304699\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | −4.34017 | −0.454974 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −3.07838 | −0.319213 | ||||||||
\(94\) | 3.07838 | 0.317510 | ||||||||
\(95\) | 3.07838 | 0.315835 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −4.34017 | −0.440678 | −0.220339 | − | 0.975423i | \(-0.570716\pi\) | ||||
−0.220339 | + | 0.975423i | \(0.570716\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 3.26180 | 0.327823 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −1.81658 | −0.180757 | −0.0903784 | − | 0.995908i | \(-0.528808\pi\) | ||||
−0.0903784 | + | 0.995908i | \(0.528808\pi\) | |||||||
\(102\) | −5.75872 | −0.570199 | ||||||||
\(103\) | −2.52359 | −0.248657 | −0.124328 | − | 0.992241i | \(-0.539678\pi\) | ||||
−0.124328 | + | 0.992241i | \(0.539678\pi\) | |||||||
\(104\) | −4.34017 | −0.425589 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 8.83710 | 0.858335 | ||||||||
\(107\) | 8.68035 | 0.839161 | 0.419580 | − | 0.907718i | \(-0.362177\pi\) | ||||
0.419580 | + | 0.907718i | \(0.362177\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 19.3607 | 1.85442 | 0.927209 | − | 0.374544i | \(-0.122201\pi\) | ||||
0.927209 | + | 0.374544i | \(0.122201\pi\) | |||||||
\(110\) | −3.26180 | −0.311000 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 8.15676 | 0.767323 | 0.383662 | − | 0.923474i | \(-0.374663\pi\) | ||||
0.383662 | + | 0.923474i | \(0.374663\pi\) | |||||||
\(114\) | 3.07838 | 0.288316 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0.581449 | 0.0539862 | ||||||||
\(117\) | −4.34017 | −0.401249 | ||||||||
\(118\) | 6.15676 | 0.566775 | ||||||||
\(119\) | 5.75872 | 0.527901 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −0.360692 | −0.0327902 | ||||||||
\(122\) | 8.15676 | 0.738478 | ||||||||
\(123\) | 8.83710 | 0.796815 | ||||||||
\(124\) | 3.07838 | 0.276446 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 4.73820 | 0.420448 | 0.210224 | − | 0.977653i | \(-0.432581\pi\) | ||||
0.210224 | + | 0.977653i | \(0.432581\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.738205 | −0.0649953 | ||||||||
\(130\) | 4.34017 | 0.380658 | ||||||||
\(131\) | 17.6742 | 1.54420 | 0.772101 | − | 0.635500i | \(-0.219206\pi\) | ||||
0.772101 | + | 0.635500i | \(0.219206\pi\) | |||||||
\(132\) | −3.26180 | −0.283903 | ||||||||
\(133\) | −3.07838 | −0.266929 | ||||||||
\(134\) | 0.738205 | 0.0637712 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 5.75872 | 0.493806 | ||||||||
\(137\) | 2.00000 | 0.170872 | 0.0854358 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −0.680346 | −0.0577062 | −0.0288531 | − | 0.999584i | \(-0.509186\pi\) | ||||
−0.0288531 | + | 0.999584i | \(0.509186\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −3.07838 | −0.259246 | ||||||||
\(142\) | −5.41855 | −0.454715 | ||||||||
\(143\) | −14.1568 | −1.18385 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.581449 | −0.0482867 | ||||||||
\(146\) | −6.31351 | −0.522510 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | 10.0000 | 0.819232 | 0.409616 | − | 0.912258i | \(-0.365663\pi\) | ||||
0.409616 | + | 0.912258i | \(0.365663\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | −4.68035 | −0.380881 | −0.190441 | − | 0.981699i | \(-0.560992\pi\) | ||||
−0.190441 | + | 0.981699i | \(0.560992\pi\) | |||||||
\(152\) | −3.07838 | −0.249689 | ||||||||
\(153\) | 5.75872 | 0.465565 | ||||||||
\(154\) | 3.26180 | 0.262843 | ||||||||
\(155\) | −3.07838 | −0.247261 | ||||||||
\(156\) | 4.34017 | 0.347492 | ||||||||
\(157\) | 4.52359 | 0.361022 | 0.180511 | − | 0.983573i | \(-0.442225\pi\) | ||||
0.180511 | + | 0.983573i | \(0.442225\pi\) | |||||||
\(158\) | −2.15676 | −0.171582 | ||||||||
\(159\) | −8.83710 | −0.700828 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 9.84324 | 0.770982 | 0.385491 | − | 0.922712i | \(-0.374032\pi\) | ||||
0.385491 | + | 0.922712i | \(0.374032\pi\) | |||||||
\(164\) | −8.83710 | −0.690062 | ||||||||
\(165\) | 3.26180 | 0.253930 | ||||||||
\(166\) | −9.60197 | −0.745257 | ||||||||
\(167\) | −5.91548 | −0.457754 | −0.228877 | − | 0.973455i | \(-0.573505\pi\) | ||||
−0.228877 | + | 0.973455i | \(0.573505\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 5.83710 | 0.449008 | ||||||||
\(170\) | −5.75872 | −0.441674 | ||||||||
\(171\) | −3.07838 | −0.235409 | ||||||||
\(172\) | 0.738205 | 0.0562876 | ||||||||
\(173\) | −11.2351 | −0.854191 | −0.427096 | − | 0.904206i | \(-0.640463\pi\) | ||||
−0.427096 | + | 0.904206i | \(0.640463\pi\) | |||||||
\(174\) | −0.581449 | −0.0440796 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 3.26180 | 0.245867 | ||||||||
\(177\) | −6.15676 | −0.462770 | ||||||||
\(178\) | 10.8638 | 0.814273 | ||||||||
\(179\) | 12.3135 | 0.920355 | 0.460178 | − | 0.887827i | \(-0.347786\pi\) | ||||
0.460178 | + | 0.887827i | \(0.347786\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 17.5174 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(182\) | −4.34017 | −0.321715 | ||||||||
\(183\) | −8.15676 | −0.602965 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −2.00000 | −0.147043 | ||||||||
\(186\) | −3.07838 | −0.225718 | ||||||||
\(187\) | 18.7838 | 1.37361 | ||||||||
\(188\) | 3.07838 | 0.224514 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 3.07838 | 0.223329 | ||||||||
\(191\) | −6.15676 | −0.445487 | −0.222744 | − | 0.974877i | \(-0.571501\pi\) | ||||
−0.222744 | + | 0.974877i | \(0.571501\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 4.15676 | 0.299210 | 0.149605 | − | 0.988746i | \(-0.452200\pi\) | ||||
0.149605 | + | 0.988746i | \(0.452200\pi\) | |||||||
\(194\) | −4.34017 | −0.311606 | ||||||||
\(195\) | −4.34017 | −0.310806 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 12.1568 | 0.866133 | 0.433066 | − | 0.901362i | \(-0.357432\pi\) | ||||
0.433066 | + | 0.901362i | \(0.357432\pi\) | |||||||
\(198\) | 3.26180 | 0.231806 | ||||||||
\(199\) | 18.5236 | 1.31310 | 0.656551 | − | 0.754281i | \(-0.272015\pi\) | ||||
0.656551 | + | 0.754281i | \(0.272015\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −0.738205 | −0.0520689 | ||||||||
\(202\) | −1.81658 | −0.127814 | ||||||||
\(203\) | 0.581449 | 0.0408097 | ||||||||
\(204\) | −5.75872 | −0.403191 | ||||||||
