Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4477,2,Mod(1,4477)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4477, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4477.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4477 = 11^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4477.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: | \(35.7490249849\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 16 x^{9} + 32 x^{8} + 89 x^{7} - 179 x^{6} - 201 x^{5} + 407 x^{4} + 168 x^{3} + \cdots + 75 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 407) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-1.77363\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4477.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.77363 | 1.25414 | 0.627072 | − | 0.778961i | \(-0.284253\pi\) | ||||
0.627072 | + | 0.778961i | \(0.284253\pi\) | |||||||
\(3\) | 2.13379 | 1.23194 | 0.615972 | − | 0.787768i | \(-0.288764\pi\) | ||||
0.615972 | + | 0.787768i | \(0.288764\pi\) | |||||||
\(4\) | 1.14575 | 0.572876 | ||||||||
\(5\) | 0.365878 | 0.163625 | 0.0818127 | − | 0.996648i | \(-0.473929\pi\) | ||||
0.0818127 | + | 0.996648i | \(0.473929\pi\) | |||||||
\(6\) | 3.78454 | 1.54503 | ||||||||
\(7\) | −3.16809 | −1.19742 | −0.598712 | − | 0.800964i | \(-0.704321\pi\) | ||||
−0.598712 | + | 0.800964i | \(0.704321\pi\) | |||||||
\(8\) | −1.51512 | −0.535675 | ||||||||
\(9\) | 1.55305 | 0.517685 | ||||||||
\(10\) | 0.648930 | 0.205210 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.44479 | 0.705751 | ||||||||
\(13\) | −0.746710 | −0.207100 | −0.103550 | − | 0.994624i | \(-0.533020\pi\) | ||||
−0.103550 | + | 0.994624i | \(0.533020\pi\) | |||||||
\(14\) | −5.61900 | −1.50174 | ||||||||
\(15\) | 0.780706 | 0.201577 | ||||||||
\(16\) | −4.97876 | −1.24469 | ||||||||
\(17\) | 1.19144 | 0.288967 | 0.144484 | − | 0.989507i | \(-0.453848\pi\) | ||||
0.144484 | + | 0.989507i | \(0.453848\pi\) | |||||||
\(18\) | 2.75454 | 0.649251 | ||||||||
\(19\) | −7.87275 | −1.80613 | −0.903067 | − | 0.429500i | \(-0.858690\pi\) | ||||
−0.903067 | + | 0.429500i | \(0.858690\pi\) | |||||||
\(20\) | 0.419205 | 0.0937371 | ||||||||
\(21\) | −6.76003 | −1.47516 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.823054 | −0.171619 | −0.0858093 | − | 0.996312i | \(-0.527348\pi\) | ||||
−0.0858093 | + | 0.996312i | \(0.527348\pi\) | |||||||
\(24\) | −3.23294 | −0.659921 | ||||||||
\(25\) | −4.86613 | −0.973227 | ||||||||
\(26\) | −1.32438 | −0.259733 | ||||||||
\(27\) | −3.08748 | −0.594185 | ||||||||
\(28\) | −3.62984 | −0.685975 | ||||||||
\(29\) | −0.0852041 | −0.0158220 | −0.00791100 | − | 0.999969i | \(-0.502518\pi\) | ||||
−0.00791100 | + | 0.999969i | \(0.502518\pi\) | |||||||
\(30\) | 1.38468 | 0.252807 | ||||||||
\(31\) | 4.67963 | 0.840485 | 0.420243 | − | 0.907412i | \(-0.361945\pi\) | ||||
0.420243 | + | 0.907412i | \(0.361945\pi\) | |||||||
\(32\) | −5.80022 | −1.02534 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.11317 | 0.362406 | ||||||||
\(35\) | −1.15913 | −0.195929 | ||||||||
\(36\) | 1.77941 | 0.296569 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −13.9633 | −2.26515 | ||||||||
\(39\) | −1.59332 | −0.255135 | ||||||||
\(40\) | −0.554348 | −0.0876501 | ||||||||
\(41\) | −3.00659 | −0.469551 | −0.234776 | − | 0.972050i | \(-0.575436\pi\) | ||||
−0.234776 | + | 0.972050i | \(0.575436\pi\) | |||||||
\(42\) | −11.9898 | −1.85006 | ||||||||
\(43\) | −4.23694 | −0.646128 | −0.323064 | − | 0.946377i | \(-0.604713\pi\) | ||||
−0.323064 | + | 0.946377i | \(0.604713\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.568228 | 0.0847064 | ||||||||
\(46\) | −1.45979 | −0.215234 | ||||||||
\(47\) | 0.227652 | 0.0332065 | 0.0166032 | − | 0.999862i | \(-0.494715\pi\) | ||||
0.0166032 | + | 0.999862i | \(0.494715\pi\) | |||||||
\(48\) | −10.6236 | −1.53339 | ||||||||
\(49\) | 3.03677 | 0.433824 | ||||||||
\(50\) | −8.63070 | −1.22057 | ||||||||
\(51\) | 2.54229 | 0.355991 | ||||||||
\(52\) | −0.855544 | −0.118643 | ||||||||
\(53\) | −2.21852 | −0.304737 | −0.152369 | − | 0.988324i | \(-0.548690\pi\) | ||||
−0.152369 | + | 0.988324i | \(0.548690\pi\) | |||||||
\(54\) | −5.47603 | −0.745194 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.80002 | 0.641430 | ||||||||
\(57\) | −16.7988 | −2.22505 | ||||||||
\(58\) | −0.151120 | −0.0198431 | ||||||||
\(59\) | 6.31092 | 0.821611 | 0.410806 | − | 0.911723i | \(-0.365247\pi\) | ||||
0.410806 | + | 0.911723i | \(0.365247\pi\) | |||||||
\(60\) | 0.894495 | 0.115479 | ||||||||
\(61\) | −4.85841 | −0.622055 | −0.311028 | − | 0.950401i | \(-0.600673\pi\) | ||||
−0.311028 | + | 0.950401i | \(0.600673\pi\) | |||||||
\(62\) | 8.29991 | 1.05409 | ||||||||
\(63\) | −4.92021 | −0.619888 | ||||||||
\(64\) | −0.329914 | −0.0412393 | ||||||||
\(65\) | −0.273204 | −0.0338868 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.9582 | 1.70527 | 0.852634 | − | 0.522508i | \(-0.175004\pi\) | ||||
0.852634 | + | 0.522508i | \(0.175004\pi\) | |||||||
\(68\) | 1.36510 | 0.165542 | ||||||||
\(69\) | −1.75622 | −0.211425 | ||||||||
\(70\) | −2.05587 | −0.245723 | ||||||||
\(71\) | −14.5753 | −1.72977 | −0.864887 | − | 0.501966i | \(-0.832610\pi\) | ||||
−0.864887 | + | 0.501966i | \(0.832610\pi\) | |||||||
\(72\) | −2.35306 | −0.277311 | ||||||||
\(73\) | 7.13033 | 0.834543 | 0.417271 | − | 0.908782i | \(-0.362987\pi\) | ||||
0.417271 | + | 0.908782i | \(0.362987\pi\) | |||||||
\(74\) | 1.77363 | 0.206180 | ||||||||
\(75\) | −10.3833 | −1.19896 | ||||||||
\(76\) | −9.02022 | −1.03469 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.82596 | −0.319976 | ||||||||
\(79\) | −3.19565 | −0.359539 | −0.179769 | − | 0.983709i | \(-0.557535\pi\) | ||||
−0.179769 | + | 0.983709i | \(0.557535\pi\) | |||||||
\(80\) | −1.82162 | −0.203663 | ||||||||
\(81\) | −11.2472 | −1.24969 | ||||||||
\(82\) | −5.33258 | −0.588885 | ||||||||
\(83\) | 16.0225 | 1.75870 | 0.879348 | − | 0.476179i | \(-0.157979\pi\) | ||||
0.879348 | + | 0.476179i | \(0.157979\pi\) | |||||||
\(84\) | −7.74531 | −0.845083 | ||||||||
\(85\) | 0.435922 | 0.0472824 | ||||||||
\(86\) | −7.51476 | −0.810337 | ||||||||
\(87\) | −0.181808 | −0.0194918 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.393159 | −0.0416748 | −0.0208374 | − | 0.999783i | \(-0.506633\pi\) | ||||
−0.0208374 | + | 0.999783i | \(0.506633\pi\) | |||||||
\(90\) | 1.00782 | 0.106234 | ||||||||
\(91\) | 2.36564 | 0.247986 | ||||||||
\(92\) | −0.943016 | −0.0983162 | ||||||||
\(93\) | 9.98533 | 1.03543 | ||||||||
\(94\) | 0.403770 | 0.0416457 | ||||||||
\(95\) | −2.88046 | −0.295529 | ||||||||
\(96\) | −12.3764 | −1.26317 | ||||||||
\(97\) | −17.7126 | −1.79844 | −0.899220 | − | 0.437497i | \(-0.855865\pi\) | ||||
−0.899220 | + | 0.437497i | \(0.855865\pi\) | |||||||
\(98\) | 5.38610 | 0.544078 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.57538 | −0.557538 | ||||||||
\(101\) | 10.7441 | 1.06908 | 0.534540 | − | 0.845143i | \(-0.320485\pi\) | ||||
0.534540 | + | 0.845143i | \(0.320485\pi\) | |||||||
\(102\) | 4.50906 | 0.446464 | ||||||||
\(103\) | −5.42658 | −0.534697 | −0.267348 | − | 0.963600i | \(-0.586147\pi\) | ||||
