Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [775,2,Mod(1,775)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(775, 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("775.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 775 = 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 775.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: | \(6.18840615665\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.205225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + 3x^{2} + 7x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.418933\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 775.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.581067 | −0.410876 | −0.205438 | − | 0.978670i | \(-0.565862\pi\) | ||||
−0.205438 | + | 0.978670i | \(0.565862\pi\) | |||||||
\(3\) | −2.46572 | −1.42358 | −0.711791 | − | 0.702392i | \(-0.752116\pi\) | ||||
−0.711791 | + | 0.702392i | \(0.752116\pi\) | |||||||
\(4\) | −1.66236 | −0.831181 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.43275 | 0.584916 | ||||||||
\(7\) | −1.67419 | −0.632784 | −0.316392 | − | 0.948628i | \(-0.602472\pi\) | ||||
−0.316392 | + | 0.948628i | \(0.602472\pi\) | |||||||
\(8\) | 2.12808 | 0.752389 | ||||||||
\(9\) | 3.07975 | 1.02658 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.38333 | 1.62314 | 0.811568 | − | 0.584258i | \(-0.198614\pi\) | ||||
0.811568 | + | 0.584258i | \(0.198614\pi\) | |||||||
\(12\) | 4.09891 | 1.18325 | ||||||||
\(13\) | −0.325810 | −0.0903634 | −0.0451817 | − | 0.998979i | \(-0.514387\pi\) | ||||
−0.0451817 | + | 0.998979i | \(0.514387\pi\) | |||||||
\(14\) | 0.972816 | 0.259996 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.08817 | 0.522042 | ||||||||
\(17\) | −0.627408 | −0.152169 | −0.0760844 | − | 0.997101i | \(-0.524242\pi\) | ||||
−0.0760844 | + | 0.997101i | \(0.524242\pi\) | |||||||
\(18\) | −1.78954 | −0.421799 | ||||||||
\(19\) | −1.81068 | −0.415399 | −0.207700 | − | 0.978193i | \(-0.566598\pi\) | ||||
−0.207700 | + | 0.978193i | \(0.566598\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.12808 | 0.900820 | ||||||||
\(22\) | −3.12808 | −0.666908 | ||||||||
\(23\) | 0.558839 | 0.116526 | 0.0582630 | − | 0.998301i | \(-0.481444\pi\) | ||||
0.0582630 | + | 0.998301i | \(0.481444\pi\) | |||||||
\(24\) | −5.24723 | −1.07109 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.189317 | 0.0371282 | ||||||||
\(27\) | −0.196646 | −0.0378445 | ||||||||
\(28\) | 2.78311 | 0.525958 | ||||||||
\(29\) | 1.60221 | 0.297523 | 0.148761 | − | 0.988873i | \(-0.452471\pi\) | ||||
0.148761 | + | 0.988873i | \(0.452471\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −5.46952 | −0.966883 | ||||||||
\(33\) | −13.2738 | −2.31067 | ||||||||
\(34\) | 0.364566 | 0.0625226 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.11966 | −0.853277 | ||||||||
\(37\) | −6.68929 | −1.09971 | −0.549856 | − | 0.835259i | \(-0.685317\pi\) | ||||
−0.549856 | + | 0.835259i | \(0.685317\pi\) | |||||||
\(38\) | 1.05213 | 0.170678 | ||||||||
\(39\) | 0.803354 | 0.128640 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.14768 | −1.27245 | −0.636227 | − | 0.771502i | \(-0.719506\pi\) | ||||
−0.636227 | + | 0.771502i | \(0.719506\pi\) | |||||||
\(42\) | −2.39869 | −0.370126 | ||||||||
\(43\) | −10.8130 | −1.64897 | −0.824484 | − | 0.565885i | \(-0.808535\pi\) | ||||
−0.824484 | + | 0.565885i | \(0.808535\pi\) | |||||||
\(44\) | −8.94905 | −1.34912 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.324723 | −0.0478777 | ||||||||
\(47\) | 9.93459 | 1.44911 | 0.724554 | − | 0.689218i | \(-0.242046\pi\) | ||||
0.724554 | + | 0.689218i | \(0.242046\pi\) | |||||||
\(48\) | −5.14883 | −0.743169 | ||||||||
\(49\) | −4.19709 | −0.599584 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.54701 | 0.216625 | ||||||||
\(52\) | 0.541613 | 0.0751083 | ||||||||
\(53\) | −3.51513 | −0.482840 | −0.241420 | − | 0.970421i | \(-0.577613\pi\) | ||||
−0.241420 | + | 0.970421i | \(0.577613\pi\) | |||||||
\(54\) | 0.114264 | 0.0155494 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.56281 | −0.476100 | ||||||||
\(57\) | 4.46463 | 0.591354 | ||||||||
\(58\) | −0.930990 | −0.122245 | ||||||||
\(59\) | 10.8460 | 1.41203 | 0.706013 | − | 0.708199i | \(-0.250492\pi\) | ||||
0.706013 | + | 0.708199i | \(0.250492\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.69720 | −1.11356 | −0.556781 | − | 0.830659i | \(-0.687964\pi\) | ||||
−0.556781 | + | 0.830659i | \(0.687964\pi\) | |||||||
\(62\) | −0.581067 | −0.0737956 | ||||||||
\(63\) | −5.15609 | −0.649606 | ||||||||
\(64\) | −0.998180 | −0.124773 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.71295 | 0.949398 | ||||||||
\(67\) | 0.686019 | 0.0838106 | 0.0419053 | − | 0.999122i | \(-0.486657\pi\) | ||||
0.0419053 | + | 0.999122i | \(0.486657\pi\) | |||||||
\(68\) | 1.04298 | 0.126480 | ||||||||
\(69\) | −1.37794 | −0.165884 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.00341 | 0.119083 | 0.0595416 | − | 0.998226i | \(-0.481036\pi\) | ||||
0.0595416 | + | 0.998226i | \(0.481036\pi\) | |||||||
\(72\) | 6.55395 | 0.772390 | ||||||||
\(73\) | 5.03034 | 0.588757 | 0.294378 | − | 0.955689i | \(-0.404887\pi\) | ||||
0.294378 | + | 0.955689i | \(0.404887\pi\) | |||||||
\(74\) | 3.88692 | 0.451846 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.01001 | 0.345272 | ||||||||
\(77\) | −9.01273 | −1.02710 | ||||||||
\(78\) | −0.466802 | −0.0528550 | ||||||||
\(79\) | −13.6275 | −1.53322 | −0.766609 | − | 0.642114i | \(-0.778058\pi\) | ||||
−0.766609 | + | 0.642114i | \(0.778058\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.75438 | −0.972709 | ||||||||
\(82\) | 4.73434 | 0.522821 | ||||||||
\(83\) | 4.77167 | 0.523759 | 0.261879 | − | 0.965101i | \(-0.415658\pi\) | ||||
0.261879 | + | 0.965101i | \(0.415658\pi\) | |||||||
\(84\) | −6.86236 | −0.748744 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.28308 | 0.677522 | ||||||||
\(87\) | −3.95059 | −0.423548 | ||||||||
\(88\) | 11.4561 | 1.22123 | ||||||||
\(89\) | −10.5620 | −1.11957 | −0.559785 | − | 0.828638i | \(-0.689116\pi\) | ||||
−0.559785 | + | 0.828638i | \(0.689116\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.545467 | 0.0571805 | ||||||||
\(92\) | −0.928992 | −0.0968541 | ||||||||
\(93\) | −2.46572 | −0.255683 | ||||||||
\(94\) | −5.77266 | −0.595404 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 13.4863 | 1.37644 | ||||||||
\(97\) | 15.0252 | 1.52558 | 0.762789 | − | 0.646648i | \(-0.223830\pi\) | ||||
0.762789 | + | 0.646648i | \(0.223830\pi\) | |||||||
\(98\) | 2.43879 | 0.246355 | ||||||||
\(99\) | 16.5793 | 1.66629 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.6414 | −1.85488 | −0.927442 | − | 0.373966i | \(-0.877998\pi\) | ||||
−0.927442 | + | 0.373966i | \(0.877998\pi\) | |||||||
\(102\) | −0.898916 | −0.0890060 | ||||||||
\(103\) | 16.0308 | 1.57956 | 0.789780 | − | 0.613390i | \(-0.210195\pi\) | ||||
0.789780 | + | 0.613390i | \(0.210195\pi\) | |||||||