\(205\) | 8.83710 | 0.617210 | ||||||||
\(206\) | −2.52359 | −0.175827 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −4.34017 | −0.300937 | ||||||||
\(209\) | −10.0410 | −0.694553 | ||||||||
\(210\) | 1.00000 | 0.0690066 | ||||||||
\(211\) | 27.2039 | 1.87280 | 0.936398 | − | 0.350940i | \(-0.114138\pi\) | ||||
0.936398 | + | 0.350940i | \(0.114138\pi\) | |||||||
\(212\) | 8.83710 | 0.606935 | ||||||||
\(213\) | 5.41855 | 0.371273 | ||||||||
\(214\) | 8.68035 | 0.593376 | ||||||||
\(215\) | −0.738205 | −0.0503451 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 3.07838 | 0.208974 | ||||||||
\(218\) | 19.3607 | 1.31127 | ||||||||
\(219\) | 6.31351 | 0.426628 | ||||||||
\(220\) | −3.26180 | −0.219910 | ||||||||
\(221\) | −24.9939 | −1.68127 | ||||||||
\(222\) | −2.00000 | −0.134231 | ||||||||
\(223\) | −0.496928 | −0.0332768 | −0.0166384 | − | 0.999862i | \(-0.505296\pi\) | ||||
−0.0166384 | + | 0.999862i | \(0.505296\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 8.15676 | 0.542579 | ||||||||
\(227\) | −10.5958 | −0.703270 | −0.351635 | − | 0.936137i | \(-0.614374\pi\) | ||||
−0.351635 | + | 0.936137i | \(0.614374\pi\) | |||||||
\(228\) | 3.07838 | 0.203871 | ||||||||
\(229\) | 7.16290 | 0.473338 | 0.236669 | − | 0.971590i | \(-0.423944\pi\) | ||||
0.236669 | + | 0.971590i | \(0.423944\pi\) | |||||||
\(230\) | −1.00000 | −0.0659380 | ||||||||
\(231\) | −3.26180 | −0.214610 | ||||||||
\(232\) | 0.581449 | 0.0381740 | ||||||||
\(233\) | −19.3607 | −1.26836 | −0.634181 | − | 0.773185i | \(-0.718662\pi\) | ||||
−0.634181 | + | 0.773185i | \(0.718662\pi\) | |||||||
\(234\) | −4.34017 | −0.283726 | ||||||||
\(235\) | −3.07838 | −0.200811 | ||||||||
\(236\) | 6.15676 | 0.400771 | ||||||||
\(237\) | 2.15676 | 0.140096 | ||||||||
\(238\) | 5.75872 | 0.373283 | ||||||||
\(239\) | −5.41855 | −0.350497 | −0.175248 | − | 0.984524i | \(-0.556073\pi\) | ||||
−0.175248 | + | 0.984524i | \(0.556073\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 5.75872 | 0.370952 | 0.185476 | − | 0.982649i | \(-0.440617\pi\) | ||||
0.185476 | + | 0.982649i | \(0.440617\pi\) | |||||||
\(242\) | −0.360692 | −0.0231862 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 8.15676 | 0.522183 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 8.83710 | 0.563433 | ||||||||
\(247\) | 13.3607 | 0.850120 | ||||||||
\(248\) | 3.07838 | 0.195477 | ||||||||
\(249\) | 9.60197 | 0.608500 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 17.1773 | 1.08422 | 0.542110 | − | 0.840308i | \(-0.317626\pi\) | ||||
0.542110 | + | 0.840308i | \(0.317626\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 3.26180 | 0.205067 | ||||||||
\(254\) | 4.73820 | 0.297301 | ||||||||
\(255\) | 5.75872 | 0.360625 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.6742 | −0.728217 | −0.364108 | − | 0.931357i | \(-0.618626\pi\) | ||||
−0.364108 | + | 0.931357i | \(0.618626\pi\) | |||||||
\(258\) | −0.738205 | −0.0459586 | ||||||||
\(259\) | 2.00000 | 0.124274 | ||||||||
\(260\) | 4.34017 | 0.269166 | ||||||||
\(261\) | 0.581449 | 0.0359908 | ||||||||
\(262\) | 17.6742 | 1.09192 | ||||||||
\(263\) | −19.8843 | −1.22612 | −0.613059 | − | 0.790037i | \(-0.710061\pi\) | ||||
−0.613059 | + | 0.790037i | \(0.710061\pi\) | |||||||
\(264\) | −3.26180 | −0.200750 | ||||||||
\(265\) | −8.83710 | −0.542859 | ||||||||
\(266\) | −3.07838 | −0.188747 | ||||||||
\(267\) | −10.8638 | −0.664852 | ||||||||
\(268\) | 0.738205 | 0.0450930 | ||||||||
\(269\) | −9.70086 | −0.591472 | −0.295736 | − | 0.955270i | \(-0.595565\pi\) | ||||
−0.295736 | + | 0.955270i | \(0.595565\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 3.07838 | 0.186998 | 0.0934991 | − | 0.995619i | \(-0.470195\pi\) | ||||
0.0934991 | + | 0.995619i | \(0.470195\pi\) | |||||||
\(272\) | 5.75872 | 0.349174 | ||||||||
\(273\) | 4.34017 | 0.262679 | ||||||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | 3.26180 | 0.196694 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | −5.26180 | −0.316151 | −0.158075 | − | 0.987427i | \(-0.550529\pi\) | ||||
−0.158075 | + | 0.987427i | \(0.550529\pi\) | |||||||
\(278\) | −0.680346 | −0.0408044 | ||||||||
\(279\) | 3.07838 | 0.184298 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 5.57531 | 0.332595 | 0.166297 | − | 0.986076i | \(-0.446819\pi\) | ||||
0.166297 | + | 0.986076i | \(0.446819\pi\) | |||||||
\(282\) | −3.07838 | −0.183315 | ||||||||
\(283\) | −6.65368 | −0.395520 | −0.197760 | − | 0.980250i | \(-0.563367\pi\) | ||||
−0.197760 | + | 0.980250i | \(0.563367\pi\) | |||||||
\(284\) | −5.41855 | −0.321532 | ||||||||
\(285\) | −3.07838 | −0.182347 | ||||||||
\(286\) | −14.1568 | −0.837107 | ||||||||
\(287\) | −8.83710 | −0.521638 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 16.1629 | 0.950759 | ||||||||
\(290\) | −0.581449 | −0.0341439 | ||||||||
\(291\) | 4.34017 | 0.254425 | ||||||||
\(292\) | −6.31351 | −0.369470 | ||||||||
\(293\) | 6.68035 | 0.390270 | 0.195135 | − | 0.980776i | \(-0.437486\pi\) | ||||
0.195135 | + | 0.980776i | \(0.437486\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −6.15676 | −0.358460 | ||||||||
\(296\) | 2.00000 | 0.116248 | ||||||||
\(297\) | −3.26180 | −0.189269 | ||||||||
\(298\) | 10.0000 | 0.579284 | ||||||||
\(299\) | −4.34017 | −0.250999 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 0.738205 | 0.0425494 | ||||||||
\(302\) | −4.68035 | −0.269324 | ||||||||
\(303\) | 1.81658 | 0.104360 | ||||||||
\(304\) | −3.07838 | −0.176557 | ||||||||
\(305\) | −8.15676 | −0.467054 | ||||||||
\(306\) | 5.75872 | 0.329204 | ||||||||
\(307\) | 31.8843 | 1.81973 | 0.909866 | − | 0.414902i | \(-0.136184\pi\) | ||||
0.909866 | + | 0.414902i | \(0.136184\pi\) | |||||||
\(308\) | 3.26180 | 0.185858 | ||||||||
\(309\) | 2.52359 | 0.143562 | ||||||||
\(310\) | −3.07838 | −0.174840 | ||||||||
\(311\) | 9.17727 | 0.520395 | 0.260198 | − | 0.965555i | \(-0.416212\pi\) | ||||
0.260198 | + | 0.965555i | \(0.416212\pi\) | |||||||
\(312\) | 4.34017 | 0.245714 | ||||||||
\(313\) | −21.3340 | −1.20587 | −0.602935 | − | 0.797790i | \(-0.706002\pi\) | ||||
−0.602935 | + | 0.797790i | \(0.706002\pi\) | |||||||
\(314\) | 4.52359 | 0.255281 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | −2.15676 | −0.121327 | ||||||||