−0.267348 | + | 0.963600i | \(0.586147\pi\) | |||||||
\(104\) | 1.13135 | 0.110938 | ||||||||
\(105\) | −2.47334 | −0.241374 | ||||||||
\(106\) | −3.93483 | −0.382184 | ||||||||
\(107\) | 1.93352 | 0.186921 | 0.0934604 | − | 0.995623i | \(-0.470207\pi\) | ||||
0.0934604 | + | 0.995623i | \(0.470207\pi\) | |||||||
\(108\) | −3.53748 | −0.340395 | ||||||||
\(109\) | 11.9480 | 1.14441 | 0.572204 | − | 0.820112i | \(-0.306089\pi\) | ||||
0.572204 | + | 0.820112i | \(0.306089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.13379 | 0.202530 | ||||||||
\(112\) | 15.7731 | 1.49042 | ||||||||
\(113\) | −12.8704 | −1.21074 | −0.605370 | − | 0.795944i | \(-0.706975\pi\) | ||||
−0.605370 | + | 0.795944i | \(0.706975\pi\) | |||||||
\(114\) | −29.7948 | −2.79054 | ||||||||
\(115\) | −0.301137 | −0.0280812 | ||||||||
\(116\) | −0.0976227 | −0.00906404 | ||||||||
\(117\) | −1.15968 | −0.107212 | ||||||||
\(118\) | 11.1932 | 1.03042 | ||||||||
\(119\) | −3.77459 | −0.346016 | ||||||||
\(120\) | −1.18286 | −0.107980 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −8.61700 | −0.780146 | ||||||||
\(123\) | −6.41544 | −0.578460 | ||||||||
\(124\) | 5.36169 | 0.481494 | ||||||||
\(125\) | −3.60980 | −0.322870 | ||||||||
\(126\) | −8.72661 | −0.777428 | ||||||||
\(127\) | −10.9804 | −0.974351 | −0.487175 | − | 0.873304i | \(-0.661973\pi\) | ||||
−0.487175 | + | 0.873304i | \(0.661973\pi\) | |||||||
\(128\) | 11.0153 | 0.973624 | ||||||||
\(129\) | −9.04074 | −0.795993 | ||||||||
\(130\) | −0.484563 | −0.0424989 | ||||||||
\(131\) | 10.7804 | 0.941888 | 0.470944 | − | 0.882163i | \(-0.343913\pi\) | ||||
0.470944 | + | 0.882163i | \(0.343913\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24.9416 | 2.16271 | ||||||||
\(134\) | 24.7567 | 2.13865 | ||||||||
\(135\) | −1.12964 | −0.0972239 | ||||||||
\(136\) | −1.80517 | −0.154792 | ||||||||
\(137\) | 17.2946 | 1.47758 | 0.738789 | − | 0.673937i | \(-0.235398\pi\) | ||||
0.738789 | + | 0.673937i | \(0.235398\pi\) | |||||||
\(138\) | −3.11489 | −0.265157 | ||||||||
\(139\) | 5.28772 | 0.448498 | 0.224249 | − | 0.974532i | \(-0.428007\pi\) | ||||
0.224249 | + | 0.974532i | \(0.428007\pi\) | |||||||
\(140\) | −1.32808 | −0.112243 | ||||||||
\(141\) | 0.485761 | 0.0409085 | ||||||||
\(142\) | −25.8512 | −2.16939 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −7.73228 | −0.644356 | ||||||||
\(145\) | −0.0311743 | −0.00258888 | ||||||||
\(146\) | 12.6466 | 1.04664 | ||||||||
\(147\) | 6.47983 | 0.534447 | ||||||||
\(148\) | 1.14575 | 0.0941802 | ||||||||
\(149\) | 6.31538 | 0.517376 | 0.258688 | − | 0.965961i | \(-0.416710\pi\) | ||||
0.258688 | + | 0.965961i | \(0.416710\pi\) | |||||||
\(150\) | −18.4161 | −1.50367 | ||||||||
\(151\) | −1.86028 | −0.151387 | −0.0756937 | − | 0.997131i | \(-0.524117\pi\) | ||||
−0.0756937 | + | 0.997131i | \(0.524117\pi\) | |||||||
\(152\) | 11.9281 | 0.967500 | ||||||||
\(153\) | 1.85037 | 0.149594 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.71217 | 0.137525 | ||||||||
\(156\) | −1.82555 | −0.146161 | ||||||||
\(157\) | 8.75410 | 0.698653 | 0.349326 | − | 0.937001i | \(-0.386410\pi\) | ||||
0.349326 | + | 0.937001i | \(0.386410\pi\) | |||||||
\(158\) | −5.66789 | −0.450913 | ||||||||
\(159\) | −4.73385 | −0.375419 | ||||||||
\(160\) | −2.12217 | −0.167772 | ||||||||
\(161\) | 2.60751 | 0.205500 | ||||||||
\(162\) | −19.9483 | −1.56729 | ||||||||
\(163\) | −8.83915 | −0.692335 | −0.346168 | − | 0.938173i | \(-0.612517\pi\) | ||||
−0.346168 | + | 0.938173i | \(0.612517\pi\) | |||||||
\(164\) | −3.44481 | −0.268995 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 28.4179 | 2.20566 | ||||||||
\(167\) | −9.82258 | −0.760094 | −0.380047 | − | 0.924967i | \(-0.624092\pi\) | ||||
−0.380047 | + | 0.924967i | \(0.624092\pi\) | |||||||
\(168\) | 10.2422 | 0.790205 | ||||||||
\(169\) | −12.4424 | −0.957110 | ||||||||
\(170\) | 0.773163 | 0.0592989 | ||||||||
\(171\) | −12.2268 | −0.935007 | ||||||||
\(172\) | −4.85449 | −0.370151 | ||||||||
\(173\) | −14.6677 | −1.11517 | −0.557584 | − | 0.830121i | \(-0.688271\pi\) | ||||
−0.557584 | + | 0.830121i | \(0.688271\pi\) | |||||||
\(174\) | −0.322459 | −0.0244455 | ||||||||
\(175\) | 15.4163 | 1.16537 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.4662 | 1.01218 | ||||||||
\(178\) | −0.697317 | −0.0522661 | ||||||||
\(179\) | 6.51334 | 0.486830 | 0.243415 | − | 0.969922i | \(-0.421732\pi\) | ||||
0.243415 | + | 0.969922i | \(0.421732\pi\) | |||||||
\(180\) | 0.651048 | 0.0485262 | ||||||||
\(181\) | −19.9316 | −1.48151 | −0.740754 | − | 0.671776i | \(-0.765532\pi\) | ||||
−0.740754 | + | 0.671776i | \(0.765532\pi\) | |||||||
\(182\) | 4.19576 | 0.311011 | ||||||||
\(183\) | −10.3668 | −0.766337 | ||||||||
\(184\) | 1.24702 | 0.0919318 | ||||||||
\(185\) | 0.365878 | 0.0268999 | ||||||||
\(186\) | 17.7102 | 1.29858 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.260833 | 0.0190232 | ||||||||
\(189\) | 9.78140 | 0.711492 | ||||||||
\(190\) | −5.10887 | −0.370636 | ||||||||
\(191\) | −10.6146 | −0.768045 | −0.384022 | − | 0.923324i | \(-0.625461\pi\) | ||||
−0.384022 | + | 0.923324i | \(0.625461\pi\) | |||||||
\(192\) | −0.703968 | −0.0508045 | ||||||||
\(193\) | −22.5264 | −1.62149 | −0.810743 | − | 0.585402i | \(-0.800937\pi\) | ||||
−0.810743 | + | 0.585402i | \(0.800937\pi\) | |||||||
\(194\) | −31.4155 | −2.25550 | ||||||||
\(195\) | −0.582960 | −0.0417467 | ||||||||
\(196\) | 3.47939 | 0.248528 | ||||||||
\(197\) | 8.52432 | 0.607332 | 0.303666 | − | 0.952778i | \(-0.401789\pi\) | ||||
0.303666 | + | 0.952778i | \(0.401789\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.91560 | −0.561122 | −0.280561 | − | 0.959836i | \(-0.590520\pi\) | ||||
−0.280561 | + | 0.959836i | \(0.590520\pi\) | |||||||
\(200\) | 7.37276 | 0.521333 | ||||||||
\(201\) | 29.7839 | 2.10079 | ||||||||
\(202\) | 19.0561 | 1.34078 | ||||||||
\(203\) | 0.269934 | 0.0189456 | ||||||||
\(204\) | 2.91283 | 0.203939 | ||||||||
\(205\) | −1.10005 | −0.0768305 | ||||||||
\(206\) | −9.62473 | −0.670587 | ||||||||
\(207\) | −1.27825 | −0.0888443 | ||||||||
\(208\) | 3.71768 | 0.257775 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.38679 | −0.302717 | ||||||||
\(211\) | −0.698266 | −0.0480706 | −0.0240353 | − | 0.999711i | \(-0.507651\pi\) | ||||
−0.0240353 | + | 0.999711i | \(0.507651\pi\) | |||||||
\(212\) | −2.54187 | −0.174577 | ||||||||
\(213\) | −31.1007 | −2.13098 | ||||||||
\(214\) | 3.42935 | 0.234425 | ||||||||
\(215\) | −1.55020 | −0.105723 | ||||||||
\(216\) | 4.67789 | 0.318290 | ||||||||
\(217\) | −14.8255 | −1.00642 | ||||||||
\(218\) | 21.1912 | 1.43525 | ||||||||
\(219\) | 15.2146 | 1.02811 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.889661 | −0.0598451 | ||||||||
\(222\) | 3.78454 | 0.254002 | ||||||||
\(223\) | −25.4482 | −1.70414 | −0.852068 | − | 0.523432i | \(-0.824652\pi\) | ||||
−0.852068 | + | 0.523432i | \(0.824652\pi\) | |||||||
\(224\) | 18.3756 | 1.22777 | ||||||||
\(225\) | −7.55737 | −0.503824 | ||||||||
\(226\) | −22.8272 | −1.51844 | ||||||||
\(227\) | −1.54858 | −0.102783 | −0.0513914 | − | 0.998679i | \(-0.516366\pi\) | ||||
−0.0513914 | + | 0.998679i | \(0.516366\pi\) | |||||||