\(104\) | −0.693348 | −0.0679884 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.04252 | 0.198387 | ||||||||
\(107\) | −16.5838 | −1.60322 | −0.801610 | − | 0.597847i | \(-0.796023\pi\) | ||||
−0.801610 | + | 0.597847i | \(0.796023\pi\) | |||||||
\(108\) | 0.326897 | 0.0314557 | ||||||||
\(109\) | −3.87084 | −0.370759 | −0.185379 | − | 0.982667i | \(-0.559351\pi\) | ||||
−0.185379 | + | 0.982667i | \(0.559351\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.4939 | 1.56553 | ||||||||
\(112\) | −3.49599 | −0.330340 | ||||||||
\(113\) | −3.50164 | −0.329407 | −0.164703 | − | 0.986343i | \(-0.552667\pi\) | ||||
−0.164703 | + | 0.986343i | \(0.552667\pi\) | |||||||
\(114\) | −2.59425 | −0.242974 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.66345 | −0.247295 | ||||||||
\(117\) | −1.00341 | −0.0927656 | ||||||||
\(118\) | −6.30224 | −0.580168 | ||||||||
\(119\) | 1.05040 | 0.0962901 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.9803 | 1.63457 | ||||||||
\(122\) | 5.05366 | 0.457536 | ||||||||
\(123\) | 20.0898 | 1.81144 | ||||||||
\(124\) | −1.66236 | −0.149284 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.99603 | 0.266908 | ||||||||
\(127\) | −17.1431 | −1.52121 | −0.760603 | − | 0.649218i | \(-0.775096\pi\) | ||||
−0.760603 | + | 0.649218i | \(0.775096\pi\) | |||||||
\(128\) | 11.5190 | 1.01815 | ||||||||
\(129\) | 26.6618 | 2.34744 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9361 | −1.47972 | −0.739858 | − | 0.672763i | \(-0.765107\pi\) | ||||
−0.739858 | + | 0.672763i | \(0.765107\pi\) | |||||||
\(132\) | 22.0658 | 1.92058 | ||||||||
\(133\) | 3.03143 | 0.262858 | ||||||||
\(134\) | −0.398623 | −0.0344358 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.33517 | −0.114490 | ||||||||
\(137\) | −9.79885 | −0.837173 | −0.418586 | − | 0.908177i | \(-0.637474\pi\) | ||||
−0.418586 | + | 0.908177i | \(0.637474\pi\) | |||||||
\(138\) | 0.800674 | 0.0681579 | ||||||||
\(139\) | 16.4079 | 1.39170 | 0.695849 | − | 0.718188i | \(-0.255028\pi\) | ||||
0.695849 | + | 0.718188i | \(0.255028\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.4959 | −2.06292 | ||||||||
\(142\) | −0.583050 | −0.0489285 | ||||||||
\(143\) | −1.75394 | −0.146672 | ||||||||
\(144\) | 6.43104 | 0.535920 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.92296 | −0.241906 | ||||||||
\(147\) | 10.3488 | 0.853556 | ||||||||
\(148\) | 11.1200 | 0.914060 | ||||||||
\(149\) | 1.86445 | 0.152742 | 0.0763709 | − | 0.997079i | \(-0.475667\pi\) | ||||
0.0763709 | + | 0.997079i | \(0.475667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.28758 | 0.755813 | 0.377906 | − | 0.925844i | \(-0.376644\pi\) | ||||
0.377906 | + | 0.925844i | \(0.376644\pi\) | |||||||
\(152\) | −3.85327 | −0.312542 | ||||||||
\(153\) | −1.93226 | −0.156214 | ||||||||
\(154\) | 5.23700 | 0.422009 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.33546 | −0.106923 | ||||||||
\(157\) | 12.2141 | 0.974789 | 0.487394 | − | 0.873182i | \(-0.337947\pi\) | ||||
0.487394 | + | 0.873182i | \(0.337947\pi\) | |||||||
\(158\) | 7.91851 | 0.629963 | ||||||||
\(159\) | 8.66730 | 0.687362 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.935602 | −0.0737358 | ||||||||
\(162\) | 5.08688 | 0.399663 | ||||||||
\(163\) | −12.4555 | −0.975590 | −0.487795 | − | 0.872958i | \(-0.662199\pi\) | ||||
−0.487795 | + | 0.872958i | \(0.662199\pi\) | |||||||
\(164\) | 13.5444 | 1.05764 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.77266 | −0.215200 | ||||||||
\(167\) | −6.58092 | −0.509247 | −0.254624 | − | 0.967040i | \(-0.581952\pi\) | ||||
−0.254624 | + | 0.967040i | \(0.581952\pi\) | |||||||
\(168\) | 8.78486 | 0.677767 | ||||||||
\(169\) | −12.8938 | −0.991834 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.57645 | −0.426442 | ||||||||
\(172\) | 17.9751 | 1.37059 | ||||||||
\(173\) | 4.41674 | 0.335799 | 0.167899 | − | 0.985804i | \(-0.446302\pi\) | ||||
0.167899 | + | 0.985804i | \(0.446302\pi\) | |||||||
\(174\) | 2.29556 | 0.174026 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.2413 | 0.847345 | ||||||||
\(177\) | −26.7431 | −2.01013 | ||||||||
\(178\) | 6.13723 | 0.460004 | ||||||||
\(179\) | 11.1637 | 0.834412 | 0.417206 | − | 0.908812i | \(-0.363009\pi\) | ||||
0.417206 | + | 0.908812i | \(0.363009\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.8449 | 1.32640 | 0.663200 | − | 0.748443i | \(-0.269198\pi\) | ||||
0.663200 | + | 0.748443i | \(0.269198\pi\) | |||||||
\(182\) | −0.316953 | −0.0234941 | ||||||||
\(183\) | 21.4448 | 1.58525 | ||||||||
\(184\) | 1.18925 | 0.0876728 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.43275 | 0.105054 | ||||||||
\(187\) | −3.37755 | −0.246991 | ||||||||
\(188\) | −16.5149 | −1.20447 | ||||||||
\(189\) | 0.329223 | 0.0239474 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.5220 | −1.84671 | −0.923354 | − | 0.383950i | \(-0.874563\pi\) | ||||
−0.923354 | + | 0.383950i | \(0.874563\pi\) | |||||||
\(192\) | 2.46123 | 0.177624 | ||||||||
\(193\) | −13.1431 | −0.946062 | −0.473031 | − | 0.881046i | \(-0.656840\pi\) | ||||
−0.473031 | + | 0.881046i | \(0.656840\pi\) | |||||||
\(194\) | −8.73064 | −0.626824 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.97707 | 0.498362 | ||||||||
\(197\) | 0.217382 | 0.0154879 | 0.00774393 | − | 0.999970i | \(-0.497535\pi\) | ||||
0.00774393 | + | 0.999970i | \(0.497535\pi\) | |||||||
\(198\) | −9.63370 | −0.684637 | ||||||||
\(199\) | −2.75888 | −0.195572 | −0.0977860 | − | 0.995207i | \(-0.531176\pi\) | ||||
−0.0977860 | + | 0.995207i | \(0.531176\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.69153 | −0.119311 | ||||||||
\(202\) | 10.8319 | 0.762128 | ||||||||
\(203\) | −2.68240 | −0.188268 | ||||||||
\(204\) | −2.57169 | −0.180054 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.31496 | −0.649004 | ||||||||
\(207\) | 1.72108 | 0.119624 | ||||||||
\(208\) | −0.680345 | −0.0471735 | ||||||||
\(209\) | −9.74751 | −0.674249 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.3289 | −1.19297 | −0.596484 | − | 0.802625i | \(-0.703436\pi\) | ||||
−0.596484 | + | 0.802625i | \(0.703436\pi\) | |||||||
\(212\) | 5.84341 | 0.401327 | ||||||||
\(213\) | −2.47413 | −0.169525 | ||||||||
\(214\) | 9.63632 | 0.658725 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.418478 | −0.0284738 | ||||||||
\(217\) | −1.67419 | −0.113651 | ||||||||
\(218\) | 2.24921 | 0.152336 | ||||||||
\(219\) | −12.4034 | −0.838143 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.204416 | 0.0137505 | ||||||||
\(222\) | −9.58405 | −0.643239 | ||||||||
\(223\) | 20.1921 | 1.35216 | 0.676081 | − | 0.736827i | \(-0.263677\pi\) | ||||
0.676081 | + | 0.736827i | \(0.263677\pi\) | |||||||
\(224\) | 9.15701 | 0.611829 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.03469 | 0.135345 | ||||||||
\(227\) | −6.31694 | −0.419270 | −0.209635 | − | 0.977780i | \(-0.567228\pi\) | ||||
−0.209635 | + | 0.977780i | \(0.567228\pi\) | |||||||
\(228\) | −7.42183 | −0.491522 | ||||||||
\(229\) | −12.0127 | −0.793822 | −0.396911 | − | 0.917857i | \(-0.629918\pi\) | ||||