\(317\) | 6.99386 | 0.392814 | 0.196407 | − | 0.980522i | \(-0.437073\pi\) | ||||
0.196407 | + | 0.980522i | \(0.437073\pi\) | |||||||
\(318\) | −8.83710 | −0.495560 | ||||||||
\(319\) | 1.89657 | 0.106187 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −8.68035 | −0.484490 | ||||||||
\(322\) | 1.00000 | 0.0557278 | ||||||||
\(323\) | −17.7275 | −0.986386 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.34017 | −0.240749 | ||||||||
\(326\) | 9.84324 | 0.545167 | ||||||||
\(327\) | −19.3607 | −1.07065 | ||||||||
\(328\) | −8.83710 | −0.487947 | ||||||||
\(329\) | 3.07838 | 0.169716 | ||||||||
\(330\) | 3.26180 | 0.179556 | ||||||||
\(331\) | 2.83710 | 0.155941 | 0.0779706 | − | 0.996956i | \(-0.475156\pi\) | ||||
0.0779706 | + | 0.996956i | \(0.475156\pi\) | |||||||
\(332\) | −9.60197 | −0.526976 | ||||||||
\(333\) | 2.00000 | 0.109599 | ||||||||
\(334\) | −5.91548 | −0.323681 | ||||||||
\(335\) | −0.738205 | −0.0403324 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 8.94828 | 0.487444 | 0.243722 | − | 0.969845i | \(-0.421632\pi\) | ||||
0.243722 | + | 0.969845i | \(0.421632\pi\) | |||||||
\(338\) | 5.83710 | 0.317496 | ||||||||
\(339\) | −8.15676 | −0.443014 | ||||||||
\(340\) | −5.75872 | −0.312311 | ||||||||
\(341\) | 10.0410 | 0.543753 | ||||||||
\(342\) | −3.07838 | −0.166460 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.738205 | 0.0398013 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | −11.2351 | −0.604005 | ||||||||
\(347\) | 8.68035 | 0.465985 | 0.232993 | − | 0.972478i | \(-0.425148\pi\) | ||||
0.232993 | + | 0.972478i | \(0.425148\pi\) | |||||||
\(348\) | −0.581449 | −0.0311690 | ||||||||
\(349\) | 17.0784 | 0.914185 | 0.457092 | − | 0.889419i | \(-0.348891\pi\) | ||||
0.457092 | + | 0.889419i | \(0.348891\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 4.34017 | 0.231661 | ||||||||
\(352\) | 3.26180 | 0.173854 | ||||||||
\(353\) | −11.1629 | −0.594141 | −0.297071 | − | 0.954856i | \(-0.596010\pi\) | ||||
−0.297071 | + | 0.954856i | \(0.596010\pi\) | |||||||
\(354\) | −6.15676 | −0.327228 | ||||||||
\(355\) | 5.41855 | 0.287587 | ||||||||
\(356\) | 10.8638 | 0.575778 | ||||||||
\(357\) | −5.75872 | −0.304784 | ||||||||
\(358\) | 12.3135 | 0.650789 | ||||||||
\(359\) | 16.8781 | 0.890794 | 0.445397 | − | 0.895333i | \(-0.353063\pi\) | ||||
0.445397 | + | 0.895333i | \(0.353063\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −9.52359 | −0.501242 | ||||||||
\(362\) | 17.5174 | 0.920697 | ||||||||
\(363\) | 0.360692 | 0.0189314 | ||||||||
\(364\) | −4.34017 | −0.227487 | ||||||||
\(365\) | 6.31351 | 0.330464 | ||||||||
\(366\) | −8.15676 | −0.426360 | ||||||||
\(367\) | 16.1978 | 0.845518 | 0.422759 | − | 0.906242i | \(-0.361062\pi\) | ||||
0.422759 | + | 0.906242i | \(0.361062\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −8.83710 | −0.460041 | ||||||||
\(370\) | −2.00000 | −0.103975 | ||||||||
\(371\) | 8.83710 | 0.458799 | ||||||||
\(372\) | −3.07838 | −0.159606 | ||||||||
\(373\) | 7.67420 | 0.397355 | 0.198678 | − | 0.980065i | \(-0.436335\pi\) | ||||
0.198678 | + | 0.980065i | \(0.436335\pi\) | |||||||
\(374\) | 18.7838 | 0.971286 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 3.07838 | 0.158755 | ||||||||
\(377\) | −2.52359 | −0.129972 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 11.6332 | 0.597556 | 0.298778 | − | 0.954323i | \(-0.403421\pi\) | ||||
0.298778 | + | 0.954323i | \(0.403421\pi\) | |||||||
\(380\) | 3.07838 | 0.157917 | ||||||||
\(381\) | −4.73820 | −0.242746 | ||||||||
\(382\) | −6.15676 | −0.315007 | ||||||||
\(383\) | −5.36069 | −0.273919 | −0.136959 | − | 0.990577i | \(-0.543733\pi\) | ||||
−0.136959 | + | 0.990577i | \(0.543733\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −3.26180 | −0.166236 | ||||||||
\(386\) | 4.15676 | 0.211573 | ||||||||
\(387\) | 0.738205 | 0.0375251 | ||||||||
\(388\) | −4.34017 | −0.220339 | ||||||||
\(389\) | −18.9939 | −0.963027 | −0.481513 | − | 0.876439i | \(-0.659913\pi\) | ||||
−0.481513 | + | 0.876439i | \(0.659913\pi\) | |||||||
\(390\) | −4.34017 | −0.219773 | ||||||||
\(391\) | 5.75872 | 0.291231 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −17.6742 | −0.891546 | ||||||||
\(394\) | 12.1568 | 0.612448 | ||||||||
\(395\) | 2.15676 | 0.108518 | ||||||||
\(396\) | 3.26180 | 0.163911 | ||||||||
\(397\) | 0.707008 | 0.0354837 | 0.0177419 | − | 0.999843i | \(-0.494352\pi\) | ||||
0.0177419 | + | 0.999843i | \(0.494352\pi\) | |||||||
\(398\) | 18.5236 | 0.928504 | ||||||||
\(399\) | 3.07838 | 0.154112 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −22.6225 | −1.12971 | −0.564857 | − | 0.825189i | \(-0.691069\pi\) | ||||
−0.564857 | + | 0.825189i | \(0.691069\pi\) | |||||||
\(402\) | −0.738205 | −0.0368183 | ||||||||
\(403\) | −13.3607 | −0.665543 | ||||||||
\(404\) | −1.81658 | −0.0903784 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0.581449 | 0.0288568 | ||||||||
\(407\) | 6.52359 | 0.323362 | ||||||||
\(408\) | −5.75872 | −0.285099 | ||||||||
\(409\) | −6.36683 | −0.314820 | −0.157410 | − | 0.987533i | \(-0.550314\pi\) | ||||
−0.157410 | + | 0.987533i | \(0.550314\pi\) | |||||||
\(410\) | 8.83710 | 0.436433 | ||||||||
\(411\) | −2.00000 | −0.0986527 | ||||||||
\(412\) | −2.52359 | −0.124328 | ||||||||
\(413\) | 6.15676 | 0.302954 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 9.60197 | 0.471342 | ||||||||
\(416\) | −4.34017 | −0.212794 | ||||||||
\(417\) | 0.680346 | 0.0333167 | ||||||||
\(418\) | −10.0410 | −0.491123 | ||||||||
\(419\) | −19.0205 | −0.929213 | −0.464607 | − | 0.885517i | \(-0.653804\pi\) | ||||
−0.464607 | + | 0.885517i | \(0.653804\pi\) | |||||||
\(420\) | 1.00000 | 0.0487950 | ||||||||
\(421\) | 14.6270 | 0.712877 | 0.356439 | − | 0.934319i | \(-0.383991\pi\) | ||||
0.356439 | + | 0.934319i | \(0.383991\pi\) | |||||||
\(422\) | 27.2039 | 1.32427 | ||||||||
\(423\) | 3.07838 | 0.149676 | ||||||||
\(424\) | 8.83710 | 0.429168 | ||||||||
\(425\) | 5.75872 | 0.279339 | ||||||||
\(426\) | 5.41855 | 0.262530 | ||||||||
\(427\) | 8.15676 | 0.394733 | ||||||||
\(428\) | 8.68035 | 0.419580 | ||||||||
\(429\) | 14.1568 | 0.683495 | ||||||||
\(430\) | −0.738205 | −0.0355994 | ||||||||
\(431\) | 15.8310 | 0.762550 | 0.381275 | − | 0.924462i | \(-0.375485\pi\) | ||||