\(228\) | −19.2472 | −1.27468 | ||||||||
\(229\) | −1.31151 | −0.0866669 | −0.0433334 | − | 0.999061i | \(-0.513798\pi\) | ||||
−0.0433334 | + | 0.999061i | \(0.513798\pi\) | |||||||
\(230\) | −0.534105 | −0.0352178 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.129094 | 0.00847545 | ||||||||
\(233\) | −26.1180 | −1.71105 | −0.855524 | − | 0.517763i | \(-0.826765\pi\) | ||||
−0.855524 | + | 0.517763i | \(0.826765\pi\) | |||||||
\(234\) | −2.05684 | −0.134460 | ||||||||
\(235\) | 0.0832928 | 0.00543342 | ||||||||
\(236\) | 7.23074 | 0.470681 | ||||||||
\(237\) | −6.81885 | −0.442932 | ||||||||
\(238\) | −6.69472 | −0.433954 | ||||||||
\(239\) | 7.98922 | 0.516780 | 0.258390 | − | 0.966041i | \(-0.416808\pi\) | ||||
0.258390 | + | 0.966041i | \(0.416808\pi\) | |||||||
\(240\) | −3.88694 | −0.250901 | ||||||||
\(241\) | −7.64335 | −0.492351 | −0.246176 | − | 0.969225i | \(-0.579174\pi\) | ||||
−0.246176 | + | 0.969225i | \(0.579174\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7367 | −0.945359 | ||||||||
\(244\) | −5.56653 | −0.356360 | ||||||||
\(245\) | 1.11109 | 0.0709847 | ||||||||
\(246\) | −11.3786 | −0.725472 | ||||||||
\(247\) | 5.87866 | 0.374050 | ||||||||
\(248\) | −7.09018 | −0.450227 | ||||||||
\(249\) | 34.1886 | 2.16662 | ||||||||
\(250\) | −6.40243 | −0.404926 | ||||||||
\(251\) | 6.63199 | 0.418607 | 0.209304 | − | 0.977851i | \(-0.432880\pi\) | ||||
0.209304 | + | 0.977851i | \(0.432880\pi\) | |||||||
\(252\) | −5.63734 | −0.355119 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −19.4751 | −1.22198 | ||||||||
\(255\) | 0.930165 | 0.0582492 | ||||||||
\(256\) | 20.1969 | 1.26230 | ||||||||
\(257\) | 31.9252 | 1.99144 | 0.995720 | − | 0.0924213i | \(-0.0294607\pi\) | ||||
0.995720 | + | 0.0924213i | \(0.0294607\pi\) | |||||||
\(258\) | −16.0349 | −0.998289 | ||||||||
\(259\) | −3.16809 | −0.196855 | ||||||||
\(260\) | −0.313024 | −0.0194130 | ||||||||
\(261\) | −0.132327 | −0.00819081 | ||||||||
\(262\) | 19.1204 | 1.18126 | ||||||||
\(263\) | 13.8295 | 0.852766 | 0.426383 | − | 0.904543i | \(-0.359788\pi\) | ||||
0.426383 | + | 0.904543i | \(0.359788\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.811707 | −0.0498628 | ||||||||
\(266\) | 44.2370 | 2.71235 | ||||||||
\(267\) | −0.838918 | −0.0513409 | ||||||||
\(268\) | 15.9927 | 0.976908 | ||||||||
\(269\) | 24.5273 | 1.49546 | 0.747728 | − | 0.664005i | \(-0.231145\pi\) | ||||
0.747728 | + | 0.664005i | \(0.231145\pi\) | |||||||
\(270\) | −2.00356 | −0.121933 | ||||||||
\(271\) | −18.2933 | −1.11124 | −0.555619 | − | 0.831437i | \(-0.687518\pi\) | ||||
−0.555619 | + | 0.831437i | \(0.687518\pi\) | |||||||
\(272\) | −5.93190 | −0.359674 | ||||||||
\(273\) | 5.04778 | 0.305505 | ||||||||
\(274\) | 30.6742 | 1.85309 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.01220 | −0.121120 | ||||||||
\(277\) | 28.6174 | 1.71945 | 0.859727 | − | 0.510755i | \(-0.170634\pi\) | ||||
0.859727 | + | 0.510755i | \(0.170634\pi\) | |||||||
\(278\) | 9.37844 | 0.562481 | ||||||||
\(279\) | 7.26771 | 0.435106 | ||||||||
\(280\) | 1.75622 | 0.104954 | ||||||||
\(281\) | −9.92157 | −0.591871 | −0.295936 | − | 0.955208i | \(-0.595631\pi\) | ||||
−0.295936 | + | 0.955208i | \(0.595631\pi\) | |||||||
\(282\) | 0.861559 | 0.0513051 | ||||||||
\(283\) | −3.08639 | −0.183467 | −0.0917333 | − | 0.995784i | \(-0.529241\pi\) | ||||
−0.0917333 | + | 0.995784i | \(0.529241\pi\) | |||||||
\(284\) | −16.6997 | −0.990946 | ||||||||
\(285\) | −6.14630 | −0.364076 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.52515 | 0.562252 | ||||||||
\(288\) | −9.00805 | −0.530805 | ||||||||
\(289\) | −15.5805 | −0.916498 | ||||||||
\(290\) | −0.0552915 | −0.00324683 | ||||||||
\(291\) | −37.7949 | −2.21558 | ||||||||
\(292\) | 8.16959 | 0.478089 | ||||||||
\(293\) | 29.9275 | 1.74838 | 0.874191 | − | 0.485583i | \(-0.161393\pi\) | ||||
0.874191 | + | 0.485583i | \(0.161393\pi\) | |||||||
\(294\) | 11.4928 | 0.670273 | ||||||||
\(295\) | 2.30902 | 0.134437 | ||||||||
\(296\) | −1.51512 | −0.0880644 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.2011 | 0.648864 | ||||||||
\(299\) | 0.614582 | 0.0355422 | ||||||||
\(300\) | −11.8967 | −0.686855 | ||||||||
\(301\) | 13.4230 | 0.773689 | ||||||||
\(302\) | −3.29944 | −0.189862 | ||||||||
\(303\) | 22.9257 | 1.31705 | ||||||||
\(304\) | 39.1965 | 2.24807 | ||||||||
\(305\) | −1.77758 | −0.101784 | ||||||||
\(306\) | 3.28187 | 0.187612 | ||||||||
\(307\) | −12.5774 | −0.717831 | −0.358916 | − | 0.933370i | \(-0.616853\pi\) | ||||
−0.358916 | + | 0.933370i | \(0.616853\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.5792 | −0.658716 | ||||||||
\(310\) | 3.03675 | 0.172476 | ||||||||
\(311\) | −10.4206 | −0.590896 | −0.295448 | − | 0.955359i | \(-0.595469\pi\) | ||||
−0.295448 | + | 0.955359i | \(0.595469\pi\) | |||||||
\(312\) | 2.41407 | 0.136670 | ||||||||
\(313\) | 8.06183 | 0.455681 | 0.227841 | − | 0.973698i | \(-0.426833\pi\) | ||||
0.227841 | + | 0.973698i | \(0.426833\pi\) | |||||||
\(314\) | 15.5265 | 0.876211 | ||||||||
\(315\) | −1.80019 | −0.101429 | ||||||||
\(316\) | −3.66142 | −0.205971 | ||||||||
\(317\) | 4.45385 | 0.250153 | 0.125076 | − | 0.992147i | \(-0.460082\pi\) | ||||
0.125076 | + | 0.992147i | \(0.460082\pi\) | |||||||
\(318\) | −8.39609 | −0.470829 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.120708 | −0.00674780 | ||||||||
\(321\) | 4.12573 | 0.230276 | ||||||||
\(322\) | 4.62474 | 0.257727 | ||||||||
\(323\) | −9.37993 | −0.521913 | ||||||||
\(324\) | −12.8865 | −0.715916 | ||||||||
\(325\) | 3.63359 | 0.201555 | ||||||||
\(326\) | −15.6773 | −0.868288 | ||||||||
\(327\) | 25.4944 | 1.40984 | ||||||||
\(328\) | 4.55534 | 0.251527 | ||||||||
\(329\) | −0.721222 | −0.0397622 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.20130 | 0.285889 | 0.142945 | − | 0.989731i | \(-0.454343\pi\) | ||||
0.142945 | + | 0.989731i | \(0.454343\pi\) | |||||||
\(332\) | 18.3578 | 1.00752 | ||||||||
\(333\) | 1.55305 | 0.0851068 | ||||||||
\(334\) | −17.4216 | −0.953267 | ||||||||
\(335\) | 5.10700 | 0.279025 | ||||||||
\(336\) | 33.6565 | 1.83611 | ||||||||
\(337\) | −14.1868 | −0.772806 | −0.386403 | − | 0.922330i | \(-0.626283\pi\) | ||||
−0.386403 | + | 0.922330i | \(0.626283\pi\) | |||||||
\(338\) | −22.0682 | −1.20035 | ||||||||
\(339\) | −27.4626 | −1.49156 | ||||||||
\(340\) | 0.499458 | 0.0270869 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −21.6858 | −1.17263 | ||||||||
\(343\) | 12.5559 | 0.677952 | ||||||||
\(344\) | 6.41947 | 0.346114 | ||||||||
\(345\) | −0.642563 | −0.0345944 | ||||||||
\(346\) | −26.0151 | −1.39858 | ||||||||
\(347\) | 2.81106 | 0.150906 | 0.0754528 | − | 0.997149i | \(-0.475960\pi\) | ||||
0.0754528 | + | 0.997149i | \(0.475960\pi\) | |||||||
\(348\) | −0.208306 | −0.0111664 | ||||||||
\(349\) | 17.3210 | 0.927173 | 0.463586 | − | 0.886052i | \(-0.346562\pi\) | ||||
0.463586 | + | 0.886052i | \(0.346562\pi\) | |||||||
\(350\) | 27.3428 | 1.46154 | ||||||||
\(351\) | 2.30545 | 0.123056 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.1411 | 1.17845 | 0.589227 | − | 0.807968i | \(-0.299432\pi\) | ||||
0.589227 | + | 0.807968i | \(0.299432\pi\) | |||||||