−0.396911 | + | 0.917857i | \(0.629918\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 22.2228 | 1.46215 | ||||||||
\(232\) | 3.40962 | 0.223853 | ||||||||
\(233\) | −28.3769 | −1.85903 | −0.929516 | − | 0.368781i | \(-0.879775\pi\) | ||||
−0.929516 | + | 0.368781i | \(0.879775\pi\) | |||||||
\(234\) | 0.583050 | 0.0381152 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −18.0299 | −1.17365 | ||||||||
\(237\) | 33.6016 | 2.18266 | ||||||||
\(238\) | −0.610353 | −0.0395633 | ||||||||
\(239\) | 8.20713 | 0.530875 | 0.265438 | − | 0.964128i | \(-0.414484\pi\) | ||||
0.265438 | + | 0.964128i | \(0.414484\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5115 | −0.741521 | −0.370761 | − | 0.928728i | \(-0.620903\pi\) | ||||
−0.370761 | + | 0.928728i | \(0.620903\pi\) | |||||||
\(242\) | −10.4477 | −0.671607 | ||||||||
\(243\) | 22.1758 | 1.42258 | ||||||||
\(244\) | 14.4579 | 0.925572 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.6735 | −0.744278 | ||||||||
\(247\) | 0.589938 | 0.0375369 | ||||||||
\(248\) | 2.12808 | 0.135133 | ||||||||
\(249\) | −11.7656 | −0.745613 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.4877 | 0.661977 | 0.330988 | − | 0.943635i | \(-0.392618\pi\) | ||||
0.330988 | + | 0.943635i | \(0.392618\pi\) | |||||||
\(252\) | 8.57129 | 0.539940 | ||||||||
\(253\) | 3.00842 | 0.189137 | ||||||||
\(254\) | 9.96129 | 0.625027 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.69698 | −0.293561 | ||||||||
\(257\) | −19.3291 | −1.20571 | −0.602857 | − | 0.797849i | \(-0.705971\pi\) | ||||
−0.602857 | + | 0.797849i | \(0.705971\pi\) | |||||||
\(258\) | −15.4923 | −0.964508 | ||||||||
\(259\) | 11.1991 | 0.695881 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.93440 | 0.305432 | ||||||||
\(262\) | 9.84102 | 0.607980 | ||||||||
\(263\) | −4.86634 | −0.300071 | −0.150036 | − | 0.988681i | \(-0.547939\pi\) | ||||
−0.150036 | + | 0.988681i | \(0.547939\pi\) | |||||||
\(264\) | −28.2476 | −1.73852 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.76146 | −0.108002 | ||||||||
\(267\) | 26.0429 | 1.59380 | ||||||||
\(268\) | −1.14041 | −0.0696617 | ||||||||
\(269\) | 17.7368 | 1.08143 | 0.540717 | − | 0.841204i | \(-0.318153\pi\) | ||||
0.540717 | + | 0.841204i | \(0.318153\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.2534 | −1.41254 | −0.706272 | − | 0.707941i | \(-0.749624\pi\) | ||||
−0.706272 | + | 0.707941i | \(0.749624\pi\) | |||||||
\(272\) | −1.31013 | −0.0794385 | ||||||||
\(273\) | −1.34497 | −0.0814011 | ||||||||
\(274\) | 5.69379 | 0.343974 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.29063 | 0.137880 | ||||||||
\(277\) | −6.12148 | −0.367804 | −0.183902 | − | 0.982945i | \(-0.558873\pi\) | ||||
−0.183902 | + | 0.982945i | \(0.558873\pi\) | |||||||
\(278\) | −9.53408 | −0.571816 | ||||||||
\(279\) | 3.07975 | 0.184380 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.0759 | −0.899354 | −0.449677 | − | 0.893191i | \(-0.648461\pi\) | ||||
−0.449677 | + | 0.893191i | \(0.648461\pi\) | |||||||
\(282\) | 14.2337 | 0.847607 | ||||||||
\(283\) | 11.8948 | 0.707072 | 0.353536 | − | 0.935421i | \(-0.384979\pi\) | ||||
0.353536 | + | 0.935421i | \(0.384979\pi\) | |||||||
\(284\) | −1.66804 | −0.0989797 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.01916 | 0.0602641 | ||||||||
\(287\) | 13.6408 | 0.805189 | ||||||||
\(288\) | −16.8448 | −0.992587 | ||||||||
\(289\) | −16.6064 | −0.976845 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −37.0479 | −2.17178 | ||||||||
\(292\) | −8.36224 | −0.489363 | ||||||||
\(293\) | −11.2627 | −0.657974 | −0.328987 | − | 0.944334i | \(-0.606707\pi\) | ||||
−0.328987 | + | 0.944334i | \(0.606707\pi\) | |||||||
\(294\) | −6.01336 | −0.350706 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −14.2353 | −0.827411 | ||||||||
\(297\) | −1.05861 | −0.0614268 | ||||||||
\(298\) | −1.08337 | −0.0627580 | ||||||||
\(299\) | −0.182075 | −0.0105297 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.1030 | 1.04344 | ||||||||
\(302\) | −5.39671 | −0.310545 | ||||||||
\(303\) | 45.9643 | 2.64058 | ||||||||
\(304\) | −3.78101 | −0.216856 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.12277 | 0.0641847 | ||||||||
\(307\) | −15.1566 | −0.865034 | −0.432517 | − | 0.901626i | \(-0.642374\pi\) | ||||
−0.432517 | + | 0.901626i | \(0.642374\pi\) | |||||||
\(308\) | 14.9824 | 0.853702 | ||||||||
\(309\) | −39.5273 | −2.24863 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.6418 | 1.05708 | 0.528539 | − | 0.848909i | \(-0.322740\pi\) | ||||
0.528539 | + | 0.848909i | \(0.322740\pi\) | |||||||
\(312\) | 1.70960 | 0.0967870 | ||||||||
\(313\) | 1.23926 | 0.0700469 | 0.0350235 | − | 0.999386i | \(-0.488849\pi\) | ||||
0.0350235 | + | 0.999386i | \(0.488849\pi\) | |||||||
\(314\) | −7.09719 | −0.400518 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 22.6539 | 1.27438 | ||||||||
\(317\) | 9.07207 | 0.509538 | 0.254769 | − | 0.967002i | \(-0.418001\pi\) | ||||
0.254769 | + | 0.967002i | \(0.418001\pi\) | |||||||
\(318\) | −5.03628 | −0.282421 | ||||||||
\(319\) | 8.62522 | 0.482920 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 40.8910 | 2.28231 | ||||||||
\(322\) | 0.543648 | 0.0302963 | ||||||||
\(323\) | 1.13604 | 0.0632108 | ||||||||
\(324\) | 14.5529 | 0.808497 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.23748 | 0.400847 | ||||||||
\(327\) | 9.54438 | 0.527805 | ||||||||
\(328\) | −17.3389 | −0.957379 | ||||||||
\(329\) | −16.6324 | −0.916973 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.2154 | 1.66079 | 0.830394 | − | 0.557176i | \(-0.188115\pi\) | ||||
0.830394 | + | 0.557176i | \(0.188115\pi\) | |||||||
\(332\) | −7.93224 | −0.435338 | ||||||||
\(333\) | −20.6014 | −1.12895 | ||||||||
\(334\) | 3.82396 | 0.209238 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.62012 | 0.470266 | ||||||||
\(337\) | 7.31819 | 0.398647 | 0.199324 | − | 0.979934i | \(-0.436125\pi\) | ||||
0.199324 | + | 0.979934i | \(0.436125\pi\) | |||||||
\(338\) | 7.49219 | 0.407521 | ||||||||
\(339\) | 8.63405 | 0.468937 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.38333 | 0.291524 | ||||||||
\(342\) | 3.24029 | 0.175215 | ||||||||
\(343\) | 18.7461 | 1.01219 | ||||||||
\(344\) | −23.0109 | −1.24067 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.56642 | −0.137972 | ||||||||
\(347\) | −18.8592 | −1.01241 | −0.506206 | − | 0.862412i | \(-0.668953\pi\) | ||||
−0.506206 | + | 0.862412i | \(0.668953\pi\) | |||||||
\(348\) | 6.56731 | 0.352045 | ||||||||
\(349\) | −3.95224 | −0.211559 | −0.105779 | − | 0.994390i | \(-0.533734\pi\) | ||||
−0.105779 | + | 0.994390i | \(0.533734\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.0640692 | 0.00341976 | ||||||||
\(352\) | −29.4442 | −1.56938 | ||||||||
\(353\) | −29.1807 | −1.55313 | −0.776565 | − | 0.630037i | \(-0.783040\pi\) | ||||
−0.776565 | + | 0.630037i | \(0.783040\pi\) | |||||||
\(354\) | 15.5395 | 0.825916 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 17.5579 | 0.930564 | ||||||||