0.381275 | + | 0.924462i | \(0.375485\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 10.6947 | 0.513956 | 0.256978 | − | 0.966417i | \(-0.417273\pi\) | ||||
0.256978 | + | 0.966417i | \(0.417273\pi\) | |||||||
\(434\) | 3.07838 | 0.147767 | ||||||||
\(435\) | 0.581449 | 0.0278784 | ||||||||
\(436\) | 19.3607 | 0.927209 | ||||||||
\(437\) | −3.07838 | −0.147259 | ||||||||
\(438\) | 6.31351 | 0.301671 | ||||||||
\(439\) | 16.3857 | 0.782049 | 0.391024 | − | 0.920380i | \(-0.372121\pi\) | ||||
0.391024 | + | 0.920380i | \(0.372121\pi\) | |||||||
\(440\) | −3.26180 | −0.155500 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −24.9939 | −1.18884 | ||||||||
\(443\) | 0.680346 | 0.0323242 | 0.0161621 | − | 0.999869i | \(-0.494855\pi\) | ||||
0.0161621 | + | 0.999869i | \(0.494855\pi\) | |||||||
\(444\) | −2.00000 | −0.0949158 | ||||||||
\(445\) | −10.8638 | −0.514992 | ||||||||
\(446\) | −0.496928 | −0.0235302 | ||||||||
\(447\) | −10.0000 | −0.472984 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 33.7152 | 1.59112 | 0.795560 | − | 0.605874i | \(-0.207177\pi\) | ||||
0.795560 | + | 0.605874i | \(0.207177\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −28.8248 | −1.35731 | ||||||||
\(452\) | 8.15676 | 0.383662 | ||||||||
\(453\) | 4.68035 | 0.219902 | ||||||||
\(454\) | −10.5958 | −0.497287 | ||||||||
\(455\) | 4.34017 | 0.203470 | ||||||||
\(456\) | 3.07838 | 0.144158 | ||||||||
\(457\) | −29.0928 | −1.36090 | −0.680451 | − | 0.732794i | \(-0.738216\pi\) | ||||
−0.680451 | + | 0.732794i | \(0.738216\pi\) | |||||||
\(458\) | 7.16290 | 0.334700 | ||||||||
\(459\) | −5.75872 | −0.268794 | ||||||||
\(460\) | −1.00000 | −0.0466252 | ||||||||
\(461\) | −38.8638 | −1.81007 | −0.905033 | − | 0.425341i | \(-0.860154\pi\) | ||||
−0.905033 | + | 0.425341i | \(0.860154\pi\) | |||||||
\(462\) | −3.26180 | −0.151752 | ||||||||
\(463\) | −20.2557 | −0.941360 | −0.470680 | − | 0.882304i | \(-0.655991\pi\) | ||||
−0.470680 | + | 0.882304i | \(0.655991\pi\) | |||||||
\(464\) | 0.581449 | 0.0269931 | ||||||||
\(465\) | 3.07838 | 0.142756 | ||||||||
\(466\) | −19.3607 | −0.896867 | ||||||||
\(467\) | −12.0722 | −0.558636 | −0.279318 | − | 0.960199i | \(-0.590108\pi\) | ||||
−0.279318 | + | 0.960199i | \(0.590108\pi\) | |||||||
\(468\) | −4.34017 | −0.200625 | ||||||||
\(469\) | 0.738205 | 0.0340871 | ||||||||
\(470\) | −3.07838 | −0.141995 | ||||||||
\(471\) | −4.52359 | −0.208436 | ||||||||
\(472\) | 6.15676 | 0.283388 | ||||||||
\(473\) | 2.40787 | 0.110714 | ||||||||
\(474\) | 2.15676 | 0.0990631 | ||||||||
\(475\) | −3.07838 | −0.141246 | ||||||||
\(476\) | 5.75872 | 0.263951 | ||||||||
\(477\) | 8.83710 | 0.404623 | ||||||||
\(478\) | −5.41855 | −0.247839 | ||||||||
\(479\) | −41.5585 | −1.89886 | −0.949428 | − | 0.313985i | \(-0.898336\pi\) | ||||
−0.949428 | + | 0.313985i | \(0.898336\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −8.68035 | −0.395790 | ||||||||
\(482\) | 5.75872 | 0.262303 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | −0.360692 | −0.0163951 | ||||||||
\(485\) | 4.34017 | 0.197077 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −36.8827 | −1.67131 | −0.835657 | − | 0.549252i | \(-0.814913\pi\) | ||||
−0.835657 | + | 0.549252i | \(0.814913\pi\) | |||||||
\(488\) | 8.15676 | 0.369239 | ||||||||
\(489\) | −9.84324 | −0.445127 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | −23.5708 | −1.06373 | −0.531867 | − | 0.846828i | \(-0.678509\pi\) | ||||
−0.531867 | + | 0.846828i | \(0.678509\pi\) | |||||||
\(492\) | 8.83710 | 0.398407 | ||||||||
\(493\) | 3.34841 | 0.150805 | ||||||||
\(494\) | 13.3607 | 0.601126 | ||||||||
\(495\) | −3.26180 | −0.146607 | ||||||||
\(496\) | 3.07838 | 0.138223 | ||||||||
\(497\) | −5.41855 | −0.243055 | ||||||||
\(498\) | 9.60197 | 0.430274 | ||||||||
\(499\) | 4.79606 | 0.214701 | 0.107351 | − | 0.994221i | \(-0.465763\pi\) | ||||
0.107351 | + | 0.994221i | \(0.465763\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 5.91548 | 0.264284 | ||||||||
\(502\) | 17.1773 | 0.766659 | ||||||||
\(503\) | −14.4703 | −0.645197 | −0.322599 | − | 0.946536i | \(-0.604556\pi\) | ||||
−0.322599 | + | 0.946536i | \(0.604556\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | 1.81658 | 0.0808369 | ||||||||
\(506\) | 3.26180 | 0.145004 | ||||||||
\(507\) | −5.83710 | −0.259235 | ||||||||
\(508\) | 4.73820 | 0.210224 | ||||||||
\(509\) | 4.82273 | 0.213764 | 0.106882 | − | 0.994272i | \(-0.465913\pi\) | ||||
0.106882 | + | 0.994272i | \(0.465913\pi\) | |||||||
\(510\) | 5.75872 | 0.255001 | ||||||||
\(511\) | −6.31351 | −0.279293 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.07838 | 0.135914 | ||||||||
\(514\) | −11.6742 | −0.514927 | ||||||||
\(515\) | 2.52359 | 0.111203 | ||||||||
\(516\) | −0.738205 | −0.0324977 | ||||||||
\(517\) | 10.0410 | 0.441604 | ||||||||
\(518\) | 2.00000 | 0.0878750 | ||||||||
\(519\) | 11.2351 | 0.493168 | ||||||||
\(520\) | 4.34017 | 0.190329 | ||||||||
\(521\) | −31.8576 | −1.39571 | −0.697854 | − | 0.716240i | \(-0.745862\pi\) | ||||
−0.697854 | + | 0.716240i | \(0.745862\pi\) | |||||||
\(522\) | 0.581449 | 0.0254493 | ||||||||
\(523\) | −0.979481 | −0.0428297 | −0.0214149 | − | 0.999771i | \(-0.506817\pi\) | ||||
−0.0214149 | + | 0.999771i | \(0.506817\pi\) | |||||||
\(524\) | 17.6742 | 0.772101 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | −19.8843 | −0.866996 | ||||||||
\(527\) | 17.7275 | 0.772223 | ||||||||
\(528\) | −3.26180 | −0.141951 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −8.83710 | −0.383859 | ||||||||
\(531\) | 6.15676 | 0.267180 | ||||||||
\(532\) | −3.07838 | −0.133465 | ||||||||
\(533\) | 38.3545 | 1.66132 | ||||||||
\(534\) | −10.8638 | −0.470121 | ||||||||
\(535\) | −8.68035 | −0.375284 | ||||||||
\(536\) | 0.738205 | 0.0318856 | ||||||||
\(537\) | −12.3135 | −0.531367 | ||||||||
\(538\) | −9.70086 | −0.418234 | ||||||||
\(539\) | 3.26180 | 0.140495 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −3.47641 | −0.149463 | −0.0747313 | − | 0.997204i | \(-0.523810\pi\) | ||||
−0.0747313 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(542\) | 3.07838 | 0.132228 | ||||||||
\(543\) | −17.5174 | −0.751746 | ||||||||
\(544\) | 5.75872 | 0.246903 | ||||||||
\(545\) | −19.3607 | −0.829321 | ||||||||