\(354\) | 23.8839 | 1.26942 | ||||||||
\(355\) | −5.33279 | −0.283035 | ||||||||
\(356\) | −0.450463 | −0.0238745 | ||||||||
\(357\) | −8.05418 | −0.426272 | ||||||||
\(358\) | 11.5522 | 0.610554 | ||||||||
\(359\) | −15.4235 | −0.814022 | −0.407011 | − | 0.913423i | \(-0.633429\pi\) | ||||
−0.407011 | + | 0.913423i | \(0.633429\pi\) | |||||||
\(360\) | −0.860932 | −0.0453751 | ||||||||
\(361\) | 42.9802 | 2.26212 | ||||||||
\(362\) | −35.3513 | −1.85802 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.71044 | 0.142065 | ||||||||
\(365\) | 2.60883 | 0.136552 | ||||||||
\(366\) | −18.3869 | −0.961096 | ||||||||
\(367\) | −4.73070 | −0.246940 | −0.123470 | − | 0.992348i | \(-0.539402\pi\) | ||||
−0.123470 | + | 0.992348i | \(0.539402\pi\) | |||||||
\(368\) | 4.09779 | 0.213612 | ||||||||
\(369\) | −4.66940 | −0.243079 | ||||||||
\(370\) | 0.648930 | 0.0337363 | ||||||||
\(371\) | 7.02847 | 0.364900 | ||||||||
\(372\) | 11.4407 | 0.593173 | ||||||||
\(373\) | −20.0506 | −1.03818 | −0.519090 | − | 0.854720i | \(-0.673729\pi\) | ||||
−0.519090 | + | 0.854720i | \(0.673729\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.70255 | −0.397758 | ||||||||
\(376\) | −0.344920 | −0.0177879 | ||||||||
\(377\) | 0.0636227 | 0.00327674 | ||||||||
\(378\) | 17.3485 | 0.892313 | ||||||||
\(379\) | −22.6858 | −1.16529 | −0.582645 | − | 0.812727i | \(-0.697982\pi\) | ||||
−0.582645 | + | 0.812727i | \(0.697982\pi\) | |||||||
\(380\) | −3.30030 | −0.169302 | ||||||||
\(381\) | −23.4298 | −1.20034 | ||||||||
\(382\) | −18.8263 | −0.963239 | ||||||||
\(383\) | −36.7395 | −1.87730 | −0.938649 | − | 0.344873i | \(-0.887922\pi\) | ||||
−0.938649 | + | 0.344873i | \(0.887922\pi\) | |||||||
\(384\) | 23.5043 | 1.19945 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −39.9534 | −2.03358 | ||||||||
\(387\) | −6.58020 | −0.334490 | ||||||||
\(388\) | −20.2942 | −1.03028 | ||||||||
\(389\) | 31.4471 | 1.59443 | 0.797216 | − | 0.603694i | \(-0.206305\pi\) | ||||
0.797216 | + | 0.603694i | \(0.206305\pi\) | |||||||
\(390\) | −1.03395 | −0.0523563 | ||||||||
\(391\) | −0.980621 | −0.0495922 | ||||||||
\(392\) | −4.60106 | −0.232389 | ||||||||
\(393\) | 23.0031 | 1.16035 | ||||||||
\(394\) | 15.1190 | 0.761682 | ||||||||
\(395\) | −1.16922 | −0.0588297 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.69240 | 0.285693 | 0.142847 | − | 0.989745i | \(-0.454374\pi\) | ||||
0.142847 | + | 0.989745i | \(0.454374\pi\) | |||||||
\(398\) | −14.0393 | −0.703727 | ||||||||
\(399\) | 53.2200 | 2.66433 | ||||||||
\(400\) | 24.2273 | 1.21136 | ||||||||
\(401\) | 27.0625 | 1.35144 | 0.675718 | − | 0.737160i | \(-0.263834\pi\) | ||||
0.675718 | + | 0.737160i | \(0.263834\pi\) | |||||||
\(402\) | 52.8255 | 2.63470 | ||||||||
\(403\) | −3.49432 | −0.174065 | ||||||||
\(404\) | 12.3101 | 0.612450 | ||||||||
\(405\) | −4.11509 | −0.204481 | ||||||||
\(406\) | 0.478762 | 0.0237606 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −3.85186 | −0.190695 | ||||||||
\(409\) | −3.46673 | −0.171419 | −0.0857094 | − | 0.996320i | \(-0.527316\pi\) | ||||
−0.0857094 | + | 0.996320i | \(0.527316\pi\) | |||||||
\(410\) | −1.95107 | −0.0963565 | ||||||||
\(411\) | 36.9030 | 1.82029 | ||||||||
\(412\) | −6.21752 | −0.306315 | ||||||||
\(413\) | −19.9935 | −0.983817 | ||||||||
\(414\) | −2.26713 | −0.111424 | ||||||||
\(415\) | 5.86227 | 0.287768 | ||||||||
\(416\) | 4.33108 | 0.212349 | ||||||||
\(417\) | 11.2829 | 0.552524 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.4521 | −1.43883 | −0.719415 | − | 0.694581i | \(-0.755590\pi\) | ||||
−0.719415 | + | 0.694581i | \(0.755590\pi\) | |||||||
\(420\) | −2.83384 | −0.138277 | ||||||||
\(421\) | −22.5811 | −1.10053 | −0.550267 | − | 0.834989i | \(-0.685474\pi\) | ||||
−0.550267 | + | 0.834989i | \(0.685474\pi\) | |||||||
\(422\) | −1.23846 | −0.0602875 | ||||||||
\(423\) | 0.353556 | 0.0171905 | ||||||||
\(424\) | 3.36132 | 0.163240 | ||||||||
\(425\) | −5.79772 | −0.281231 | ||||||||
\(426\) | −55.1610 | −2.67256 | ||||||||
\(427\) | 15.3918 | 0.744864 | ||||||||
\(428\) | 2.21534 | 0.107082 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.74948 | −0.132592 | ||||||||
\(431\) | −8.11365 | −0.390821 | −0.195410 | − | 0.980722i | \(-0.562604\pi\) | ||||
−0.195410 | + | 0.980722i | \(0.562604\pi\) | |||||||
\(432\) | 15.3718 | 0.739576 | ||||||||
\(433\) | −3.29511 | −0.158353 | −0.0791764 | − | 0.996861i | \(-0.525229\pi\) | ||||
−0.0791764 | + | 0.996861i | \(0.525229\pi\) | |||||||
\(434\) | −26.2948 | −1.26219 | ||||||||
\(435\) | −0.0665193 | −0.00318936 | ||||||||
\(436\) | 13.6894 | 0.655603 | ||||||||
\(437\) | 6.47970 | 0.309966 | ||||||||
\(438\) | 26.9851 | 1.28940 | ||||||||
\(439\) | 32.6880 | 1.56011 | 0.780057 | − | 0.625709i | \(-0.215190\pi\) | ||||
0.780057 | + | 0.625709i | \(0.215190\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.71627 | 0.224584 | ||||||||
\(442\) | −1.57793 | −0.0750543 | ||||||||
\(443\) | 27.4215 | 1.30283 | 0.651417 | − | 0.758720i | \(-0.274175\pi\) | ||||
0.651417 | + | 0.758720i | \(0.274175\pi\) | |||||||
\(444\) | 2.44479 | 0.116025 | ||||||||
\(445\) | −0.143848 | −0.00681905 | ||||||||
\(446\) | −45.1355 | −2.13723 | ||||||||
\(447\) | 13.4757 | 0.637378 | ||||||||
\(448\) | 1.04520 | 0.0493809 | ||||||||
\(449\) | −10.0371 | −0.473678 | −0.236839 | − | 0.971549i | \(-0.576111\pi\) | ||||
−0.236839 | + | 0.971549i | \(0.576111\pi\) | |||||||
\(450\) | −13.4039 | −0.631868 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −14.7462 | −0.693604 | ||||||||
\(453\) | −3.96944 | −0.186501 | ||||||||
\(454\) | −2.74660 | −0.128904 | ||||||||
\(455\) | 0.865535 | 0.0405769 | ||||||||
\(456\) | 25.4521 | 1.19191 | ||||||||
\(457\) | 1.43413 | 0.0670857 | 0.0335429 | − | 0.999437i | \(-0.489321\pi\) | ||||
0.0335429 | + | 0.999437i | \(0.489321\pi\) | |||||||
\(458\) | −2.32613 | −0.108693 | ||||||||
\(459\) | −3.67855 | −0.171700 | ||||||||
\(460\) | −0.345029 | −0.0160870 | ||||||||
\(461\) | −3.64734 | −0.169873 | −0.0849367 | − | 0.996386i | \(-0.527069\pi\) | ||||
−0.0849367 | + | 0.996386i | \(0.527069\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.1233 | 1.07463 | 0.537315 | − | 0.843381i | \(-0.319439\pi\) | ||||
0.537315 | + | 0.843381i | \(0.319439\pi\) | |||||||
\(464\) | 0.424210 | 0.0196935 | ||||||||
\(465\) | 3.65341 | 0.169423 | ||||||||
\(466\) | −46.3236 | −2.14590 | ||||||||
\(467\) | 15.5741 | 0.720686 | 0.360343 | − | 0.932820i | \(-0.382660\pi\) | ||||
0.360343 | + | 0.932820i | \(0.382660\pi\) | |||||||
\(468\) | −1.32871 | −0.0614194 | ||||||||
\(469\) | −44.2209 | −2.04193 | ||||||||
\(470\) | 0.147730 | 0.00681429 | ||||||||
\(471\) | 18.6794 | 0.860701 | ||||||||
\(472\) | −9.56178 | −0.440116 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −12.0941 | −0.555500 | ||||||||
\(475\) | 38.3099 | 1.75778 | ||||||||
\(476\) | −4.32474 | −0.198224 | ||||||||
\(477\) | −3.44548 | −0.157758 | ||||||||
\(478\) | 14.1699 | 0.648116 | ||||||||
\(479\) | −3.40934 | −0.155777 | −0.0778883 | − | 0.996962i | \(-0.524818\pi\) | ||||
−0.0778883 | + | 0.996962i | \(0.524818\pi\) | |||||||
\(480\) | −4.52827 | −0.206686 | ||||||||