\(357\) | −2.58999 | −0.137077 | ||||||||
\(358\) | −6.48684 | −0.342840 | ||||||||
\(359\) | −19.0423 | −1.00502 | −0.502508 | − | 0.864573i | \(-0.667589\pi\) | ||||
−0.502508 | + | 0.864573i | \(0.667589\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.7214 | −0.827444 | ||||||||
\(362\) | −10.3691 | −0.544986 | ||||||||
\(363\) | −44.3343 | −2.32695 | ||||||||
\(364\) | −0.906764 | −0.0475273 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −12.4609 | −0.651340 | ||||||||
\(367\) | −21.8273 | −1.13938 | −0.569689 | − | 0.821861i | \(-0.692936\pi\) | ||||
−0.569689 | + | 0.821861i | \(0.692936\pi\) | |||||||
\(368\) | 1.16695 | 0.0608314 | ||||||||
\(369\) | −25.0928 | −1.30628 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.88499 | 0.305534 | ||||||||
\(372\) | 4.09891 | 0.212519 | ||||||||
\(373\) | 0.572836 | 0.0296603 | 0.0148302 | − | 0.999890i | \(-0.495279\pi\) | ||||
0.0148302 | + | 0.999890i | \(0.495279\pi\) | |||||||
\(374\) | 1.96258 | 0.101483 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 21.1416 | 1.09029 | ||||||||
\(377\) | −0.522015 | −0.0268851 | ||||||||
\(378\) | −0.191300 | −0.00983943 | ||||||||
\(379\) | 23.4864 | 1.20642 | 0.603208 | − | 0.797584i | \(-0.293889\pi\) | ||||
0.603208 | + | 0.797584i | \(0.293889\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 42.2700 | 2.16556 | ||||||||
\(382\) | 14.8300 | 0.758768 | ||||||||
\(383\) | −24.4037 | −1.24697 | −0.623485 | − | 0.781835i | \(-0.714284\pi\) | ||||
−0.623485 | + | 0.781835i | \(0.714284\pi\) | |||||||
\(384\) | −28.4027 | −1.44942 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.63703 | 0.388714 | ||||||||
\(387\) | −33.3014 | −1.69280 | ||||||||
\(388\) | −24.9773 | −1.26803 | ||||||||
\(389\) | 22.0685 | 1.11892 | 0.559458 | − | 0.828859i | \(-0.311009\pi\) | ||||
0.559458 | + | 0.828859i | \(0.311009\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.350620 | −0.0177316 | ||||||||
\(392\) | −8.93172 | −0.451120 | ||||||||
\(393\) | 41.7597 | 2.10650 | ||||||||
\(394\) | −0.126314 | −0.00636359 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −27.5608 | −1.38498 | ||||||||
\(397\) | 12.7949 | 0.642156 | 0.321078 | − | 0.947053i | \(-0.395955\pi\) | ||||
0.321078 | + | 0.947053i | \(0.395955\pi\) | |||||||
\(398\) | 1.60310 | 0.0803559 | ||||||||
\(399\) | −7.47464 | −0.374200 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.9209 | 0.545362 | 0.272681 | − | 0.962104i | \(-0.412090\pi\) | ||||
0.272681 | + | 0.962104i | \(0.412090\pi\) | |||||||
\(402\) | 0.982891 | 0.0490221 | ||||||||
\(403\) | −0.325810 | −0.0162297 | ||||||||
\(404\) | 30.9887 | 1.54174 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.55865 | 0.0773547 | ||||||||
\(407\) | −36.0107 | −1.78498 | ||||||||
\(408\) | 3.29216 | 0.162986 | ||||||||
\(409\) | 10.9359 | 0.540744 | 0.270372 | − | 0.962756i | \(-0.412853\pi\) | ||||
0.270372 | + | 0.962756i | \(0.412853\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.1612 | 1.19178 | ||||||||
\(412\) | −26.6490 | −1.31290 | ||||||||
\(413\) | −18.1582 | −0.893508 | ||||||||
\(414\) | −1.00007 | −0.0491505 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.78202 | 0.0873708 | ||||||||
\(417\) | −40.4572 | −1.98120 | ||||||||
\(418\) | 5.66395 | 0.277033 | ||||||||
\(419\) | 10.6004 | 0.517863 | 0.258932 | − | 0.965896i | \(-0.416630\pi\) | ||||
0.258932 | + | 0.965896i | \(0.416630\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.7943 | −1.30587 | −0.652936 | − | 0.757413i | \(-0.726463\pi\) | ||||
−0.652936 | + | 0.757413i | \(0.726463\pi\) | |||||||
\(422\) | 10.0692 | 0.490162 | ||||||||
\(423\) | 30.5961 | 1.48763 | ||||||||
\(424\) | −7.48046 | −0.363283 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.43764 | 0.0696537 | ||||||||
\(427\) | 14.5608 | 0.704645 | ||||||||
\(428\) | 27.5683 | 1.33257 | ||||||||
\(429\) | 4.32472 | 0.208800 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.9475 | 1.05717 | 0.528586 | − | 0.848880i | \(-0.322722\pi\) | ||||
0.528586 | + | 0.848880i | \(0.322722\pi\) | |||||||
\(432\) | −0.410630 | −0.0197564 | ||||||||
\(433\) | −20.8138 | −1.00025 | −0.500124 | − | 0.865954i | \(-0.666712\pi\) | ||||
−0.500124 | + | 0.865954i | \(0.666712\pi\) | |||||||
\(434\) | 0.972816 | 0.0466967 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.43473 | 0.308168 | ||||||||
\(437\) | −1.01188 | −0.0484048 | ||||||||
\(438\) | 7.20720 | 0.344373 | ||||||||
\(439\) | −17.8641 | −0.852608 | −0.426304 | − | 0.904580i | \(-0.640185\pi\) | ||||
−0.426304 | + | 0.904580i | \(0.640185\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.9260 | −0.615523 | ||||||||
\(442\) | −0.118779 | −0.00564975 | ||||||||
\(443\) | 0.492530 | 0.0234008 | 0.0117004 | − | 0.999932i | \(-0.496276\pi\) | ||||
0.0117004 | + | 0.999932i | \(0.496276\pi\) | |||||||
\(444\) | −27.4188 | −1.30124 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.7330 | −0.555571 | ||||||||
\(447\) | −4.59721 | −0.217440 | ||||||||
\(448\) | 1.67114 | 0.0789541 | ||||||||
\(449\) | 22.5350 | 1.06349 | 0.531746 | − | 0.846904i | \(-0.321536\pi\) | ||||
0.531746 | + | 0.846904i | \(0.321536\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −43.8617 | −2.06536 | ||||||||
\(452\) | 5.82100 | 0.273797 | ||||||||
\(453\) | −22.9005 | −1.07596 | ||||||||
\(454\) | 3.67056 | 0.172268 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.50107 | 0.444928 | ||||||||
\(457\) | 5.72325 | 0.267722 | 0.133861 | − | 0.991000i | \(-0.457262\pi\) | ||||
0.133861 | + | 0.991000i | \(0.457262\pi\) | |||||||
\(458\) | 6.98019 | 0.326163 | ||||||||
\(459\) | 0.123377 | 0.00575876 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.00807 | −0.0935249 | −0.0467625 | − | 0.998906i | \(-0.514890\pi\) | ||||
−0.0467625 | + | 0.998906i | \(0.514890\pi\) | |||||||
\(462\) | −12.9129 | −0.600764 | ||||||||
\(463\) | 20.5390 | 0.954528 | 0.477264 | − | 0.878760i | \(-0.341629\pi\) | ||||
0.477264 | + | 0.878760i | \(0.341629\pi\) | |||||||
\(464\) | 3.34568 | 0.155319 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.4889 | 0.763832 | ||||||||
\(467\) | 5.95062 | 0.275362 | 0.137681 | − | 0.990477i | \(-0.456035\pi\) | ||||
0.137681 | + | 0.990477i | \(0.456035\pi\) | |||||||
\(468\) | 1.66804 | 0.0771050 | ||||||||
\(469\) | −1.14853 | −0.0530340 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.1164 | −1.38769 | ||||||||
\(472\) | 23.0811 | 1.06239 | ||||||||
\(473\) | −58.2100 | −2.67650 | ||||||||
\(474\) | −19.5248 | −0.896804 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.74615 | −0.0800344 | ||||||||
\(477\) | −10.8257 | −0.495676 | ||||||||
\(478\) | −4.76889 | −0.218124 | ||||||||
\(479\) | −22.2840 | −1.01818 | −0.509090 | − | 0.860713i | \(-0.670018\pi\) | ||||
−0.509090 | + | 0.860713i | \(0.670018\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.17944 | 0.0993737 | ||||||||
\(482\) | 6.68896 | 0.304674 | ||||||||
\(483\) | 2.30693 | 0.104969 | ||||||||