\(546\) | 4.34017 | 0.185742 | ||||||||
\(547\) | −36.0288 | −1.54048 | −0.770239 | − | 0.637755i | \(-0.779863\pi\) | ||||
−0.770239 | + | 0.637755i | \(0.779863\pi\) | |||||||
\(548\) | 2.00000 | 0.0854358 | ||||||||
\(549\) | 8.15676 | 0.348122 | ||||||||
\(550\) | 3.26180 | 0.139083 | ||||||||
\(551\) | −1.78992 | −0.0762532 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | −2.15676 | −0.0917146 | ||||||||
\(554\) | −5.26180 | −0.223552 | ||||||||
\(555\) | 2.00000 | 0.0848953 | ||||||||
\(556\) | −0.680346 | −0.0288531 | ||||||||
\(557\) | 2.62702 | 0.111310 | 0.0556552 | − | 0.998450i | \(-0.482275\pi\) | ||||
0.0556552 | + | 0.998450i | \(0.482275\pi\) | |||||||
\(558\) | 3.07838 | 0.130318 | ||||||||
\(559\) | −3.20394 | −0.135512 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | −18.7838 | −0.793052 | ||||||||
\(562\) | 5.57531 | 0.235180 | ||||||||
\(563\) | 6.39803 | 0.269645 | 0.134822 | − | 0.990870i | \(-0.456954\pi\) | ||||
0.134822 | + | 0.990870i | \(0.456954\pi\) | |||||||
\(564\) | −3.07838 | −0.129623 | ||||||||
\(565\) | −8.15676 | −0.343157 | ||||||||
\(566\) | −6.65368 | −0.279675 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −5.41855 | −0.227357 | ||||||||
\(569\) | −14.6225 | −0.613007 | −0.306503 | − | 0.951870i | \(-0.599159\pi\) | ||||
−0.306503 | + | 0.951870i | \(0.599159\pi\) | |||||||
\(570\) | −3.07838 | −0.128939 | ||||||||
\(571\) | 6.10343 | 0.255421 | 0.127710 | − | 0.991812i | \(-0.459237\pi\) | ||||
0.127710 | + | 0.991812i | \(0.459237\pi\) | |||||||
\(572\) | −14.1568 | −0.591924 | ||||||||
\(573\) | 6.15676 | 0.257202 | ||||||||
\(574\) | −8.83710 | −0.368853 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −15.7275 | −0.654746 | −0.327373 | − | 0.944895i | \(-0.606163\pi\) | ||||
−0.327373 | + | 0.944895i | \(0.606163\pi\) | |||||||
\(578\) | 16.1629 | 0.672288 | ||||||||
\(579\) | −4.15676 | −0.172749 | ||||||||
\(580\) | −0.581449 | −0.0241434 | ||||||||
\(581\) | −9.60197 | −0.398357 | ||||||||
\(582\) | 4.34017 | 0.179906 | ||||||||
\(583\) | 28.8248 | 1.19380 | ||||||||
\(584\) | −6.31351 | −0.261255 | ||||||||
\(585\) | 4.34017 | 0.179444 | ||||||||
\(586\) | 6.68035 | 0.275963 | ||||||||
\(587\) | −6.32580 | −0.261094 | −0.130547 | − | 0.991442i | \(-0.541673\pi\) | ||||
−0.130547 | + | 0.991442i | \(0.541673\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | −9.47641 | −0.390469 | ||||||||
\(590\) | −6.15676 | −0.253470 | ||||||||
\(591\) | −12.1568 | −0.500062 | ||||||||
\(592\) | 2.00000 | 0.0821995 | ||||||||
\(593\) | 3.36069 | 0.138007 | 0.0690035 | − | 0.997616i | \(-0.478018\pi\) | ||||
0.0690035 | + | 0.997616i | \(0.478018\pi\) | |||||||
\(594\) | −3.26180 | −0.133833 | ||||||||
\(595\) | −5.75872 | −0.236085 | ||||||||
\(596\) | 10.0000 | 0.409616 | ||||||||
\(597\) | −18.5236 | −0.758120 | ||||||||
\(598\) | −4.34017 | −0.177483 | ||||||||
\(599\) | −2.09890 | −0.0857586 | −0.0428793 | − | 0.999080i | \(-0.513653\pi\) | ||||
−0.0428793 | + | 0.999080i | \(0.513653\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −24.8371 | −1.01313 | −0.506563 | − | 0.862203i | \(-0.669084\pi\) | ||||
−0.506563 | + | 0.862203i | \(0.669084\pi\) | |||||||
\(602\) | 0.738205 | 0.0300870 | ||||||||
\(603\) | 0.738205 | 0.0300620 | ||||||||
\(604\) | −4.68035 | −0.190441 | ||||||||
\(605\) | 0.360692 | 0.0146642 | ||||||||
\(606\) | 1.81658 | 0.0737936 | ||||||||
\(607\) | 8.38121 | 0.340183 | 0.170091 | − | 0.985428i | \(-0.445594\pi\) | ||||
0.170091 | + | 0.985428i | \(0.445594\pi\) | |||||||
\(608\) | −3.07838 | −0.124845 | ||||||||
\(609\) | −0.581449 | −0.0235615 | ||||||||
\(610\) | −8.15676 | −0.330257 | ||||||||
\(611\) | −13.3607 | −0.540516 | ||||||||
\(612\) | 5.75872 | 0.232783 | ||||||||
\(613\) | 14.9939 | 0.605596 | 0.302798 | − | 0.953055i | \(-0.402079\pi\) | ||||
0.302798 | + | 0.953055i | \(0.402079\pi\) | |||||||
\(614\) | 31.8843 | 1.28674 | ||||||||
\(615\) | −8.83710 | −0.356346 | ||||||||
\(616\) | 3.26180 | 0.131421 | ||||||||
\(617\) | −30.5113 | −1.22834 | −0.614169 | − | 0.789174i | \(-0.710509\pi\) | ||||
−0.614169 | + | 0.789174i | \(0.710509\pi\) | |||||||
\(618\) | 2.52359 | 0.101514 | ||||||||
\(619\) | −9.23513 | −0.371191 | −0.185596 | − | 0.982626i | \(-0.559421\pi\) | ||||
−0.185596 | + | 0.982626i | \(0.559421\pi\) | |||||||
\(620\) | −3.07838 | −0.123631 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 9.17727 | 0.367975 | ||||||||
\(623\) | 10.8638 | 0.435247 | ||||||||
\(624\) | 4.34017 | 0.173746 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −21.3340 | −0.852679 | ||||||||
\(627\) | 10.0410 | 0.401000 | ||||||||
\(628\) | 4.52359 | 0.180511 | ||||||||
\(629\) | 11.5174 | 0.459231 | ||||||||
\(630\) | −1.00000 | −0.0398410 | ||||||||
\(631\) | 2.89043 | 0.115066 | 0.0575330 | − | 0.998344i | \(-0.481677\pi\) | ||||
0.0575330 | + | 0.998344i | \(0.481677\pi\) | |||||||
\(632\) | −2.15676 | −0.0857911 | ||||||||
\(633\) | −27.2039 | −1.08126 | ||||||||
\(634\) | 6.99386 | 0.277762 | ||||||||
\(635\) | −4.73820 | −0.188030 | ||||||||
\(636\) | −8.83710 | −0.350414 | ||||||||
\(637\) | −4.34017 | −0.171964 | ||||||||
\(638\) | 1.89657 | 0.0750859 | ||||||||
\(639\) | −5.41855 | −0.214355 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −37.7731 | −1.49195 | −0.745974 | − | 0.665975i | \(-0.768016\pi\) | ||||
−0.745974 | + | 0.665975i | \(0.768016\pi\) | |||||||
\(642\) | −8.68035 | −0.342586 | ||||||||
\(643\) | 40.8638 | 1.61151 | 0.805755 | − | 0.592249i | \(-0.201760\pi\) | ||||
0.805755 | + | 0.592249i | \(0.201760\pi\) | |||||||
\(644\) | 1.00000 | 0.0394055 | ||||||||
\(645\) | 0.738205 | 0.0290668 | ||||||||
\(646\) | −17.7275 | −0.697480 | ||||||||
\(647\) | −6.03120 | −0.237111 | −0.118555 | − | 0.992947i | \(-0.537826\pi\) | ||||
−0.118555 | + | 0.992947i | \(0.537826\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 20.0821 | 0.788290 | ||||||||
\(650\) | −4.34017 | −0.170236 | ||||||||
\(651\) | −3.07838 | −0.120651 | ||||||||
\(652\) | 9.84324 | 0.385491 | ||||||||
\(653\) | −38.8248 | −1.51933 | −0.759666 | − | 0.650313i | \(-0.774638\pi\) | ||||
−0.759666 | + | 0.650313i | \(0.774638\pi\) | |||||||
\(654\) | −19.3607 | −0.757063 | ||||||||
\(655\) | −17.6742 | −0.690588 | ||||||||