\(481\) | −0.746710 | −0.0340470 | ||||||||
\(482\) | −13.5564 | −0.617479 | ||||||||
\(483\) | 5.56387 | 0.253165 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.48064 | −0.294271 | ||||||||
\(486\) | −26.1374 | −1.18562 | ||||||||
\(487\) | −24.2220 | −1.09760 | −0.548802 | − | 0.835953i | \(-0.684916\pi\) | ||||
−0.548802 | + | 0.835953i | \(0.684916\pi\) | |||||||
\(488\) | 7.36105 | 0.333219 | ||||||||
\(489\) | −18.8609 | −0.852918 | ||||||||
\(490\) | 1.97065 | 0.0890251 | ||||||||
\(491\) | −12.1851 | −0.549906 | −0.274953 | − | 0.961458i | \(-0.588662\pi\) | ||||
−0.274953 | + | 0.961458i | \(0.588662\pi\) | |||||||
\(492\) | −7.35050 | −0.331386 | ||||||||
\(493\) | −0.101516 | −0.00457204 | ||||||||
\(494\) | 10.4265 | 0.469113 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23.2987 | −1.04614 | ||||||||
\(497\) | 46.1759 | 2.07127 | ||||||||
\(498\) | 60.6378 | 2.71725 | ||||||||
\(499\) | −5.12265 | −0.229321 | −0.114661 | − | 0.993405i | \(-0.536578\pi\) | ||||
−0.114661 | + | 0.993405i | \(0.536578\pi\) | |||||||
\(500\) | −4.13593 | −0.184965 | ||||||||
\(501\) | −20.9593 | −0.936392 | ||||||||
\(502\) | 11.7627 | 0.524994 | ||||||||
\(503\) | 23.5969 | 1.05214 | 0.526068 | − | 0.850443i | \(-0.323666\pi\) | ||||
0.526068 | + | 0.850443i | \(0.323666\pi\) | |||||||
\(504\) | 7.45469 | 0.332058 | ||||||||
\(505\) | 3.93103 | 0.174929 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −26.5495 | −1.17910 | ||||||||
\(508\) | −12.5808 | −0.558182 | ||||||||
\(509\) | 10.5938 | 0.469562 | 0.234781 | − | 0.972048i | \(-0.424563\pi\) | ||||
0.234781 | + | 0.972048i | \(0.424563\pi\) | |||||||
\(510\) | 1.64977 | 0.0730529 | ||||||||
\(511\) | −22.5895 | −0.999301 | ||||||||
\(512\) | 13.7911 | 0.609486 | ||||||||
\(513\) | 24.3070 | 1.07318 | ||||||||
\(514\) | 56.6234 | 2.49755 | ||||||||
\(515\) | −1.98547 | −0.0874900 | ||||||||
\(516\) | −10.3584 | −0.456005 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −5.61900 | −0.246885 | ||||||||
\(519\) | −31.2979 | −1.37382 | ||||||||
\(520\) | 0.413937 | 0.0181523 | ||||||||
\(521\) | −16.3901 | −0.718065 | −0.359032 | − | 0.933325i | \(-0.616893\pi\) | ||||
−0.359032 | + | 0.933325i | \(0.616893\pi\) | |||||||
\(522\) | −0.234698 | −0.0102724 | ||||||||
\(523\) | 7.37161 | 0.322338 | 0.161169 | − | 0.986927i | \(-0.448474\pi\) | ||||
0.161169 | + | 0.986927i | \(0.448474\pi\) | |||||||
\(524\) | 12.3517 | 0.539585 | ||||||||
\(525\) | 32.8952 | 1.43566 | ||||||||
\(526\) | 24.5284 | 1.06949 | ||||||||
\(527\) | 5.57550 | 0.242873 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3226 | −0.970547 | ||||||||
\(530\) | −1.43967 | −0.0625351 | ||||||||
\(531\) | 9.80119 | 0.425335 | ||||||||
\(532\) | 28.5768 | 1.23896 | ||||||||
\(533\) | 2.24505 | 0.0972440 | ||||||||
\(534\) | −1.48793 | −0.0643889 | ||||||||
\(535\) | 0.707433 | 0.0305850 | ||||||||
\(536\) | −21.1484 | −0.913470 | ||||||||
\(537\) | 13.8981 | 0.599747 | ||||||||
\(538\) | 43.5023 | 1.87552 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.29429 | −0.0556972 | ||||||||
\(541\) | 6.55483 | 0.281814 | 0.140907 | − | 0.990023i | \(-0.454998\pi\) | ||||
0.140907 | + | 0.990023i | \(0.454998\pi\) | |||||||
\(542\) | −32.4454 | −1.39365 | ||||||||
\(543\) | −42.5299 | −1.82513 | ||||||||
\(544\) | −6.91063 | −0.296291 | ||||||||
\(545\) | 4.37149 | 0.187254 | ||||||||
\(546\) | 8.95287 | 0.383148 | ||||||||
\(547\) | −22.4865 | −0.961453 | −0.480726 | − | 0.876871i | \(-0.659627\pi\) | ||||
−0.480726 | + | 0.876871i | \(0.659627\pi\) | |||||||
\(548\) | 19.8153 | 0.846469 | ||||||||
\(549\) | −7.54536 | −0.322028 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.670791 | 0.0285766 | ||||||||
\(552\) | 2.66089 | 0.113255 | ||||||||
\(553\) | 10.1241 | 0.430521 | ||||||||
\(554\) | 50.7566 | 2.15644 | ||||||||
\(555\) | 0.780706 | 0.0331391 | ||||||||
\(556\) | 6.05841 | 0.256934 | ||||||||
\(557\) | −44.7280 | −1.89519 | −0.947593 | − | 0.319481i | \(-0.896491\pi\) | ||||
−0.947593 | + | 0.319481i | \(0.896491\pi\) | |||||||
\(558\) | 12.8902 | 0.545686 | ||||||||
\(559\) | 3.16377 | 0.133813 | ||||||||
\(560\) | 5.77104 | 0.243871 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.5972 | −0.742292 | ||||||||
\(563\) | −29.6105 | −1.24793 | −0.623966 | − | 0.781451i | \(-0.714480\pi\) | ||||
−0.623966 | + | 0.781451i | \(0.714480\pi\) | |||||||
\(564\) | 0.556562 | 0.0234355 | ||||||||
\(565\) | −4.70897 | −0.198108 | ||||||||
\(566\) | −5.47410 | −0.230093 | ||||||||
\(567\) | 35.6321 | 1.49641 | ||||||||
\(568\) | 22.0833 | 0.926597 | ||||||||
\(569\) | 0.324144 | 0.0135888 | 0.00679440 | − | 0.999977i | \(-0.497837\pi\) | ||||
0.00679440 | + | 0.999977i | \(0.497837\pi\) | |||||||
\(570\) | −10.9012 | −0.456603 | ||||||||
\(571\) | 8.54812 | 0.357728 | 0.178864 | − | 0.983874i | \(-0.442758\pi\) | ||||
0.178864 | + | 0.983874i | \(0.442758\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.6493 | −0.946188 | ||||||||
\(574\) | 16.8941 | 0.705145 | ||||||||
\(575\) | 4.00509 | 0.167024 | ||||||||
\(576\) | −0.512375 | −0.0213490 | ||||||||
\(577\) | 20.1719 | 0.839768 | 0.419884 | − | 0.907578i | \(-0.362071\pi\) | ||||
0.419884 | + | 0.907578i | \(0.362071\pi\) | |||||||
\(578\) | −27.6339 | −1.14942 | ||||||||
\(579\) | −48.0666 | −1.99758 | ||||||||
\(580\) | −0.0357180 | −0.00148311 | ||||||||
\(581\) | −50.7606 | −2.10591 | ||||||||
\(582\) | −67.0341 | −2.77865 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.8033 | −0.447043 | ||||||||
\(585\) | −0.424301 | −0.0175427 | ||||||||
\(586\) | 53.0802 | 2.19272 | ||||||||
\(587\) | −2.92805 | −0.120853 | −0.0604267 | − | 0.998173i | \(-0.519246\pi\) | ||||
−0.0604267 | + | 0.998173i | \(0.519246\pi\) | |||||||
\(588\) | 7.42428 | 0.306172 | ||||||||
\(589\) | −36.8415 | −1.51803 | ||||||||
\(590\) | 4.09535 | 0.168603 | ||||||||
\(591\) | 18.1891 | 0.748199 | ||||||||
\(592\) | −4.97876 | −0.204626 | ||||||||
\(593\) | −27.3279 | −1.12222 | −0.561111 | − | 0.827740i | \(-0.689626\pi\) | ||||
−0.561111 | + | 0.827740i | \(0.689626\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.38104 | −0.0566171 | ||||||||
\(596\) | 7.23586 | 0.296393 | ||||||||
\(597\) | −16.8902 | −0.691270 | ||||||||
\(598\) | 1.09004 | 0.0445750 | ||||||||
\(599\) | 41.5454 | 1.69750 | 0.848750 | − | 0.528794i | \(-0.177356\pi\) | ||||
0.848750 | + | 0.528794i | \(0.177356\pi\) | |||||||
\(600\) | 15.7319 | 0.642253 | ||||||||
\(601\) | −15.8668 | −0.647219 | −0.323610 | − | 0.946191i | \(-0.604896\pi\) | ||||
−0.323610 | + | 0.946191i | \(0.604896\pi\) | |||||||
\(602\) | 23.8074 | 0.970317 | ||||||||
\(603\) | 21.6779 | 0.882791 | ||||||||
\(604\) | −2.13142 | −0.0867262 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 40.6616 | 1.65176 | ||||||||
\(607\) | −12.2585 | −0.497558 | −0.248779 | − | 0.968560i | \(-0.580029\pi\) | ||||
−0.248779 | + | 0.968560i | \(0.580029\pi\) | |||||||
\(608\) | 45.6637 | 1.85191 | ||||||||
\(609\) | 0.575982 | 0.0233400 | ||||||||
\(610\) | −3.15277 | −0.127652 | ||||||||
\(611\) | −0.169990 | −0.00687706 | ||||||||
\(612\) | 2.12007 | 0.0856987 | ||||||||