\(484\) | −29.8897 | −1.35862 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −12.8856 | −0.584502 | ||||||||
\(487\) | 38.0611 | 1.72472 | 0.862358 | − | 0.506300i | \(-0.168987\pi\) | ||||
0.862358 | + | 0.506300i | \(0.168987\pi\) | |||||||
\(488\) | −18.5083 | −0.837832 | ||||||||
\(489\) | 30.7117 | 1.38883 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.5955 | 0.794073 | 0.397037 | − | 0.917803i | \(-0.370039\pi\) | ||||
0.397037 | + | 0.917803i | \(0.370039\pi\) | |||||||
\(492\) | −33.3966 | −1.50563 | ||||||||
\(493\) | −1.00524 | −0.0452737 | ||||||||
\(494\) | −0.342793 | −0.0154230 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.08817 | 0.0937615 | ||||||||
\(497\) | −1.67990 | −0.0753540 | ||||||||
\(498\) | 6.83659 | 0.306355 | ||||||||
\(499\) | −7.07301 | −0.316632 | −0.158316 | − | 0.987389i | \(-0.550606\pi\) | ||||
−0.158316 | + | 0.987389i | \(0.550606\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.2267 | 0.724955 | ||||||||
\(502\) | −6.09405 | −0.271991 | ||||||||
\(503\) | −4.43425 | −0.197713 | −0.0988567 | − | 0.995102i | \(-0.531519\pi\) | ||||
−0.0988567 | + | 0.995102i | \(0.531519\pi\) | |||||||
\(504\) | −10.9726 | −0.488757 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.74809 | −0.0777121 | ||||||||
\(507\) | 31.7926 | 1.41196 | ||||||||
\(508\) | 28.4980 | 1.26440 | ||||||||
\(509\) | 15.4718 | 0.685775 | 0.342888 | − | 0.939376i | \(-0.388595\pi\) | ||||
0.342888 | + | 0.939376i | \(0.388595\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.42175 | −0.372556 | ||||||||
\(512\) | −20.3088 | −0.897532 | ||||||||
\(513\) | 0.356064 | 0.0157206 | ||||||||
\(514\) | 11.2315 | 0.495400 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −44.3215 | −1.95115 | ||||||||
\(517\) | 53.4812 | 2.35210 | ||||||||
\(518\) | −6.50745 | −0.285921 | ||||||||
\(519\) | −10.8904 | −0.478037 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.92019 | 0.390800 | 0.195400 | − | 0.980724i | \(-0.437399\pi\) | ||||
0.195400 | + | 0.980724i | \(0.437399\pi\) | |||||||
\(522\) | −2.86722 | −0.125495 | ||||||||
\(523\) | −37.7360 | −1.65008 | −0.825039 | − | 0.565075i | \(-0.808847\pi\) | ||||
−0.825039 | + | 0.565075i | \(0.808847\pi\) | |||||||
\(524\) | 28.1540 | 1.22991 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.82767 | 0.123292 | ||||||||
\(527\) | −0.627408 | −0.0273303 | ||||||||
\(528\) | −27.7179 | −1.20626 | ||||||||
\(529\) | −22.6877 | −0.986422 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 33.4029 | 1.44956 | ||||||||
\(532\) | −5.03933 | −0.218483 | ||||||||
\(533\) | 2.65459 | 0.114983 | ||||||||
\(534\) | −15.1327 | −0.654854 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.45990 | 0.0630581 | ||||||||
\(537\) | −27.5264 | −1.18785 | ||||||||
\(538\) | −10.3063 | −0.444336 | ||||||||
\(539\) | −22.5943 | −0.973206 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.8561 | 1.28361 | 0.641806 | − | 0.766867i | \(-0.278185\pi\) | ||||
0.641806 | + | 0.766867i | \(0.278185\pi\) | |||||||
\(542\) | 13.5118 | 0.580381 | ||||||||
\(543\) | −44.0004 | −1.88824 | ||||||||
\(544\) | 3.43162 | 0.147130 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.781516 | 0.0334458 | ||||||||
\(547\) | 42.0150 | 1.79643 | 0.898215 | − | 0.439556i | \(-0.144864\pi\) | ||||
0.898215 | + | 0.439556i | \(0.144864\pi\) | |||||||
\(548\) | 16.2892 | 0.695842 | ||||||||
\(549\) | −26.7852 | −1.14317 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.90109 | −0.123591 | ||||||||
\(552\) | −2.93236 | −0.124809 | ||||||||
\(553\) | 22.8151 | 0.970197 | ||||||||
\(554\) | 3.55699 | 0.151122 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −27.2758 | −1.15675 | ||||||||
\(557\) | 24.1764 | 1.02439 | 0.512194 | − | 0.858870i | \(-0.328833\pi\) | ||||
0.512194 | + | 0.858870i | \(0.328833\pi\) | |||||||
\(558\) | −1.78954 | −0.0757573 | ||||||||
\(559\) | 3.52298 | 0.149006 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.32807 | 0.351611 | ||||||||
\(562\) | 8.76012 | 0.369523 | ||||||||
\(563\) | 2.85978 | 0.120525 | 0.0602627 | − | 0.998183i | \(-0.480806\pi\) | ||||
0.0602627 | + | 0.998183i | \(0.480806\pi\) | |||||||
\(564\) | 40.7210 | 1.71466 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.91167 | −0.290519 | ||||||||
\(567\) | 14.6565 | 0.615515 | ||||||||
\(568\) | 2.13534 | 0.0895969 | ||||||||
\(569\) | 9.28905 | 0.389417 | 0.194709 | − | 0.980861i | \(-0.437624\pi\) | ||||
0.194709 | + | 0.980861i | \(0.437624\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.1986 | −0.803437 | −0.401719 | − | 0.915763i | \(-0.631587\pi\) | ||||
−0.401719 | + | 0.915763i | \(0.631587\pi\) | |||||||
\(572\) | 2.91569 | 0.121911 | ||||||||
\(573\) | 62.9300 | 2.62894 | ||||||||
\(574\) | −7.92619 | −0.330833 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.07415 | −0.128089 | ||||||||
\(577\) | 34.8805 | 1.45209 | 0.726047 | − | 0.687645i | \(-0.241355\pi\) | ||||
0.726047 | + | 0.687645i | \(0.241355\pi\) | |||||||
\(578\) | 9.64940 | 0.401362 | ||||||||
\(579\) | 32.4072 | 1.34680 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.98868 | −0.331426 | ||||||||
\(582\) | 21.5273 | 0.892334 | ||||||||
\(583\) | −18.9231 | −0.783715 | ||||||||
\(584\) | 10.7050 | 0.442974 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.54438 | 0.270346 | ||||||||
\(587\) | 44.2409 | 1.82602 | 0.913009 | − | 0.407938i | \(-0.133752\pi\) | ||||
0.913009 | + | 0.407938i | \(0.133752\pi\) | |||||||
\(588\) | −17.2035 | −0.709460 | ||||||||
\(589\) | −1.81068 | −0.0746079 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.536003 | −0.0220482 | ||||||||
\(592\) | −13.9684 | −0.574096 | ||||||||
\(593\) | −23.2861 | −0.956247 | −0.478124 | − | 0.878293i | \(-0.658683\pi\) | ||||
−0.478124 | + | 0.878293i | \(0.658683\pi\) | |||||||
\(594\) | 0.615124 | 0.0252388 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.09939 | −0.126956 | ||||||||
\(597\) | 6.80262 | 0.278413 | ||||||||
\(598\) | 0.105798 | 0.00432639 | ||||||||
\(599\) | 24.4588 | 0.999359 | 0.499679 | − | 0.866210i | \(-0.333451\pi\) | ||||
0.499679 | + | 0.866210i | \(0.333451\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.7169 | 0.845061 | 0.422531 | − | 0.906349i | \(-0.361142\pi\) | ||||
0.422531 | + | 0.906349i | \(0.361142\pi\) | |||||||
\(602\) | −10.5191 | −0.428725 | ||||||||
\(603\) | 2.11277 | 0.0860386 | ||||||||
\(604\) | −15.4393 | −0.628217 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −26.7083 | −1.08495 | ||||||||
\(607\) | −29.4411 | −1.19498 | −0.597488 | − | 0.801878i | \(-0.703835\pi\) | ||||
−0.597488 | + | 0.801878i | \(0.703835\pi\) | |||||||
\(608\) | 9.90356 | 0.401643 | ||||||||
\(609\) | 6.61404 | 0.268014 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.23679 | −0.130946 | ||||||||
\(612\) | 3.21212 | 0.129842 | ||||||||
\(613\) | 21.8105 | 0.880916 | 0.440458 | − | 0.897773i | \(-0.354816\pi\) | ||||
0.440458 | + | 0.897773i | \(0.354816\pi\) | |||||||
\(614\) | 8.80701 | 0.355422 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −19.1798 | −0.772775 | ||||||||
\(617\) | −23.2460 | −0.935848 | −0.467924 | − | 0.883769i | \(-0.654998\pi\) | ||||
−0.467924 | + | 0.883769i | \(0.654998\pi\) | |||||||
\(618\) | 22.9680 | 0.923910 | ||||||||
\(619\) | −2.69894 | −0.108480 | −0.0542398 | − | 0.998528i | \(-0.517274\pi\) | ||||
−0.0542398 | + | 0.998528i | \(0.517274\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.109893 | −0.00440987 | ||||||||
\(622\) | −10.8321 | −0.434328 | ||||||||
\(623\) | 17.6828 | 0.708446 | ||||||||
\(624\) | 1.67754 | 0.0671553 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.720091 | −0.0287806 | ||||||||
\(627\) | 24.0346 | 0.959849 | ||||||||
\(628\) | −20.3042 | −0.810226 | ||||||||
\(629\) | 4.19691 | 0.167342 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.16304 | 0.125918 | 0.0629592 | − | 0.998016i | \(-0.479946\pi\) | ||||
0.0629592 | + | 0.998016i | \(0.479946\pi\) | |||||||
\(632\) | −29.0005 | −1.15358 | ||||||||
\(633\) | 42.7281 | 1.69829 | ||||||||
\(634\) | −5.27148 | −0.209357 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −14.4082 | −0.571322 | ||||||||
\(637\) | 1.36745 | 0.0541804 | ||||||||
\(638\) | −5.01183 | −0.198420 | ||||||||
\(639\) | 3.09026 | 0.122249 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.1094 | −0.952264 | −0.476132 | − | 0.879374i | \(-0.657962\pi\) | ||||
−0.476132 | + | 0.879374i | \(0.657962\pi\) | |||||||
\(642\) | −23.7604 | −0.937749 | ||||||||
\(643\) | −6.01512 | −0.237213 | −0.118607 | − | 0.992941i | \(-0.537843\pi\) | ||||
−0.118607 | + | 0.992941i | \(0.537843\pi\) | |||||||
\(644\) | 1.55531 | 0.0612878 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.660113 | −0.0259718 | ||||||||
\(647\) | −2.25081 | −0.0884884 | −0.0442442 | − | 0.999021i | \(-0.514088\pi\) | ||||
−0.0442442 | + | 0.999021i | \(0.514088\pi\) | |||||||
\(648\) | −18.6300 | −0.731855 | ||||||||
\(649\) | 58.3875 | 2.29191 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.12808 | 0.161792 | ||||||||
\(652\) | 20.7055 | 0.810892 | ||||||||
\(653\) | 24.7232 | 0.967495 | 0.483747 | − | 0.875208i | \(-0.339275\pi\) | ||||
0.483747 | + | 0.875208i | \(0.339275\pi\) | |||||||
\(654\) | −5.54592 | −0.216863 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17.0137 | −0.664274 | ||||||||
\(657\) | 15.4922 | 0.604408 | ||||||||
\(658\) | 9.66453 | 0.376763 | ||||||||
\(659\) | −21.5721 | −0.840330 | −0.420165 | − | 0.907448i | \(-0.638028\pi\) | ||||
−0.420165 | + | 0.907448i | \(0.638028\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.9338 | 1.12540 | 0.562698 | − | 0.826663i | \(-0.309763\pi\) | ||||
0.562698 | + | 0.826663i | \(0.309763\pi\) | |||||||
\(662\) | −17.5572 | −0.682379 | ||||||||
\(663\) | −0.504031 | −0.0195749 | ||||||||
\(664\) | 10.1545 | 0.394070 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.9708 | 0.463858 | ||||||||
\(667\) | 0.895376 | 0.0346691 | ||||||||
\(668\) | 10.9399 | 0.423276 | ||||||||
\(669\) | −49.7879 | −1.92491 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −46.8199 | −1.80746 | ||||||||
\(672\) | −22.5786 | −0.870988 | ||||||||
\(673\) | −11.0864 | −0.427350 | −0.213675 | − | 0.976905i | \(-0.568543\pi\) | ||||
−0.213675 | + | 0.976905i | \(0.568543\pi\) | |||||||
\(674\) | −4.25236 | −0.163795 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.4342 | 0.824394 | ||||||||
\(677\) | −31.0895 | −1.19487 | −0.597434 | − | 0.801918i | \(-0.703813\pi\) | ||||
−0.597434 | + | 0.801918i | \(0.703813\pi\) | |||||||
\(678\) | −5.01696 | −0.192675 | ||||||||
\(679\) | −25.1550 | −0.965362 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.5758 | 0.596865 | ||||||||
\(682\) | −3.12808 | −0.119780 | ||||||||
\(683\) | 4.07538 | 0.155940 | 0.0779701 | − | 0.996956i | \(-0.475156\pi\) | ||||
0.0779701 | + | 0.996956i | \(0.475156\pi\) | |||||||
\(684\) | 9.27008 | 0.354450 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.8927 | −0.415886 | ||||||||
\(687\) | 29.6199 | 1.13007 | ||||||||
\(688\) | −22.5794 | −0.860831 | ||||||||
\(689\) | 1.14526 | 0.0436310 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.04037 | 0.267828 | 0.133914 | − | 0.990993i | \(-0.457245\pi\) | ||||
0.133914 | + | 0.990993i | \(0.457245\pi\) | |||||||
\(692\) | −7.34223 | −0.279110 | ||||||||
\(693\) | −27.7570 | −1.05440 | ||||||||
\(694\) | 10.9584 | 0.415976 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.40716 | −0.318672 | ||||||||
\(697\) | 5.11192 | 0.193628 | ||||||||
\(698\) | 2.29652 | 0.0869245 | ||||||||
\(699\) | 69.9694 | 2.64648 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.8283 | 0.862211 | 0.431106 | − | 0.902301i | \(-0.358124\pi\) | ||||
0.431106 | + | 0.902301i | \(0.358124\pi\) | |||||||
\(702\) | −0.0372285 | −0.00140510 | ||||||||
\(703\) | 12.1122 | 0.456820 | ||||||||
\(704\) | −5.37354 | −0.202523 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.9559 | 0.638144 | ||||||||
\(707\) | 31.2092 | 1.17374 | ||||||||
\(708\) | 44.4567 | 1.67078 | ||||||||
\(709\) | −19.3406 | −0.726352 | −0.363176 | − | 0.931721i | \(-0.618308\pi\) | ||||
−0.363176 | + | 0.931721i | \(0.618308\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −41.9695 | −1.57398 | ||||||||
\(712\) | −22.4767 | −0.842351 | ||||||||
\(713\) | 0.558839 | 0.0209287 | ||||||||
\(714\) | 1.50496 | 0.0563216 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.5581 | −0.693547 | ||||||||
\(717\) | −20.2365 | −0.755744 | ||||||||
\(718\) | 11.0649 | 0.412937 | ||||||||
\(719\) | −42.3226 | −1.57837 | −0.789184 | − | 0.614157i | \(-0.789496\pi\) | ||||
−0.789184 | + | 0.614157i | \(0.789496\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.8386 | −0.999521 | ||||||||
\(722\) | 9.13520 | 0.339977 | ||||||||
\(723\) | 28.3841 | 1.05562 | ||||||||
\(724\) | −29.6646 | −1.10248 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 25.7612 | 0.956087 | ||||||||
\(727\) | 25.0220 | 0.928015 | 0.464008 | − | 0.885831i | \(-0.346411\pi\) | ||||
0.464008 | + | 0.885831i | \(0.346411\pi\) | |||||||
\(728\) | 1.16080 | 0.0430220 | ||||||||
\(729\) | −28.4159 | −1.05244 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.78417 | 0.250922 | ||||||||
\(732\) | −35.6490 | −1.31763 | ||||||||
\(733\) | 38.1240 | 1.40814 | 0.704071 | − | 0.710130i | \(-0.251364\pi\) | ||||
0.704071 | + | 0.710130i | \(0.251364\pi\) | |||||||
\(734\) | 12.6831 | 0.468143 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.05658 | −0.112667 | ||||||||
\(737\) | 3.69307 | 0.136036 | ||||||||
\(738\) | 14.5806 | 0.536719 | ||||||||
\(739\) | 47.7727 | 1.75735 | 0.878673 | − | 0.477424i | \(-0.158429\pi\) | ||||
0.878673 | + | 0.477424i | \(0.158429\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.45462 | −0.0534368 | ||||||||
\(742\) | −3.41957 | −0.125536 | ||||||||
\(743\) | 53.5451 | 1.96438 | 0.982189 | − | 0.187896i | \(-0.0601667\pi\) | ||||
0.982189 | + | 0.187896i | \(0.0601667\pi\) | |||||||