\(656\) | −8.83710 | −0.345031 | ||||||||
\(657\) | −6.31351 | −0.246314 | ||||||||
\(658\) | 3.07838 | 0.120008 | ||||||||
\(659\) | −3.62863 | −0.141351 | −0.0706757 | − | 0.997499i | \(-0.522516\pi\) | ||||
−0.0706757 | + | 0.997499i | \(0.522516\pi\) | |||||||
\(660\) | 3.26180 | 0.126965 | ||||||||
\(661\) | 4.10343 | 0.159605 | 0.0798025 | − | 0.996811i | \(-0.474571\pi\) | ||||
0.0798025 | + | 0.996811i | \(0.474571\pi\) | |||||||
\(662\) | 2.83710 | 0.110267 | ||||||||
\(663\) | 24.9939 | 0.970681 | ||||||||
\(664\) | −9.60197 | −0.372629 | ||||||||
\(665\) | 3.07838 | 0.119374 | ||||||||
\(666\) | 2.00000 | 0.0774984 | ||||||||
\(667\) | 0.581449 | 0.0225138 | ||||||||
\(668\) | −5.91548 | −0.228877 | ||||||||
\(669\) | 0.496928 | 0.0192124 | ||||||||
\(670\) | −0.738205 | −0.0285193 | ||||||||
\(671\) | 26.6057 | 1.02710 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | −9.00614 | −0.347161 | −0.173581 | − | 0.984820i | \(-0.555534\pi\) | ||||
−0.173581 | + | 0.984820i | \(0.555534\pi\) | |||||||
\(674\) | 8.94828 | 0.344675 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 5.83710 | 0.224504 | ||||||||
\(677\) | 32.3012 | 1.24144 | 0.620718 | − | 0.784034i | \(-0.286841\pi\) | ||||
0.620718 | + | 0.784034i | \(0.286841\pi\) | |||||||
\(678\) | −8.15676 | −0.313258 | ||||||||
\(679\) | −4.34017 | −0.166561 | ||||||||
\(680\) | −5.75872 | −0.220837 | ||||||||
\(681\) | 10.5958 | 0.406033 | ||||||||
\(682\) | 10.0410 | 0.384491 | ||||||||
\(683\) | −29.7275 | −1.13749 | −0.568746 | − | 0.822513i | \(-0.692571\pi\) | ||||
−0.568746 | + | 0.822513i | \(0.692571\pi\) | |||||||
\(684\) | −3.07838 | −0.117705 | ||||||||
\(685\) | −2.00000 | −0.0764161 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −7.16290 | −0.273282 | ||||||||
\(688\) | 0.738205 | 0.0281438 | ||||||||
\(689\) | −38.3545 | −1.46119 | ||||||||
\(690\) | 1.00000 | 0.0380693 | ||||||||
\(691\) | −20.5113 | −0.780287 | −0.390143 | − | 0.920754i | \(-0.627575\pi\) | ||||
−0.390143 | + | 0.920754i | \(0.627575\pi\) | |||||||
\(692\) | −11.2351 | −0.427096 | ||||||||
\(693\) | 3.26180 | 0.123905 | ||||||||
\(694\) | 8.68035 | 0.329501 | ||||||||
\(695\) | 0.680346 | 0.0258070 | ||||||||
\(696\) | −0.581449 | −0.0220398 | ||||||||
\(697\) | −50.8904 | −1.92761 | ||||||||
\(698\) | 17.0784 | 0.646426 | ||||||||
\(699\) | 19.3607 | 0.732289 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 7.16290 | 0.270539 | 0.135269 | − | 0.990809i | \(-0.456810\pi\) | ||||
0.135269 | + | 0.990809i | \(0.456810\pi\) | |||||||
\(702\) | 4.34017 | 0.163809 | ||||||||
\(703\) | −6.15676 | −0.232206 | ||||||||
\(704\) | 3.26180 | 0.122934 | ||||||||
\(705\) | 3.07838 | 0.115938 | ||||||||
\(706\) | −11.1629 | −0.420121 | ||||||||
\(707\) | −1.81658 | −0.0683196 | ||||||||
\(708\) | −6.15676 | −0.231385 | ||||||||
\(709\) | 10.8494 | 0.407457 | 0.203729 | − | 0.979027i | \(-0.434694\pi\) | ||||
0.203729 | + | 0.979027i | \(0.434694\pi\) | |||||||
\(710\) | 5.41855 | 0.203355 | ||||||||
\(711\) | −2.15676 | −0.0808847 | ||||||||
\(712\) | 10.8638 | 0.407137 | ||||||||
\(713\) | 3.07838 | 0.115286 | ||||||||
\(714\) | −5.75872 | −0.215515 | ||||||||
\(715\) | 14.1568 | 0.529433 | ||||||||
\(716\) | 12.3135 | 0.460178 | ||||||||
\(717\) | 5.41855 | 0.202359 | ||||||||
\(718\) | 16.8781 | 0.629887 | ||||||||
\(719\) | −8.44360 | −0.314893 | −0.157447 | − | 0.987527i | \(-0.550326\pi\) | ||||
−0.157447 | + | 0.987527i | \(0.550326\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | −2.52359 | −0.0939834 | ||||||||
\(722\) | −9.52359 | −0.354431 | ||||||||
\(723\) | −5.75872 | −0.214169 | ||||||||
\(724\) | 17.5174 | 0.651031 | ||||||||
\(725\) | 0.581449 | 0.0215945 | ||||||||
\(726\) | 0.360692 | 0.0133865 | ||||||||
\(727\) | −9.72753 | −0.360774 | −0.180387 | − | 0.983596i | \(-0.557735\pi\) | ||||
−0.180387 | + | 0.983596i | \(0.557735\pi\) | |||||||
\(728\) | −4.34017 | −0.160858 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.31351 | 0.233674 | ||||||||
\(731\) | 4.25112 | 0.157233 | ||||||||
\(732\) | −8.15676 | −0.301482 | ||||||||
\(733\) | −14.4826 | −0.534925 | −0.267463 | − | 0.963568i | \(-0.586185\pi\) | ||||
−0.267463 | + | 0.963568i | \(0.586185\pi\) | |||||||
\(734\) | 16.1978 | 0.597871 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 2.40787 | 0.0886951 | ||||||||
\(738\) | −8.83710 | −0.325298 | ||||||||
\(739\) | 15.3197 | 0.563543 | 0.281771 | − | 0.959482i | \(-0.409078\pi\) | ||||
0.281771 | + | 0.959482i | \(0.409078\pi\) | |||||||
\(740\) | −2.00000 | −0.0735215 | ||||||||
\(741\) | −13.3607 | −0.490817 | ||||||||
\(742\) | 8.83710 | 0.324420 | ||||||||
\(743\) | 49.1917 | 1.80467 | 0.902333 | − | 0.431039i | \(-0.141853\pi\) | ||||
0.902333 | + | 0.431039i | \(0.141853\pi\) | |||||||
\(744\) | −3.07838 | −0.112859 | ||||||||
\(745\) | −10.0000 | −0.366372 | ||||||||
\(746\) | 7.67420 | 0.280973 | ||||||||
\(747\) | −9.60197 | −0.351318 | ||||||||
\(748\) | 18.7838 | 0.686803 | ||||||||
\(749\) | 8.68035 | 0.317173 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 8.73367 | 0.318696 | 0.159348 | − | 0.987222i | \(-0.449061\pi\) | ||||
0.159348 | + | 0.987222i | \(0.449061\pi\) | |||||||
\(752\) | 3.07838 | 0.112257 | ||||||||
\(753\) | −17.1773 | −0.625975 | ||||||||
\(754\) | −2.52359 | −0.0919037 | ||||||||
\(755\) | 4.68035 | 0.170335 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 7.72753 | 0.280862 | 0.140431 | − | 0.990090i | \(-0.455151\pi\) | ||||
0.140431 | + | 0.990090i | \(0.455151\pi\) | |||||||
\(758\) | 11.6332 | 0.422536 | ||||||||
\(759\) | −3.26180 | −0.118396 | ||||||||
\(760\) | 3.07838 | 0.111664 | ||||||||
\(761\) | 11.7899 | 0.427384 | 0.213692 | − | 0.976901i | \(-0.431451\pi\) | ||||
0.213692 | + | 0.976901i | \(0.431451\pi\) | |||||||
\(762\) | −4.73820 | −0.171647 | ||||||||
\(763\) | 19.3607 | 0.700904 | ||||||||
\(764\) | −6.15676 | −0.222744 | ||||||||
\(765\) | −5.75872 | −0.208207 | ||||||||
\(766\) | −5.36069 | −0.193690 | ||||||||
\(767\) | −26.7214 | −0.964853 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −12.4514 | −0.449007 | −0.224504 | − | 0.974473i | \(-0.572076\pi\) | ||||
−0.224504 | + | 0.974473i | \(0.572076\pi\) | |||||||
\(770\) | −3.26180 | −0.117547 | ||||||||