\(613\) | 47.6835 | 1.92592 | 0.962959 | − | 0.269646i | \(-0.0869067\pi\) | ||||
0.962959 | + | 0.269646i | \(0.0869067\pi\) | |||||||
\(614\) | −22.3076 | −0.900263 | ||||||||
\(615\) | −2.34727 | −0.0946509 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.4418 | 1.38657 | 0.693287 | − | 0.720662i | \(-0.256162\pi\) | ||||
0.693287 | + | 0.720662i | \(0.256162\pi\) | |||||||
\(618\) | −20.5371 | −0.826125 | ||||||||
\(619\) | −5.16751 | −0.207700 | −0.103850 | − | 0.994593i | \(-0.533116\pi\) | ||||
−0.103850 | + | 0.994593i | \(0.533116\pi\) | |||||||
\(620\) | 1.96172 | 0.0787847 | ||||||||
\(621\) | 2.54116 | 0.101973 | ||||||||
\(622\) | −18.4822 | −0.741068 | ||||||||
\(623\) | 1.24556 | 0.0499024 | ||||||||
\(624\) | 7.93275 | 0.317564 | ||||||||
\(625\) | 23.0099 | 0.920397 | ||||||||
\(626\) | 14.2987 | 0.571490 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.0300 | 0.400241 | ||||||||
\(629\) | 1.19144 | 0.0475059 | ||||||||
\(630\) | −3.19287 | −0.127207 | ||||||||
\(631\) | −26.0934 | −1.03876 | −0.519382 | − | 0.854542i | \(-0.673838\pi\) | ||||
−0.519382 | + | 0.854542i | \(0.673838\pi\) | |||||||
\(632\) | 4.84179 | 0.192596 | ||||||||
\(633\) | −1.48995 | −0.0592203 | ||||||||
\(634\) | 7.89946 | 0.313728 | ||||||||
\(635\) | −4.01747 | −0.159429 | ||||||||
\(636\) | −5.42382 | −0.215069 | ||||||||
\(637\) | −2.26759 | −0.0898450 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.6363 | −0.895477 | ||||||||
\(640\) | 4.03025 | 0.159310 | ||||||||
\(641\) | −38.1079 | −1.50517 | −0.752586 | − | 0.658494i | \(-0.771194\pi\) | ||||
−0.752586 | + | 0.658494i | \(0.771194\pi\) | |||||||
\(642\) | 7.31751 | 0.288799 | ||||||||
\(643\) | 17.9660 | 0.708510 | 0.354255 | − | 0.935149i | \(-0.384734\pi\) | ||||
0.354255 | + | 0.935149i | \(0.384734\pi\) | |||||||
\(644\) | 2.98756 | 0.117726 | ||||||||
\(645\) | −3.30781 | −0.130245 | ||||||||
\(646\) | −16.6365 | −0.654554 | ||||||||
\(647\) | −37.4720 | −1.47318 | −0.736589 | − | 0.676341i | \(-0.763565\pi\) | ||||
−0.736589 | + | 0.676341i | \(0.763565\pi\) | |||||||
\(648\) | 17.0408 | 0.669426 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 6.44463 | 0.252779 | ||||||||
\(651\) | −31.6344 | −1.23985 | ||||||||
\(652\) | −10.1275 | −0.396622 | ||||||||
\(653\) | 14.0047 | 0.548048 | 0.274024 | − | 0.961723i | \(-0.411645\pi\) | ||||
0.274024 | + | 0.961723i | \(0.411645\pi\) | |||||||
\(654\) | 45.2176 | 1.76815 | ||||||||
\(655\) | 3.94431 | 0.154117 | ||||||||
\(656\) | 14.9691 | 0.584445 | ||||||||
\(657\) | 11.0738 | 0.432030 | ||||||||
\(658\) | −1.27918 | −0.0498675 | ||||||||
\(659\) | −25.4552 | −0.991594 | −0.495797 | − | 0.868439i | \(-0.665124\pi\) | ||||
−0.495797 | + | 0.868439i | \(0.665124\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.7275 | −0.922891 | −0.461446 | − | 0.887169i | \(-0.652669\pi\) | ||||
−0.461446 | + | 0.887169i | \(0.652669\pi\) | |||||||
\(662\) | 9.22516 | 0.358546 | ||||||||
\(663\) | −1.89835 | −0.0737257 | ||||||||
\(664\) | −24.2760 | −0.942090 | ||||||||
\(665\) | 9.12556 | 0.353874 | ||||||||
\(666\) | 2.75454 | 0.106736 | ||||||||
\(667\) | 0.0701276 | 0.00271535 | ||||||||
\(668\) | −11.2542 | −0.435439 | ||||||||
\(669\) | −54.3010 | −2.09940 | ||||||||
\(670\) | 9.05792 | 0.349938 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 39.2096 | 1.51254 | ||||||||
\(673\) | −37.0634 | −1.42869 | −0.714344 | − | 0.699795i | \(-0.753275\pi\) | ||||
−0.714344 | + | 0.699795i | \(0.753275\pi\) | |||||||
\(674\) | −25.1622 | −0.969210 | ||||||||
\(675\) | 15.0241 | 0.578277 | ||||||||
\(676\) | −14.2559 | −0.548305 | ||||||||
\(677\) | −12.2870 | −0.472229 | −0.236115 | − | 0.971725i | \(-0.575874\pi\) | ||||
−0.236115 | + | 0.971725i | \(0.575874\pi\) | |||||||
\(678\) | −48.7084 | −1.87064 | ||||||||
\(679\) | 56.1150 | 2.15350 | ||||||||
\(680\) | −0.660473 | −0.0253280 | ||||||||
\(681\) | −3.30434 | −0.126623 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.92103 | 0.226562 | 0.113281 | − | 0.993563i | \(-0.463864\pi\) | ||||
0.113281 | + | 0.993563i | \(0.463864\pi\) | |||||||
\(684\) | −14.0089 | −0.535643 | ||||||||
\(685\) | 6.32771 | 0.241769 | ||||||||
\(686\) | 22.2694 | 0.850249 | ||||||||
\(687\) | −2.79848 | −0.106769 | ||||||||
\(688\) | 21.0947 | 0.804228 | ||||||||
\(689\) | 1.65659 | 0.0631111 | ||||||||
\(690\) | −1.13967 | −0.0433864 | ||||||||
\(691\) | −42.3208 | −1.60996 | −0.804979 | − | 0.593303i | \(-0.797823\pi\) | ||||
−0.804979 | + | 0.593303i | \(0.797823\pi\) | |||||||
\(692\) | −16.8056 | −0.638853 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.98577 | 0.189257 | ||||||||
\(695\) | 1.93466 | 0.0733857 | ||||||||
\(696\) | 0.275460 | 0.0104413 | ||||||||
\(697\) | −3.58218 | −0.135685 | ||||||||
\(698\) | 30.7210 | 1.16281 | ||||||||
\(699\) | −55.7303 | −2.10791 | ||||||||
\(700\) | 17.6633 | 0.667610 | ||||||||
\(701\) | −12.6847 | −0.479095 | −0.239548 | − | 0.970885i | \(-0.576999\pi\) | ||||
−0.239548 | + | 0.970885i | \(0.576999\pi\) | |||||||
\(702\) | 4.08901 | 0.154330 | ||||||||
\(703\) | −7.87275 | −0.296927 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.177729 | 0.00669367 | ||||||||
\(706\) | 39.2701 | 1.47795 | ||||||||
\(707\) | −34.0383 | −1.28014 | ||||||||
\(708\) | 15.4289 | 0.579853 | ||||||||
\(709\) | 29.9368 | 1.12430 | 0.562149 | − | 0.827036i | \(-0.309975\pi\) | ||||
0.562149 | + | 0.827036i | \(0.309975\pi\) | |||||||
\(710\) | −9.45838 | −0.354967 | ||||||||
\(711\) | −4.96302 | −0.186128 | ||||||||
\(712\) | 0.595682 | 0.0223241 | ||||||||
\(713\) | −3.85159 | −0.144243 | ||||||||
\(714\) | −14.2851 | −0.534607 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.46267 | 0.278893 | ||||||||
\(717\) | 17.0473 | 0.636643 | ||||||||
\(718\) | −27.3556 | −1.02090 | ||||||||
\(719\) | −30.3440 | −1.13164 | −0.565820 | − | 0.824529i | \(-0.691440\pi\) | ||||
−0.565820 | + | 0.824529i | \(0.691440\pi\) | |||||||
\(720\) | −2.82907 | −0.105433 | ||||||||
\(721\) | 17.1919 | 0.640259 | ||||||||
\(722\) | 76.2309 | 2.83702 | ||||||||
\(723\) | −16.3093 | −0.606549 | ||||||||
\(724\) | −22.8367 | −0.848720 | ||||||||
\(725\) | 0.414614 | 0.0153984 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.0157 | 1.40992 | 0.704962 | − | 0.709245i | \(-0.250964\pi\) | ||||
0.704962 | + | 0.709245i | \(0.250964\pi\) | |||||||
\(728\) | −3.58422 | −0.132840 | ||||||||
\(729\) | 2.29659 | 0.0850590 | ||||||||
\(730\) | 4.62709 | 0.171256 | ||||||||
\(731\) | −5.04807 | −0.186710 | ||||||||
\(732\) | −11.8778 | −0.439016 | ||||||||
\(733\) | 13.4001 | 0.494945 | 0.247473 | − | 0.968895i | \(-0.420400\pi\) | ||||
0.247473 | + | 0.968895i | \(0.420400\pi\) | |||||||
\(734\) | −8.39049 | −0.309699 | ||||||||
\(735\) | 2.37082 | 0.0874492 | ||||||||
\(736\) | 4.77390 | 0.175968 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −8.28178 | −0.304856 | ||||||||
\(739\) | −43.0142 | −1.58230 | −0.791152 | − | 0.611619i | \(-0.790518\pi\) | ||||
−0.791152 | + | 0.611619i | \(0.790518\pi\) | |||||||
\(740\) | 0.419205 | 0.0154103 | ||||||||
\(741\) | 12.5438 | 0.460809 | ||||||||
\(742\) | 12.4659 | 0.457637 | ||||||||
\(743\) | −39.6785 | −1.45566 | −0.727831 | − | 0.685757i | \(-0.759471\pi\) | ||||
−0.727831 | + | 0.685757i | \(0.759471\pi\) | |||||||
\(744\) | −15.1289 | −0.554654 | ||||||||
\(745\) | 2.31066 | 0.0846560 | ||||||||
\(746\) | −35.5622 | −1.30203 | ||||||||
\(747\) | 24.8838 | 0.910450 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.12557 | −0.223823 | ||||||||
\(750\) | −13.6614 | −0.498845 | ||||||||
\(751\) | 1.72854 | 0.0630752 | 0.0315376 | − | 0.999503i | \(-0.489960\pi\) | ||||
0.0315376 | + | 0.999503i | \(0.489960\pi\) | |||||||
\(752\) | −1.13342 | −0.0413317 | ||||||||
\(753\) | 14.1513 | 0.515701 | ||||||||
\(754\) | 0.112843 | 0.00410950 | ||||||||
\(755\) | −0.680635 | −0.0247708 | ||||||||
\(756\) | 11.2071 | 0.407597 | ||||||||
\(757\) | 22.3680 | 0.812981 | 0.406490 | − | 0.913655i | \(-0.366752\pi\) | ||||
0.406490 | + | 0.913655i | \(0.366752\pi\) | |||||||
\(758\) | −40.2361 | −1.46144 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.36424 | 0.158308 | ||||||||
\(761\) | −22.0349 | −0.798764 | −0.399382 | − | 0.916785i | \(-0.630775\pi\) | ||||
−0.399382 | + | 0.916785i | \(0.630775\pi\) | |||||||
\(762\) | −41.5557 | −1.50540 | ||||||||
\(763\) | −37.8522 | −1.37034 | ||||||||
\(764\) | −12.1617 | −0.439994 | ||||||||
\(765\) | 0.677010 | 0.0244774 | ||||||||
\(766\) | −65.1621 | −2.35440 | ||||||||
\(767\) | −4.71242 | −0.170156 | ||||||||
\(768\) | 43.0958 | 1.55509 | ||||||||
\(769\) | −52.6410 | −1.89828 | −0.949142 | − | 0.314849i | \(-0.898046\pi\) | ||||
−0.949142 | + | 0.314849i | \(0.898046\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 68.1217 | 2.45334 | ||||||||
\(772\) | −25.8097 | −0.928910 | ||||||||
\(773\) | 7.54837 | 0.271496 | 0.135748 | − | 0.990743i | \(-0.456656\pi\) | ||||
0.135748 | + | 0.990743i | \(0.456656\pi\) | |||||||
\(774\) | −11.6708 | −0.419499 | ||||||||
\(775\) | −22.7717 | −0.817983 | ||||||||
\(776\) | 26.8366 | 0.963379 | ||||||||
\(777\) | −6.76003 | −0.242515 | ||||||||
\(778\) | 55.7755 | 1.99965 | ||||||||
\(779\) | 23.6702 | 0.848072 | ||||||||
\(780\) | −0.667928 | −0.0239157 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.73926 | −0.0621957 | ||||||||
\(783\) | 0.263066 | 0.00940120 | ||||||||
\(784\) | −15.1193 | −0.539977 | ||||||||
\(785\) | 3.20293 | 0.114317 | ||||||||
\(786\) | 40.7989 | 1.45525 | ||||||||
\(787\) | −27.9979 | −0.998018 | −0.499009 | − | 0.866597i | \(-0.666302\pi\) | ||||
−0.499009 | + | 0.866597i | \(0.666302\pi\) | |||||||
\(788\) | 9.76675 | 0.347926 | ||||||||
\(789\) | 29.5093 | 1.05056 | ||||||||
\(790\) | −2.07376 | −0.0737809 | ||||||||
\(791\) | 40.7744 | 1.44977 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.62782 | 0.128828 | ||||||||
\(794\) | 10.0962 | 0.358301 | ||||||||
\(795\) | −1.73201 | −0.0614281 | ||||||||
\(796\) | −9.06931 | −0.321453 | ||||||||
\(797\) | 27.9468 | 0.989928 | 0.494964 | − | 0.868913i | \(-0.335181\pi\) | ||||
0.494964 | + | 0.868913i | \(0.335181\pi\) | |||||||
\(798\) | 94.3925 | 3.34146 | ||||||||
\(799\) | 0.271234 | 0.00959558 | ||||||||
\(800\) | 28.2246 | 0.997892 | ||||||||
\(801\) | −0.610597 | −0.0215744 | ||||||||
\(802\) | 47.9988 | 1.69489 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 34.1250 | 1.20349 | ||||||||
\(805\) | 0.954029 | 0.0336251 | ||||||||
\(806\) | −6.19762 | −0.218302 | ||||||||
\(807\) | 52.3361 | 1.84232 | ||||||||
\(808\) | −16.2786 | −0.572679 | ||||||||
\(809\) | 3.09949 | 0.108972 | 0.0544862 | − | 0.998515i | \(-0.482648\pi\) | ||||
0.0544862 | + | 0.998515i | \(0.482648\pi\) | |||||||
\(810\) | −7.29864 | −0.256448 | ||||||||
\(811\) | 29.1041 | 1.02198 | 0.510992 | − | 0.859586i | \(-0.329278\pi\) | ||||
0.510992 | + | 0.859586i | \(0.329278\pi\) | |||||||
\(812\) | 0.309277 | 0.0108535 | ||||||||
\(813\) | −39.0340 | −1.36898 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.23405 | −0.113284 | ||||||||
\(816\) | −12.6574 | −0.443098 | ||||||||
\(817\) | 33.3564 | 1.16699 | ||||||||
\(818\) | −6.14868 | −0.214984 | ||||||||
\(819\) | 3.67397 | 0.128379 | ||||||||
\(820\) | −1.26038 | −0.0440144 | ||||||||
\(821\) | 51.8546 | 1.80974 | 0.904870 | − | 0.425689i | \(-0.139968\pi\) | ||||
0.904870 | + | 0.425689i | \(0.139968\pi\) | |||||||
\(822\) | 65.4522 | 2.28291 | ||||||||
\(823\) | −20.2194 | −0.704803 | −0.352401 | − | 0.935849i | \(-0.614635\pi\) | ||||
−0.352401 | + | 0.935849i | \(0.614635\pi\) | |||||||
\(824\) | 8.22191 | 0.286424 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −35.4611 | −1.23385 | ||||||||
\(827\) | −2.68883 | −0.0934999 | −0.0467500 | − | 0.998907i | \(-0.514886\pi\) | ||||
−0.0467500 | + | 0.998907i | \(0.514886\pi\) | |||||||
\(828\) | −1.46455 | −0.0508968 | ||||||||
\(829\) | 19.0362 | 0.661154 | 0.330577 | − | 0.943779i | \(-0.392757\pi\) | ||||
0.330577 | + | 0.943779i | \(0.392757\pi\) | |||||||
\(830\) | 10.3975 | 0.360902 | ||||||||
\(831\) | 61.0635 | 2.11827 | ||||||||
\(832\) | 0.246350 | 0.00854066 | ||||||||
\(833\) | 3.61814 | 0.125361 | ||||||||
\(834\) | 20.0116 | 0.692945 | ||||||||
\(835\) | −3.59386 | −0.124371 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14.4482 | −0.499404 | ||||||||
\(838\) | −52.2371 | −1.80450 | ||||||||
\(839\) | 29.9265 | 1.03318 | 0.516588 | − | 0.856234i | \(-0.327202\pi\) | ||||
0.516588 | + | 0.856234i | \(0.327202\pi\) | |||||||
\(840\) | 3.74740 | 0.129298 | ||||||||
\(841\) | −28.9927 | −0.999750 | ||||||||
\(842\) | −40.0504 | −1.38023 | ||||||||
\(843\) | −21.1705 | −0.729152 | ||||||||
\(844\) | −0.800040 | −0.0275385 | ||||||||
\(845\) | −4.55241 | −0.156608 | ||||||||
\(846\) | 0.627076 | 0.0215593 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11.0455 | 0.379303 | ||||||||
\(849\) | −6.58570 | −0.226020 | ||||||||
\(850\) | −10.2830 | −0.352703 | ||||||||
\(851\) | −0.823054 | −0.0282139 | ||||||||
\(852\) | −35.6337 | −1.22079 | ||||||||
\(853\) | −31.9692 | −1.09460 | −0.547302 | − | 0.836935i | \(-0.684345\pi\) | ||||
−0.547302 | + | 0.836935i | \(0.684345\pi\) | |||||||
\(854\) | 27.2994 | 0.934166 | ||||||||
\(855\) | −4.47352 | −0.152991 | ||||||||
\(856\) | −2.92952 | −0.100129 | ||||||||
\(857\) | 2.18482 | 0.0746319 | 0.0373160 | − | 0.999304i | \(-0.488119\pi\) | ||||
0.0373160 | + | 0.999304i | \(0.488119\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.0759 | 1.67445 | 0.837224 | − | 0.546860i | \(-0.184177\pi\) | ||||
0.837224 | + | 0.546860i | \(0.184177\pi\) | |||||||
\(860\) | −1.77615 | −0.0605662 | ||||||||
\(861\) | 20.3247 | 0.692663 | ||||||||
\(862\) | −14.3906 | −0.490146 | ||||||||
\(863\) | 42.7019 | 1.45359 | 0.726794 | − | 0.686856i | \(-0.241009\pi\) | ||||
0.726794 | + | 0.686856i | \(0.241009\pi\) | |||||||
\(864\) | 17.9081 | 0.609244 | ||||||||
\(865\) | −5.36660 | −0.182470 | ||||||||
\(866\) | −5.84429 | −0.198597 | ||||||||
\(867\) | −33.2454 | −1.12907 | ||||||||
\(868\) | −16.9863 | −0.576552 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.117980 | −0.00399991 | ||||||||
\(871\) | −10.4227 | −0.353161 | ||||||||
\(872\) | −18.1026 | −0.613030 | ||||||||
\(873\) | −27.5086 | −0.931025 | ||||||||
\(874\) | 11.4926 | 0.388742 | ||||||||
\(875\) | 11.4362 | 0.386613 | ||||||||
\(876\) | 17.4322 | 0.588979 | ||||||||
\(877\) | −11.9608 | −0.403888 | −0.201944 | − | 0.979397i | \(-0.564726\pi\) | ||||
−0.201944 | + | 0.979397i | \(0.564726\pi\) | |||||||
\(878\) | 57.9763 | 1.95661 | ||||||||
\(879\) | 63.8589 | 2.15391 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.3717 | 0.585268 | 0.292634 | − | 0.956225i | \(-0.405468\pi\) | ||||
0.292634 | + | 0.956225i | \(0.405468\pi\) | |||||||
\(882\) | 8.36490 | 0.281661 | ||||||||
\(883\) | −49.7231 | −1.67332 | −0.836658 | − | 0.547725i | \(-0.815494\pi\) | ||||
−0.836658 | + | 0.547725i | \(0.815494\pi\) | |||||||
\(884\) | −1.01933 | −0.0342838 | ||||||||
\(885\) | 4.92697 | 0.165618 | ||||||||
\(886\) | 48.6355 | 1.63394 | ||||||||
\(887\) | 46.2787 | 1.55389 | 0.776944 | − | 0.629570i | \(-0.216769\pi\) | ||||
0.776944 | + | 0.629570i | \(0.216769\pi\) | |||||||
\(888\) | −3.23294 | −0.108490 | ||||||||
\(889\) | 34.7868 | 1.16671 | ||||||||
\(890\) | −0.255133 | −0.00855207 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −29.1573 | −0.976258 | ||||||||
\(893\) | −1.79225 | −0.0599753 | ||||||||
\(894\) | 23.9009 | 0.799364 | ||||||||
\(895\) | 2.38309 | 0.0796578 | ||||||||
\(896\) | −34.8974 | −1.16584 | ||||||||
\(897\) | 1.31139 | 0.0437860 | ||||||||
\(898\) | −17.8020 | −0.594060 | ||||||||
\(899\) | −0.398723 | −0.0132982 | ||||||||
\(900\) | −8.65887 | −0.288629 | ||||||||
\(901\) | −2.64324 | −0.0880591 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.6419 | 0.953141 | ||||||||
\(904\) | 19.5001 | 0.648563 | ||||||||
\(905\) | −7.29255 | −0.242412 | ||||||||
\(906\) | −7.04031 | −0.233899 | ||||||||
\(907\) | −50.0943 | −1.66335 | −0.831677 | − | 0.555259i | \(-0.812619\pi\) | ||||
−0.831677 | + | 0.555259i | \(0.812619\pi\) | |||||||
\(908\) | −1.77429 | −0.0588818 | ||||||||
\(909\) | 16.6862 | 0.553446 | ||||||||
\(910\) | 1.53514 | 0.0508893 | ||||||||
\(911\) | −27.6733 | −0.916857 | −0.458428 | − | 0.888731i | \(-0.651587\pi\) | ||||
−0.458428 | + | 0.888731i | \(0.651587\pi\) | |||||||
\(912\) | 83.6371 | 2.76950 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 2.54361 | 0.0841351 | ||||||||
\(915\) | −3.79298 | −0.125392 | ||||||||
\(916\) | −1.50266 | −0.0496494 | ||||||||
\(917\) | −34.1532 | −1.12784 | ||||||||
\(918\) | −6.52438 | −0.215336 | ||||||||
\(919\) | −34.6759 | −1.14385 | −0.571926 | − | 0.820305i | \(-0.693804\pi\) | ||||
−0.571926 | + | 0.820305i | \(0.693804\pi\) | |||||||
\(920\) | 0.456258 | 0.0150424 | ||||||||
\(921\) | −26.8376 | −0.884328 | ||||||||
\(922\) | −6.46901 | −0.213046 | ||||||||
\(923\) | 10.8835 | 0.358236 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.86613 | −0.159997 | ||||||||
\(926\) | 41.0121 | 1.34774 | ||||||||
\(927\) | −8.42777 | −0.276804 | ||||||||
\(928\) | 0.494203 | 0.0162230 | ||||||||
\(929\) | −25.9610 | −0.851754 | −0.425877 | − | 0.904781i | \(-0.640034\pi\) | ||||
−0.425877 | + | 0.904781i | \(0.640034\pi\) | |||||||
\(930\) | 6.47979 | 0.212481 | ||||||||
\(931\) | −23.9078 | −0.783545 | ||||||||
\(932\) | −29.9248 | −0.980218 | ||||||||
\(933\) | −22.2353 | −0.727950 | ||||||||
\(934\) | 27.6227 | 0.903843 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.75705 | 0.0574310 | ||||||||
\(937\) | −8.38853 | −0.274041 | −0.137021 | − | 0.990568i | \(-0.543753\pi\) | ||||
−0.137021 | + | 0.990568i | \(0.543753\pi\) | |||||||
\(938\) | −78.4313 | −2.56087 | ||||||||
\(939\) | 17.2022 | 0.561374 | ||||||||
\(940\) | 0.0954329 | 0.00311268 | ||||||||
\(941\) | 30.5845 | 0.997028 | 0.498514 | − | 0.866882i | \(-0.333879\pi\) | ||||
0.498514 | + | 0.866882i | \(0.333879\pi\) | |||||||
\(942\) | 33.1303 | 1.07944 | ||||||||
\(943\) | 2.47459 | 0.0805838 | ||||||||
\(944\) | −31.4205 | −1.02265 | ||||||||
\(945\) | 3.57879 | 0.116418 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.2375 | −0.495153 | −0.247577 | − | 0.968868i | \(-0.579634\pi\) | ||||
−0.247577 | + | 0.968868i | \(0.579634\pi\) | |||||||
\(948\) | −7.81271 | −0.253745 | ||||||||
\(949\) | −5.32429 | −0.172834 | ||||||||
\(950\) | 67.9474 | 2.20451 | ||||||||
\(951\) | 9.50356 | 0.308174 | ||||||||
\(952\) | 5.71895 | 0.185352 | ||||||||
\(953\) | 53.1365 | 1.72126 | 0.860631 | − | 0.509230i | \(-0.170070\pi\) | ||||
0.860631 | + | 0.509230i | \(0.170070\pi\) | |||||||
\(954\) | −6.11100 | −0.197851 | ||||||||
\(955\) | −3.88364 | −0.125672 | ||||||||
\(956\) | 9.15367 | 0.296051 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.04690 | −0.195366 | ||||||||
\(959\) | −54.7908 | −1.76929 | ||||||||
\(960\) | −0.257566 | −0.00831291 | ||||||||
\(961\) | −9.10111 | −0.293584 | ||||||||
\(962\) | −1.32438 | −0.0426999 | ||||||||
\(963\) | 3.00287 | 0.0967660 | ||||||||
\(964\) | −8.75738 | −0.282056 | ||||||||
\(965\) | −8.24191 | −0.265316 | ||||||||
\(966\) | 9.86823 | 0.317505 | ||||||||
\(967\) | −42.3775 | −1.36277 | −0.681384 | − | 0.731926i | \(-0.738622\pi\) | ||||
−0.681384 | + | 0.731926i | \(0.738622\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.0148 | −0.642967 | ||||||||
\(970\) | −11.4942 | −0.369058 | ||||||||
\(971\) | −35.6629 | −1.14448 | −0.572239 | − | 0.820087i | \(-0.693925\pi\) | ||||
−0.572239 | + | 0.820087i | \(0.693925\pi\) | |||||||
\(972\) | −16.8846 | −0.541573 | ||||||||
\(973\) | −16.7519 | −0.537043 | ||||||||
\(974\) | −42.9608 | −1.37655 | ||||||||
\(975\) | 7.75331 | 0.248305 | ||||||||
\(976\) | 24.1888 | 0.774265 | ||||||||
\(977\) | 27.5346 | 0.880911 | 0.440455 | − | 0.897775i | \(-0.354817\pi\) | ||||
0.440455 | + | 0.897775i | \(0.354817\pi\) | |||||||
\(978\) | −33.4521 | −1.06968 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.27303 | 0.0406655 | ||||||||
\(981\) | 18.5558 | 0.592442 | ||||||||
\(982\) | −21.6118 | −0.689661 | ||||||||
\(983\) | −6.02146 | −0.192055 | −0.0960273 | − | 0.995379i | \(-0.530614\pi\) | ||||
−0.0960273 | + | 0.995379i | \(0.530614\pi\) | |||||||
\(984\) | 9.72014 | 0.309867 | ||||||||
\(985\) | 3.11886 | 0.0993750 | ||||||||
\(986\) | −0.180051 | −0.00573399 | ||||||||
\(987\) | −1.53893 | −0.0489848 | ||||||||
\(988\) | 6.73549 | 0.214284 | ||||||||
\(989\) | 3.48724 | 0.110888 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.9691 | 1.07906 | 0.539532 | − | 0.841965i | \(-0.318601\pi\) | ||||
0.539532 | + | 0.841965i | \(0.318601\pi\) | |||||||
\(992\) | −27.1429 | −0.861787 | ||||||||
\(993\) | 11.0985 | 0.352199 | ||||||||
\(994\) | 81.8989 | 2.59767 | ||||||||
\(995\) | −2.89614 | −0.0918138 | ||||||||
\(996\) | 39.1717 | 1.24120 | ||||||||
\(997\) | 60.0391 | 1.90146 | 0.950729 | − | 0.310022i | \(-0.100336\pi\) | ||||
0.950729 | + | 0.310022i | \(0.100336\pi\) | |||||||
\(998\) | −9.08567 | −0.287602 | ||||||||
\(999\) | −3.08748 | −0.0976835 |
(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 | 4477.2.a.k.1.9 | 11 | ||
11.10 | odd | 2 | 407.2.a.c.1.3 | ✓ | 11 | ||
33.32 | even | 2 | 3663.2.a.u.1.9 | 11 | |||
44.43 | even | 2 | 6512.2.a.bb.1.3 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
407.2.a.c.1.3 | ✓ | 11 | 11.10 | odd | 2 | ||
3663.2.a.u.1.9 | 11 | 33.32 | even | 2 | |||
4477.2.a.k.1.9 | 11 | 1.1 | even | 1 | trivial | ||
6512.2.a.bb.1.3 | 11 | 44.43 | even | 2 |