\(744\) | −5.24723 | −0.192373 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.332856 | −0.0121867 | ||||||||
\(747\) | 14.6956 | 0.537682 | ||||||||
\(748\) | 5.61470 | 0.205294 | ||||||||
\(749\) | 27.7645 | 1.01449 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.9303 | −1.38410 | −0.692048 | − | 0.721852i | \(-0.743291\pi\) | ||||
−0.692048 | + | 0.721852i | \(0.743291\pi\) | |||||||
\(752\) | 20.7451 | 0.756495 | ||||||||
\(753\) | −25.8597 | −0.942378 | ||||||||
\(754\) | 0.303326 | 0.0110465 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.547287 | −0.0199046 | ||||||||
\(757\) | −30.4110 | −1.10531 | −0.552653 | − | 0.833412i | \(-0.686384\pi\) | ||||
−0.552653 | + | 0.833412i | \(0.686384\pi\) | |||||||
\(758\) | −13.6472 | −0.495688 | ||||||||
\(759\) | −7.41790 | −0.269253 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.8253 | 0.791167 | 0.395583 | − | 0.918430i | \(-0.370542\pi\) | ||||
0.395583 | + | 0.918430i | \(0.370542\pi\) | |||||||
\(762\) | −24.5617 | −0.889777 | ||||||||
\(763\) | 6.48052 | 0.234610 | ||||||||
\(764\) | 42.4268 | 1.53495 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14.1802 | 0.512350 | ||||||||
\(767\) | −3.53373 | −0.127595 | ||||||||
\(768\) | 11.5814 | 0.417908 | ||||||||
\(769\) | 37.4313 | 1.34981 | 0.674904 | − | 0.737905i | \(-0.264185\pi\) | ||||
0.674904 | + | 0.737905i | \(0.264185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 47.6600 | 1.71643 | ||||||||
\(772\) | 21.8486 | 0.786348 | ||||||||
\(773\) | −22.0976 | −0.794797 | −0.397398 | − | 0.917646i | \(-0.630087\pi\) | ||||
−0.397398 | + | 0.917646i | \(0.630087\pi\) | |||||||
\(774\) | 19.3503 | 0.695533 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 31.9748 | 1.14783 | ||||||||
\(777\) | −27.6139 | −0.990643 | ||||||||
\(778\) | −12.8233 | −0.459736 | ||||||||
\(779\) | 14.7529 | 0.528576 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.40171 | 0.193288 | ||||||||
\(782\) | 0.203734 | 0.00728550 | ||||||||
\(783\) | −0.315068 | −0.0112596 | ||||||||
\(784\) | −8.76422 | −0.313008 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −24.2652 | −0.865510 | ||||||||
\(787\) | 20.3038 | 0.723753 | 0.361877 | − | 0.932226i | \(-0.382136\pi\) | ||||
0.361877 | + | 0.932226i | \(0.382136\pi\) | |||||||
\(788\) | −0.361368 | −0.0128732 | ||||||||
\(789\) | 11.9990 | 0.427176 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.86242 | 0.208444 | ||||||||
\(792\) | 35.2821 | 1.25369 | ||||||||
\(793\) | 2.83363 | 0.100625 | ||||||||
\(794\) | −7.43468 | −0.263847 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.58626 | 0.162556 | ||||||||
\(797\) | −15.5996 | −0.552565 | −0.276282 | − | 0.961077i | \(-0.589102\pi\) | ||||
−0.276282 | + | 0.961077i | \(0.589102\pi\) | |||||||
\(798\) | 4.34326 | 0.153750 | ||||||||
\(799\) | −6.23304 | −0.220509 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.5283 | −1.14933 | ||||||||
\(802\) | −6.34576 | −0.224076 | ||||||||
\(803\) | 27.0800 | 0.955633 | ||||||||
\(804\) | 2.81193 | 0.0991692 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.189317 | 0.00666841 | ||||||||
\(807\) | −43.7340 | −1.53951 | ||||||||
\(808\) | −39.6702 | −1.39559 | ||||||||
\(809\) | 18.5700 | 0.652887 | 0.326443 | − | 0.945217i | \(-0.394150\pi\) | ||||
0.326443 | + | 0.945217i | \(0.394150\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.53602 | −0.0539369 | −0.0269684 | − | 0.999636i | \(-0.508585\pi\) | ||||
−0.0269684 | + | 0.999636i | \(0.508585\pi\) | |||||||
\(812\) | 4.45912 | 0.156484 | ||||||||
\(813\) | 57.3363 | 2.01087 | ||||||||
\(814\) | 20.9246 | 0.733407 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.23042 | 0.113087 | ||||||||
\(817\) | 19.5789 | 0.684980 | ||||||||
\(818\) | −6.35447 | −0.222179 | ||||||||
\(819\) | 1.67990 | 0.0587006 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.9559 | 0.766267 | 0.383133 | − | 0.923693i | \(-0.374845\pi\) | ||||
0.383133 | + | 0.923693i | \(0.374845\pi\) | |||||||
\(822\) | −14.0393 | −0.489676 | ||||||||
\(823\) | 50.5105 | 1.76069 | 0.880343 | − | 0.474338i | \(-0.157313\pi\) | ||||
0.880343 | + | 0.474338i | \(0.157313\pi\) | |||||||
\(824\) | 34.1147 | 1.18844 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.5511 | 0.367121 | ||||||||
\(827\) | 20.7591 | 0.721864 | 0.360932 | − | 0.932592i | \(-0.382459\pi\) | ||||
0.360932 | + | 0.932592i | \(0.382459\pi\) | |||||||
\(828\) | −2.86107 | −0.0994289 | ||||||||
\(829\) | 14.7970 | 0.513920 | 0.256960 | − | 0.966422i | \(-0.417279\pi\) | ||||
0.256960 | + | 0.966422i | \(0.417279\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.0938 | 0.523599 | ||||||||
\(832\) | 0.325217 | 0.0112749 | ||||||||
\(833\) | 2.63329 | 0.0912380 | ||||||||
\(834\) | 23.5083 | 0.814027 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16.2039 | 0.560423 | ||||||||
\(837\) | −0.196646 | −0.00679708 | ||||||||
\(838\) | −6.15954 | −0.212778 | ||||||||
\(839\) | −19.1059 | −0.659608 | −0.329804 | − | 0.944049i | \(-0.606983\pi\) | ||||
−0.329804 | + | 0.944049i | \(0.606983\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4329 | −0.911480 | ||||||||
\(842\) | 15.5693 | 0.536552 | ||||||||
\(843\) | 37.1729 | 1.28030 | ||||||||
\(844\) | 28.8068 | 0.991572 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −17.7784 | −0.611233 | ||||||||
\(847\) | −30.1024 | −1.03433 | ||||||||
\(848\) | −7.34018 | −0.252063 | ||||||||
\(849\) | −29.3292 | −1.00657 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.73823 | −0.128145 | ||||||||
\(852\) | 4.11290 | 0.140906 | ||||||||
\(853\) | −36.3723 | −1.24536 | −0.622681 | − | 0.782476i | \(-0.713957\pi\) | ||||
−0.622681 | + | 0.782476i | \(0.713957\pi\) | |||||||
\(854\) | −8.46078 | −0.289522 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −35.2917 | −1.20624 | ||||||||
\(857\) | 13.6923 | 0.467719 | 0.233859 | − | 0.972270i | \(-0.424864\pi\) | ||||
0.233859 | + | 0.972270i | \(0.424864\pi\) | |||||||
\(858\) | −2.51295 | −0.0857908 | ||||||||
\(859\) | −45.9661 | −1.56834 | −0.784171 | − | 0.620545i | \(-0.786912\pi\) | ||||
−0.784171 | + | 0.620545i | \(0.786912\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −33.6342 | −1.14625 | ||||||||
\(862\) | −12.7529 | −0.434367 | ||||||||
\(863\) | 52.8198 | 1.79801 | 0.899004 | − | 0.437941i | \(-0.144292\pi\) | ||||
0.899004 | + | 0.437941i | \(0.144292\pi\) | |||||||
\(864\) | 1.07556 | 0.0365913 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.0942 | 0.410978 | ||||||||
\(867\) | 40.9466 | 1.39062 | ||||||||
\(868\) | 2.78311 | 0.0944649 | ||||||||
\(869\) | −73.3616 | −2.48862 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.223512 | −0.00757341 | ||||||||
\(872\) | −8.23744 | −0.278955 | ||||||||
\(873\) | 46.2739 | 1.56613 | ||||||||
\(874\) | 0.587970 | 0.0198884 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.6189 | 0.696648 | ||||||||
\(877\) | −31.8767 | −1.07640 | −0.538201 | − | 0.842817i | \(-0.680896\pi\) | ||||
−0.538201 | + | 0.842817i | \(0.680896\pi\) | |||||||
\(878\) | 10.3802 | 0.350316 | ||||||||
\(879\) | 27.7706 | 0.936679 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.3499 | −0.382387 | −0.191194 | − | 0.981552i | \(-0.561236\pi\) | ||||
−0.191194 | + | 0.981552i | \(0.561236\pi\) | |||||||
\(882\) | 7.51086 | 0.252904 | ||||||||
\(883\) | −40.3011 | −1.35624 | −0.678120 | − | 0.734951i | \(-0.737205\pi\) | ||||
−0.678120 | + | 0.734951i | \(0.737205\pi\) | |||||||
\(884\) | −0.339813 | −0.0114291 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.286193 | −0.00961484 | ||||||||
\(887\) | −48.6547 | −1.63367 | −0.816833 | − | 0.576875i | \(-0.804272\pi\) | ||||
−0.816833 | + | 0.576875i | \(0.804272\pi\) | |||||||
\(888\) | 35.1002 | 1.17789 | ||||||||
\(889\) | 28.7008 | 0.962595 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −47.1278 | −1.57884 | ||||||||
\(892\) | −33.5665 | −1.12389 | ||||||||
\(893\) | −17.9884 | −0.601958 | ||||||||
\(894\) | 2.67128 | 0.0893411 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −19.2851 | −0.644269 | ||||||||
\(897\) | 0.448945 | 0.0149899 | ||||||||
\(898\) | −13.0943 | −0.436963 | ||||||||
\(899\) | 1.60221 | 0.0534366 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.20542 | 0.0734732 | ||||||||
\(902\) | 25.4866 | 0.848609 | ||||||||
\(903\) | −44.6369 | −1.48542 | ||||||||
\(904\) | −7.45176 | −0.247842 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 13.3067 | 0.442087 | ||||||||
\(907\) | −40.5901 | −1.34777 | −0.673886 | − | 0.738835i | \(-0.735376\pi\) | ||||
−0.673886 | + | 0.738835i | \(0.735376\pi\) | |||||||
\(908\) | 10.5010 | 0.348489 | ||||||||
\(909\) | −57.4108 | −1.90419 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.30922 | 0.242165 | 0.121083 | − | 0.992642i | \(-0.461363\pi\) | ||||
0.121083 | + | 0.992642i | \(0.461363\pi\) | |||||||
\(912\) | 9.32289 | 0.308712 | ||||||||
\(913\) | 25.6875 | 0.850132 | ||||||||
\(914\) | −3.32559 | −0.110001 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.9695 | 0.659810 | ||||||||
\(917\) | 28.3543 | 0.936342 | ||||||||
\(918\) | −0.0716905 | −0.00236614 | ||||||||
\(919\) | −14.5908 | −0.481305 | −0.240652 | − | 0.970611i | \(-0.577361\pi\) | ||||
−0.240652 | + | 0.970611i | \(0.577361\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 37.3719 | 1.23145 | ||||||||
\(922\) | 1.16682 | 0.0384272 | ||||||||
\(923\) | −0.326922 | −0.0107608 | ||||||||
\(924\) | −36.9423 | −1.21531 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −11.9345 | −0.392193 | ||||||||
\(927\) | 49.3708 | 1.62155 | ||||||||
\(928\) | −8.76331 | −0.287670 | ||||||||
\(929\) | −21.7265 | −0.712824 | −0.356412 | − | 0.934329i | \(-0.616000\pi\) | ||||
−0.356412 | + | 0.934329i | \(0.616000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.59959 | 0.249067 | ||||||||
\(932\) | 47.1727 | 1.54519 | ||||||||
\(933\) | −45.9653 | −1.50484 | ||||||||
\(934\) | −3.45771 | −0.113140 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.13534 | −0.0697958 | ||||||||
\(937\) | −12.8632 | −0.420221 | −0.210111 | − | 0.977678i | \(-0.567382\pi\) | ||||
−0.210111 | + | 0.977678i | \(0.567382\pi\) | |||||||
\(938\) | 0.667371 | 0.0217904 | ||||||||
\(939\) | −3.05565 | −0.0997175 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.0452 | 1.33804 | 0.669018 | − | 0.743246i | \(-0.266715\pi\) | ||||
0.669018 | + | 0.743246i | \(0.266715\pi\) | |||||||
\(942\) | 17.4997 | 0.570170 | ||||||||
\(943\) | −4.55324 | −0.148274 | ||||||||
\(944\) | 22.6482 | 0.737137 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 33.8239 | 1.09971 | ||||||||
\(947\) | −10.4562 | −0.339782 | −0.169891 | − | 0.985463i | \(-0.554342\pi\) | ||||
−0.169891 | + | 0.985463i | \(0.554342\pi\) | |||||||
\(948\) | −55.8581 | −1.81419 | ||||||||
\(949\) | −1.63893 | −0.0532020 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.3691 | −0.725369 | ||||||||
\(952\) | 2.23533 | 0.0724476 | ||||||||
\(953\) | 35.9951 | 1.16600 | 0.582998 | − | 0.812474i | \(-0.301880\pi\) | ||||
0.582998 | + | 0.812474i | \(0.301880\pi\) | |||||||
\(954\) | 6.29047 | 0.203661 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.6432 | −0.441253 | ||||||||
\(957\) | −21.2673 | −0.687475 | ||||||||
\(958\) | 12.9485 | 0.418346 | ||||||||
\(959\) | 16.4051 | 0.529750 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −1.26640 | −0.0408303 | ||||||||
\(963\) | −51.0741 | −1.64584 | ||||||||
\(964\) | 19.1363 | 0.616338 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.34048 | −0.0431292 | ||||||||
\(967\) | 34.1188 | 1.09719 | 0.548593 | − | 0.836089i | \(-0.315164\pi\) | ||||
0.548593 | + | 0.836089i | \(0.315164\pi\) | |||||||
\(968\) | 38.2634 | 1.22983 | ||||||||
\(969\) | −2.80114 | −0.0899857 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.8349 | −1.31046 | −0.655228 | − | 0.755431i | \(-0.727427\pi\) | ||||
−0.655228 | + | 0.755431i | \(0.727427\pi\) | |||||||
\(972\) | −36.8641 | −1.18242 | ||||||||
\(973\) | −27.4699 | −0.880645 | ||||||||
\(974\) | −22.1161 | −0.708645 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.1612 | −0.581326 | ||||||||
\(977\) | −7.47323 | −0.239090 | −0.119545 | − | 0.992829i | \(-0.538144\pi\) | ||||
−0.119545 | + | 0.992829i | \(0.538144\pi\) | |||||||
\(978\) | −17.8456 | −0.570638 | ||||||||
\(979\) | −56.8587 | −1.81721 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.9212 | −0.380615 | ||||||||
\(982\) | −10.2242 | −0.326266 | ||||||||
\(983\) | −27.7520 | −0.885152 | −0.442576 | − | 0.896731i | \(-0.645935\pi\) | ||||
−0.442576 | + | 0.896731i | \(0.645935\pi\) | |||||||
\(984\) | 42.7527 | 1.36291 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.584111 | 0.0186019 | ||||||||
\(987\) | 41.0107 | 1.30539 | ||||||||
\(988\) | −0.980690 | −0.0311999 | ||||||||
\(989\) | −6.04273 | −0.192148 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.0311 | −1.55752 | −0.778762 | − | 0.627320i | \(-0.784152\pi\) | ||||
−0.778762 | + | 0.627320i | \(0.784152\pi\) | |||||||
\(992\) | −5.46952 | −0.173657 | ||||||||
\(993\) | −74.5026 | −2.36427 | ||||||||
\(994\) | 0.976137 | 0.0309612 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 19.5586 | 0.619739 | ||||||||
\(997\) | 12.6691 | 0.401235 | 0.200617 | − | 0.979670i | \(-0.435705\pi\) | ||||
0.200617 | + | 0.979670i | \(0.435705\pi\) | |||||||
\(998\) | 4.10989 | 0.130096 | ||||||||
\(999\) | 1.31542 | 0.0416181 |
(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 | 775.2.a.i.1.3 | ✓ | 5 | |
3.2 | odd | 2 | 6975.2.a.bx.1.3 | 5 | |||
5.2 | odd | 4 | 775.2.b.h.249.4 | 10 | |||
5.3 | odd | 4 | 775.2.b.h.249.7 | 10 | |||
5.4 | even | 2 | 775.2.a.j.1.3 | yes | 5 | ||
15.14 | odd | 2 | 6975.2.a.bq.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
775.2.a.i.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
775.2.a.j.1.3 | yes | 5 | 5.4 | even | 2 | ||
775.2.b.h.249.4 | 10 | 5.2 | odd | 4 | |||
775.2.b.h.249.7 | 10 | 5.3 | odd | 4 | |||
6975.2.a.bq.1.3 | 5 | 15.14 | odd | 2 | |||
6975.2.a.bx.1.3 | 5 | 3.2 | odd | 2 |