\(771\) | 11.6742 | 0.420436 | ||||||||
\(772\) | 4.15676 | 0.149605 | ||||||||
\(773\) | 4.83710 | 0.173978 | 0.0869892 | − | 0.996209i | \(-0.472275\pi\) | ||||
0.0869892 | + | 0.996209i | \(0.472275\pi\) | |||||||
\(774\) | 0.738205 | 0.0265342 | ||||||||
\(775\) | 3.07838 | 0.110579 | ||||||||
\(776\) | −4.34017 | −0.155803 | ||||||||
\(777\) | −2.00000 | −0.0717496 | ||||||||
\(778\) | −18.9939 | −0.680963 | ||||||||
\(779\) | 27.2039 | 0.974682 | ||||||||
\(780\) | −4.34017 | −0.155403 | ||||||||
\(781\) | −17.6742 | −0.632433 | ||||||||
\(782\) | 5.75872 | 0.205932 | ||||||||
\(783\) | −0.581449 | −0.0207793 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −4.52359 | −0.161454 | ||||||||
\(786\) | −17.6742 | −0.630418 | ||||||||
\(787\) | 21.8043 | 0.777239 | 0.388620 | − | 0.921398i | \(-0.372952\pi\) | ||||
0.388620 | + | 0.921398i | \(0.372952\pi\) | |||||||
\(788\) | 12.1568 | 0.433066 | ||||||||
\(789\) | 19.8843 | 0.707899 | ||||||||
\(790\) | 2.15676 | 0.0767339 | ||||||||
\(791\) | 8.15676 | 0.290021 | ||||||||
\(792\) | 3.26180 | 0.115903 | ||||||||
\(793\) | −35.4017 | −1.25715 | ||||||||
\(794\) | 0.707008 | 0.0250908 | ||||||||
\(795\) | 8.83710 | 0.313420 | ||||||||
\(796\) | 18.5236 | 0.656551 | ||||||||
\(797\) | −51.1917 | −1.81330 | −0.906651 | − | 0.421882i | \(-0.861370\pi\) | ||||
−0.906651 | + | 0.421882i | \(0.861370\pi\) | |||||||
\(798\) | 3.07838 | 0.108973 | ||||||||
\(799\) | 17.7275 | 0.627155 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 10.8638 | 0.383852 | ||||||||
\(802\) | −22.6225 | −0.798828 | ||||||||
\(803\) | −20.5934 | −0.726725 | ||||||||
\(804\) | −0.738205 | −0.0260345 | ||||||||
\(805\) | −1.00000 | −0.0352454 | ||||||||
\(806\) | −13.3607 | −0.470610 | ||||||||
\(807\) | 9.70086 | 0.341487 | ||||||||
\(808\) | −1.81658 | −0.0639071 | ||||||||
\(809\) | 33.8310 | 1.18943 | 0.594717 | − | 0.803935i | \(-0.297264\pi\) | ||||
0.594717 | + | 0.803935i | \(0.297264\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 11.6332 | 0.408496 | 0.204248 | − | 0.978919i | \(-0.434525\pi\) | ||||
0.204248 | + | 0.978919i | \(0.434525\pi\) | |||||||
\(812\) | 0.581449 | 0.0204049 | ||||||||
\(813\) | −3.07838 | −0.107963 | ||||||||
\(814\) | 6.52359 | 0.228652 | ||||||||
\(815\) | −9.84324 | −0.344794 | ||||||||
\(816\) | −5.75872 | −0.201596 | ||||||||
\(817\) | −2.27247 | −0.0795038 | ||||||||
\(818\) | −6.36683 | −0.222611 | ||||||||
\(819\) | −4.34017 | −0.151658 | ||||||||
\(820\) | 8.83710 | 0.308605 | ||||||||
\(821\) | −22.4247 | −0.782627 | −0.391314 | − | 0.920257i | \(-0.627979\pi\) | ||||
−0.391314 | + | 0.920257i | \(0.627979\pi\) | |||||||
\(822\) | −2.00000 | −0.0697580 | ||||||||
\(823\) | −19.2618 | −0.671424 | −0.335712 | − | 0.941965i | \(-0.608977\pi\) | ||||
−0.335712 | + | 0.941965i | \(0.608977\pi\) | |||||||
\(824\) | −2.52359 | −0.0879134 | ||||||||
\(825\) | −3.26180 | −0.113561 | ||||||||
\(826\) | 6.15676 | 0.214221 | ||||||||
\(827\) | 24.6803 | 0.858220 | 0.429110 | − | 0.903252i | \(-0.358827\pi\) | ||||
0.429110 | + | 0.903252i | \(0.358827\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | 24.5958 | 0.854248 | 0.427124 | − | 0.904193i | \(-0.359527\pi\) | ||||
0.427124 | + | 0.904193i | \(0.359527\pi\) | |||||||
\(830\) | 9.60197 | 0.333289 | ||||||||
\(831\) | 5.26180 | 0.182530 | ||||||||
\(832\) | −4.34017 | −0.150468 | ||||||||
\(833\) | 5.75872 | 0.199528 | ||||||||
\(834\) | 0.680346 | 0.0235585 | ||||||||
\(835\) | 5.91548 | 0.204714 | ||||||||
\(836\) | −10.0410 | −0.347277 | ||||||||
\(837\) | −3.07838 | −0.106404 | ||||||||
\(838\) | −19.0205 | −0.657053 | ||||||||
\(839\) | 26.1568 | 0.903031 | 0.451516 | − | 0.892263i | \(-0.350883\pi\) | ||||
0.451516 | + | 0.892263i | \(0.350883\pi\) | |||||||
\(840\) | 1.00000 | 0.0345033 | ||||||||
\(841\) | −28.6619 | −0.988342 | ||||||||
\(842\) | 14.6270 | 0.504080 | ||||||||
\(843\) | −5.57531 | −0.192024 | ||||||||
\(844\) | 27.2039 | 0.936398 | ||||||||
\(845\) | −5.83710 | −0.200802 | ||||||||
\(846\) | 3.07838 | 0.105837 | ||||||||
\(847\) | −0.360692 | −0.0123935 | ||||||||
\(848\) | 8.83710 | 0.303467 | ||||||||
\(849\) | 6.65368 | 0.228354 | ||||||||
\(850\) | 5.75872 | 0.197523 | ||||||||
\(851\) | 2.00000 | 0.0685591 | ||||||||
\(852\) | 5.41855 | 0.185636 | ||||||||
\(853\) | 3.03281 | 0.103841 | 0.0519206 | − | 0.998651i | \(-0.483466\pi\) | ||||
0.0519206 | + | 0.998651i | \(0.483466\pi\) | |||||||
\(854\) | 8.15676 | 0.279118 | ||||||||
\(855\) | 3.07838 | 0.105278 | ||||||||
\(856\) | 8.68035 | 0.296688 | ||||||||
\(857\) | −27.1629 | −0.927867 | −0.463933 | − | 0.885870i | \(-0.653562\pi\) | ||||
−0.463933 | + | 0.885870i | \(0.653562\pi\) | |||||||
\(858\) | 14.1568 | 0.483304 | ||||||||
\(859\) | −20.5113 | −0.699837 | −0.349918 | − | 0.936780i | \(-0.613791\pi\) | ||||
−0.349918 | + | 0.936780i | \(0.613791\pi\) | |||||||
\(860\) | −0.738205 | −0.0251726 | ||||||||
\(861\) | 8.83710 | 0.301168 | ||||||||
\(862\) | 15.8310 | 0.539205 | ||||||||
\(863\) | 14.0410 | 0.477962 | 0.238981 | − | 0.971024i | \(-0.423187\pi\) | ||||
0.238981 | + | 0.971024i | \(0.423187\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 11.2351 | 0.382006 | ||||||||
\(866\) | 10.6947 | 0.363421 | ||||||||
\(867\) | −16.1629 | −0.548921 | ||||||||
\(868\) | 3.07838 | 0.104487 | ||||||||
\(869\) | −7.03489 | −0.238642 | ||||||||
\(870\) | 0.581449 | 0.0197130 | ||||||||
\(871\) | −3.20394 | −0.108561 | ||||||||
\(872\) | 19.3607 | 0.655636 | ||||||||
\(873\) | −4.34017 | −0.146893 | ||||||||
\(874\) | −3.07838 | −0.104128 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 6.31351 | 0.213314 | ||||||||
\(877\) | −35.8141 | −1.20936 | −0.604679 | − | 0.796469i | \(-0.706698\pi\) | ||||
−0.604679 | + | 0.796469i | \(0.706698\pi\) | |||||||
\(878\) | 16.3857 | 0.552992 | ||||||||
\(879\) | −6.68035 | −0.225322 | ||||||||
\(880\) | −3.26180 | −0.109955 | ||||||||
\(881\) | −42.3279 | −1.42606 | −0.713031 | − | 0.701132i | \(-0.752678\pi\) | ||||
−0.713031 | + | 0.701132i | \(0.752678\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | −6.78378 | −0.228292 | −0.114146 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(884\) | −24.9939 | −0.840634 | ||||||||
\(885\) | 6.15676 | 0.206957 | ||||||||
\(886\) | 0.680346 | 0.0228567 | ||||||||
\(887\) | 49.6307 | 1.66644 | 0.833218 | − | 0.552944i | \(-0.186496\pi\) | ||||
0.833218 | + | 0.552944i | \(0.186496\pi\) | |||||||
\(888\) | −2.00000 | −0.0671156 | ||||||||
\(889\) | 4.73820 | 0.158914 | ||||||||
\(890\) | −10.8638 | −0.364154 | ||||||||
\(891\) | 3.26180 | 0.109274 | ||||||||
\(892\) | −0.496928 | −0.0166384 | ||||||||
\(893\) | −9.47641 | −0.317116 | ||||||||
\(894\) | −10.0000 | −0.334450 | ||||||||
\(895\) | −12.3135 | −0.411595 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 4.34017 | 0.144914 | ||||||||
\(898\) | 33.7152 | 1.12509 | ||||||||
\(899\) | 1.78992 | 0.0596972 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 50.8904 | 1.69541 | ||||||||
\(902\) | −28.8248 | −0.959761 | ||||||||
\(903\) | −0.738205 | −0.0245659 | ||||||||
\(904\) | 8.15676 | 0.271290 | ||||||||
\(905\) | −17.5174 | −0.582300 | ||||||||
\(906\) | 4.68035 | 0.155494 | ||||||||
\(907\) | −33.1050 | −1.09923 | −0.549617 | − | 0.835416i | \(-0.685226\pi\) | ||||
−0.549617 | + | 0.835416i | \(0.685226\pi\) | |||||||
\(908\) | −10.5958 | −0.351635 | ||||||||
\(909\) | −1.81658 | −0.0602522 | ||||||||
\(910\) | 4.34017 | 0.143875 | ||||||||
\(911\) | −26.3545 | −0.873165 | −0.436583 | − | 0.899664i | \(-0.643811\pi\) | ||||
−0.436583 | + | 0.899664i | \(0.643811\pi\) | |||||||
\(912\) | 3.07838 | 0.101935 | ||||||||
\(913\) | −31.3197 | −1.03653 | ||||||||
\(914\) | −29.0928 | −0.962303 | ||||||||
\(915\) | 8.15676 | 0.269654 | ||||||||
\(916\) | 7.16290 | 0.236669 | ||||||||
\(917\) | 17.6742 | 0.583654 | ||||||||
\(918\) | −5.75872 | −0.190066 | ||||||||
\(919\) | 32.3668 | 1.06768 | 0.533842 | − | 0.845584i | \(-0.320748\pi\) | ||||
0.533842 | + | 0.845584i | \(0.320748\pi\) | |||||||
\(920\) | −1.00000 | −0.0329690 | ||||||||
\(921\) | −31.8843 | −1.05062 | ||||||||
\(922\) | −38.8638 | −1.27991 | ||||||||
\(923\) | 23.5174 | 0.774086 | ||||||||
\(924\) | −3.26180 | −0.107305 | ||||||||
\(925\) | 2.00000 | 0.0657596 | ||||||||
\(926\) | −20.2557 | −0.665642 | ||||||||
\(927\) | −2.52359 | −0.0828856 | ||||||||
\(928\) | 0.581449 | 0.0190870 | ||||||||
\(929\) | 43.1917 | 1.41707 | 0.708536 | − | 0.705675i | \(-0.249356\pi\) | ||||
0.708536 | + | 0.705675i | \(0.249356\pi\) | |||||||
\(930\) | 3.07838 | 0.100944 | ||||||||
\(931\) | −3.07838 | −0.100890 | ||||||||
\(932\) | −19.3607 | −0.634181 | ||||||||
\(933\) | −9.17727 | −0.300450 | ||||||||
\(934\) | −12.0722 | −0.395016 | ||||||||
\(935\) | −18.7838 | −0.614295 | ||||||||
\(936\) | −4.34017 | −0.141863 | ||||||||
\(937\) | −35.8576 | −1.17142 | −0.585709 | − | 0.810522i | \(-0.699184\pi\) | ||||
−0.585709 | + | 0.810522i | \(0.699184\pi\) | |||||||
\(938\) | 0.738205 | 0.0241032 | ||||||||
\(939\) | 21.3340 | 0.696210 | ||||||||
\(940\) | −3.07838 | −0.100406 | ||||||||
\(941\) | 11.3607 | 0.370348 | 0.185174 | − | 0.982706i | \(-0.440715\pi\) | ||||
0.185174 | + | 0.982706i | \(0.440715\pi\) | |||||||
\(942\) | −4.52359 | −0.147387 | ||||||||
\(943\) | −8.83710 | −0.287776 | ||||||||
\(944\) | 6.15676 | 0.200385 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 2.40787 | 0.0782867 | ||||||||
\(947\) | −27.9376 | −0.907850 | −0.453925 | − | 0.891040i | \(-0.649977\pi\) | ||||
−0.453925 | + | 0.891040i | \(0.649977\pi\) | |||||||
\(948\) | 2.15676 | 0.0700482 | ||||||||
\(949\) | 27.4017 | 0.889498 | ||||||||
\(950\) | −3.07838 | −0.0998758 | ||||||||
\(951\) | −6.99386 | −0.226791 | ||||||||
\(952\) | 5.75872 | 0.186641 | ||||||||
\(953\) | −38.8781 | −1.25939 | −0.629693 | − | 0.776844i | \(-0.716819\pi\) | ||||
−0.629693 | + | 0.776844i | \(0.716819\pi\) | |||||||
\(954\) | 8.83710 | 0.286112 | ||||||||
\(955\) | 6.15676 | 0.199228 | ||||||||
\(956\) | −5.41855 | −0.175248 | ||||||||
\(957\) | −1.89657 | −0.0613074 | ||||||||
\(958\) | −41.5585 | −1.34269 | ||||||||
\(959\) | 2.00000 | 0.0645834 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −21.5236 | −0.694309 | ||||||||
\(962\) | −8.68035 | −0.279866 | ||||||||
\(963\) | 8.68035 | 0.279720 | ||||||||
\(964\) | 5.75872 | 0.185476 | ||||||||
\(965\) | −4.15676 | −0.133811 | ||||||||
\(966\) | −1.00000 | −0.0321745 | ||||||||
\(967\) | 39.0928 | 1.25714 | 0.628569 | − | 0.777754i | \(-0.283641\pi\) | ||||
0.628569 | + | 0.777754i | \(0.283641\pi\) | |||||||
\(968\) | −0.360692 | −0.0115931 | ||||||||
\(969\) | 17.7275 | 0.569490 | ||||||||
\(970\) | 4.34017 | 0.139355 | ||||||||
\(971\) | −2.50921 | −0.0805245 | −0.0402623 | − | 0.999189i | \(-0.512819\pi\) | ||||
−0.0402623 | + | 0.999189i | \(0.512819\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −0.680346 | −0.0218109 | ||||||||
\(974\) | −36.8827 | −1.18180 | ||||||||
\(975\) | 4.34017 | 0.138997 | ||||||||
\(976\) | 8.15676 | 0.261091 | ||||||||
\(977\) | −47.8720 | −1.53156 | −0.765780 | − | 0.643102i | \(-0.777647\pi\) | ||||
−0.765780 | + | 0.643102i | \(0.777647\pi\) | |||||||
\(978\) | −9.84324 | −0.314752 | ||||||||
\(979\) | 35.4354 | 1.13252 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 19.3607 | 0.618139 | ||||||||
\(982\) | −23.5708 | −0.752174 | ||||||||
\(983\) | 0.313511 | 0.00999945 | 0.00499972 | − | 0.999988i | \(-0.498409\pi\) | ||||
0.00499972 | + | 0.999988i | \(0.498409\pi\) | |||||||
\(984\) | 8.83710 | 0.281717 | ||||||||
\(985\) | −12.1568 | −0.387346 | ||||||||
\(986\) | 3.34841 | 0.106635 | ||||||||
\(987\) | −3.07838 | −0.0979858 | ||||||||
\(988\) | 13.3607 | 0.425060 | ||||||||
\(989\) | 0.738205 | 0.0234735 | ||||||||
\(990\) | −3.26180 | −0.103667 | ||||||||
\(991\) | 43.7152 | 1.38866 | 0.694330 | − | 0.719657i | \(-0.255701\pi\) | ||||
0.694330 | + | 0.719657i | \(0.255701\pi\) | |||||||
\(992\) | 3.07838 | 0.0977386 | ||||||||
\(993\) | −2.83710 | −0.0900327 | ||||||||
\(994\) | −5.41855 | −0.171866 | ||||||||
\(995\) | −18.5236 | −0.587237 | ||||||||
\(996\) | 9.60197 | 0.304250 | ||||||||
\(997\) | 6.38121 | 0.202095 | 0.101047 | − | 0.994882i | \(-0.467781\pi\) | ||||
0.101047 | + | 0.994882i | \(0.467781\pi\) | |||||||
\(998\) | 4.79606 | 0.151817 | ||||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 4830.2.a.bz.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4830.2.a.bz.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial |