Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.576096652.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 8x^{4} + 11x^{3} + 16x^{2} - 6x - 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1672) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.89799\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 | 0 | ||||||||
\(3\) | 1.89799 | 1.09580 | 0.547902 | − | 0.836542i | \(-0.315427\pi\) | ||||
0.547902 | + | 0.836542i | \(0.315427\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.20786 | −0.540170 | −0.270085 | − | 0.962837i | \(-0.587052\pi\) | ||||
−0.270085 | + | 0.962837i | \(0.587052\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.24216 | −0.469493 | −0.234747 | − | 0.972057i | \(-0.575426\pi\) | ||||
−0.234747 | + | 0.972057i | \(0.575426\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.602364 | 0.200788 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.24216 | 0.344514 | 0.172257 | − | 0.985052i | \(-0.444894\pi\) | ||||
0.172257 | + | 0.985052i | \(0.444894\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.29250 | −0.591920 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.690134 | −0.167382 | −0.0836910 | − | 0.996492i | \(-0.526671\pi\) | ||||
−0.0836910 | + | 0.996492i | \(0.526671\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.35761 | −0.514473 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.95037 | 0.823709 | 0.411855 | − | 0.911250i | \(-0.364881\pi\) | ||||
0.411855 | + | 0.911250i | \(0.364881\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.54108 | −0.708217 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.55069 | −0.875780 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.09107 | −0.388301 | −0.194151 | − | 0.980972i | \(-0.562195\pi\) | ||||
−0.194151 | + | 0.980972i | \(0.562195\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.19253 | 0.932607 | 0.466303 | − | 0.884625i | \(-0.345586\pi\) | ||||
0.466303 | + | 0.884625i | \(0.345586\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.89799 | −0.330398 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.50035 | 0.253606 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.64051 | −1.09169 | −0.545846 | − | 0.837885i | \(-0.683792\pi\) | ||||
−0.545846 | + | 0.837885i | \(0.683792\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.35761 | 0.377520 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.34801 | 0.991392 | 0.495696 | − | 0.868496i | \(-0.334913\pi\) | ||||
0.495696 | + | 0.868496i | \(0.334913\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.9114 | −1.66398 | −0.831989 | − | 0.554793i | \(-0.812798\pi\) | ||||
−0.831989 | + | 0.554793i | \(0.812798\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.727569 | −0.108460 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.2803 | −1.49954 | −0.749768 | − | 0.661701i | \(-0.769835\pi\) | ||||
−0.749768 | + | 0.661701i | \(0.769835\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.45703 | −0.779576 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.30987 | −0.183418 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.93872 | 0.953107 | 0.476553 | − | 0.879146i | \(-0.341886\pi\) | ||||
0.476553 | + | 0.879146i | \(0.341886\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.20786 | 0.162867 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.89799 | −0.251395 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.1182 | −1.70784 | −0.853922 | − | 0.520401i | \(-0.825783\pi\) | ||||
−0.853922 | + | 0.520401i | \(0.825783\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.96381 | 1.14770 | 0.573849 | − | 0.818961i | \(-0.305450\pi\) | ||||
0.573849 | + | 0.818961i | \(0.305450\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.748234 | −0.0942686 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.50035 | −0.186096 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4308 | 1.51866 | 0.759330 | − | 0.650706i | \(-0.225527\pi\) | ||||
0.759330 | + | 0.650706i | \(0.225527\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.49776 | 0.902625 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.61984 | −1.02299 | −0.511493 | − | 0.859287i | \(-0.670908\pi\) | ||||
−0.511493 | + | 0.859287i | \(0.670908\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.72185 | −0.786733 | −0.393367 | − | 0.919382i | \(-0.628690\pi\) | ||||
−0.393367 | + | 0.919382i | \(0.628690\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.72094 | −0.776067 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.24216 | 0.141558 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.82770 | −1.10570 | −0.552851 | − | 0.833280i | \(-0.686460\pi\) | ||||
−0.552851 | + | 0.833280i | \(0.686460\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.4442 | −1.16047 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.7484 | −1.61885 | −0.809423 | − | 0.587225i | \(-0.800220\pi\) | ||||
−0.809423 | + | 0.587225i | \(0.800220\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.833582 | 0.0904147 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.96882 | −0.425502 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.81604 | −0.722499 | −0.361250 | − | 0.932469i | \(-0.617650\pi\) | ||||
−0.361250 | + | 0.932469i | \(0.617650\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.54297 | −0.161747 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.85537 | 1.02195 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.20786 | 0.123923 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.45498 | 0.553870 | 0.276935 | − | 0.960889i | \(-0.410681\pi\) | ||||
0.276935 | + | 0.960889i | \(0.410681\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.602364 | −0.0605398 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.16783 | −0.514218 | −0.257109 | − | 0.966382i | \(-0.582770\pi\) | ||||
−0.257109 | + | 0.966382i | \(0.582770\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.39505 | 0.433057 | 0.216528 | − | 0.976276i | \(-0.430527\pi\) | ||||
0.216528 | + | 0.976276i | \(0.430527\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.84765 | 0.277903 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.35443 | −0.904327 | −0.452164 | − | 0.891935i | \(-0.649348\pi\) | ||||
−0.452164 | + | 0.891935i | \(0.649348\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.51783 | 0.624295 | 0.312147 | − | 0.950034i | \(-0.398952\pi\) | ||||
0.312147 | + | 0.950034i | \(0.398952\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.6036 | −1.19628 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.1370 | 0.953606 | 0.476803 | − | 0.879010i | \(-0.341795\pi\) | ||||
0.476803 | + | 0.879010i | \(0.341795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.77148 | −0.444943 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.748234 | 0.0691742 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.857258 | 0.0785847 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.0485 | 1.08637 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.3164 | 0.922727 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.54810 | −0.581050 | −0.290525 | − | 0.956867i | \(-0.593830\pi\) | ||||
−0.290525 | + | 0.956867i | \(0.593830\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −20.7098 | −1.82339 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.23181 | 0.369735 | 0.184867 | − | 0.982763i | \(-0.440814\pi\) | ||||
0.184867 | + | 0.982763i | \(0.440814\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.24216 | 0.107709 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.49657 | 0.473070 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.08669 | −0.349149 | −0.174575 | − | 0.984644i | \(-0.555855\pi\) | ||||
−0.174575 | + | 0.984644i | \(0.555855\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.4334 | −0.884946 | −0.442473 | − | 0.896782i | \(-0.645899\pi\) | ||||
−0.442473 | + | 0.896782i | \(0.645899\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.5119 | −1.64320 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.24216 | −0.103875 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.52571 | 0.209748 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.3574 | −0.854263 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.5241 | 1.18986 | 0.594928 | − | 0.803779i | \(-0.297180\pi\) | ||||
0.594928 | + | 0.803779i | \(0.297180\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.2065 | −1.48162 | −0.740812 | − | 0.671712i | \(-0.765559\pi\) | ||||
−0.740812 | + | 0.671712i | \(0.765559\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.415712 | −0.0336083 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.27183 | −0.503766 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.7184 | −0.855418 | −0.427709 | − | 0.903917i | \(-0.640679\pi\) | ||||
−0.427709 | + | 0.903917i | \(0.640679\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.1696 | 1.04442 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.90700 | −0.386726 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.7222 | −1.54476 | −0.772380 | − | 0.635160i | \(-0.780934\pi\) | ||||
−0.772380 | + | 0.635160i | \(0.780934\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.29250 | 0.178471 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.3603 | 1.18862 | 0.594308 | − | 0.804237i | \(-0.297426\pi\) | ||||
0.594308 | + | 0.804237i | \(0.297426\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4570 | −0.881310 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.602364 | −0.0460639 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.3724 | 1.70094 | 0.850471 | − | 0.526021i | \(-0.176317\pi\) | ||||
0.850471 | + | 0.526021i | \(0.176317\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.39860 | 0.332503 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −24.8982 | −1.87146 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.9764 | −1.79208 | −0.896039 | − | 0.443975i | \(-0.853568\pi\) | ||||
−0.896039 | + | 0.443975i | \(0.853568\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.7766 | −1.02401 | −0.512004 | − | 0.858983i | \(-0.671097\pi\) | ||||
−0.512004 | + | 0.858983i | \(0.671097\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.0132 | 1.25765 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.02077 | 0.589699 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.690134 | 0.0504676 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.65269 | 0.411173 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.4390 | 1.26184 | 0.630920 | − | 0.775848i | \(-0.282678\pi\) | ||||
0.630920 | + | 0.775848i | \(0.282678\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.6528 | 1.12671 | 0.563355 | − | 0.826215i | \(-0.309510\pi\) | ||||
0.563355 | + | 0.826215i | \(0.309510\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.84765 | −0.203925 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.77758 | 0.482883 | 0.241441 | − | 0.970415i | \(-0.422380\pi\) | ||||
0.241441 | + | 0.970415i | \(0.422380\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.62848 | −0.540769 | −0.270384 | − | 0.962752i | \(-0.587151\pi\) | ||||
−0.270384 | + | 0.962752i | \(0.587151\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.5935 | 1.66415 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.59744 | 0.182305 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.66748 | −0.535520 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.37956 | 0.165391 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.2769 | 0.982863 | 0.491432 | − | 0.870916i | \(-0.336474\pi\) | ||||
0.491432 | + | 0.870916i | \(0.336474\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.3604 | −1.12099 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.1794 | 0.898830 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.44997 | −0.437853 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.7580 | −0.862106 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.857258 | −0.0576654 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.6353 | 0.846124 | 0.423062 | − | 0.906101i | \(-0.360955\pi\) | ||||
0.423062 | + | 0.906101i | \(0.360955\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.13302 | −0.142201 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.9660 | 1.32519 | 0.662594 | − | 0.748979i | \(-0.269456\pi\) | ||||
0.662594 | + | 0.748979i | \(0.269456\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.7465 | −0.710150 | −0.355075 | − | 0.934838i | \(-0.615545\pi\) | ||||
−0.355075 | + | 0.934838i | \(0.615545\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.35761 | 0.155119 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.41198 | 0.616600 | 0.308300 | − | 0.951289i | \(-0.400240\pi\) | ||||
0.308300 | + | 0.951289i | \(0.400240\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.4171 | 0.810004 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.6529 | −1.21163 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.1921 | 0.982695 | 0.491348 | − | 0.870963i | \(-0.336504\pi\) | ||||
0.491348 | + | 0.870963i | \(0.336504\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.01694 | −0.0655069 | −0.0327535 | − | 0.999463i | \(-0.510428\pi\) | ||||
−0.0327535 | + | 0.999463i | \(0.510428\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.17101 | −0.395870 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.59131 | 0.421103 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.24216 | −0.0790369 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −27.9923 | −1.77394 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.6269 | 0.670765 | 0.335382 | − | 0.942082i | \(-0.391135\pi\) | ||||
0.335382 | + | 0.942082i | \(0.391135\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.95037 | −0.248358 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.58213 | 0.0990768 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.78939 | −0.485889 | −0.242944 | − | 0.970040i | \(-0.578113\pi\) | ||||
−0.242944 | + | 0.970040i | \(0.578113\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.24859 | 0.512542 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.25958 | −0.0779662 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −31.5402 | −1.94485 | −0.972427 | − | 0.233206i | \(-0.925078\pi\) | ||||
−0.972427 | + | 0.233206i | \(0.925078\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.38097 | −0.514839 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.9368 | −0.791718 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.9339 | −0.666652 | −0.333326 | − | 0.942812i | \(-0.608171\pi\) | ||||
−0.333326 | + | 0.942812i | \(0.608171\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0665 | 0.975969 | 0.487984 | − | 0.872852i | \(-0.337732\pi\) | ||||
0.487984 | + | 0.872852i | \(0.337732\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.92854 | −0.177243 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.54108 | 0.213535 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.6174 | 1.35895 | 0.679473 | − | 0.733700i | \(-0.262208\pi\) | ||||
0.679473 | + | 0.733700i | \(0.262208\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.12779 | 0.187256 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.6436 | 1.52977 | 0.764884 | − | 0.644168i | \(-0.222796\pi\) | ||||
0.764884 | + | 0.644168i | \(0.222796\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.15062 | 0.0683972 | 0.0341986 | − | 0.999415i | \(-0.489112\pi\) | ||||
0.0341986 | + | 0.999415i | \(0.489112\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.29250 | 0.135796 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.88526 | −0.465452 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5237 | −0.971983 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.3535 | 0.606933 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.77069 | −0.278706 | −0.139353 | − | 0.990243i | \(-0.544502\pi\) | ||||
−0.139353 | + | 0.990243i | \(0.544502\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.8449 | 0.922526 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.55069 | 0.264058 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.90700 | 0.283779 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.5538 | 0.781226 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.80849 | −0.563483 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.8270 | −0.619952 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.7117 | −1.46745 | −0.733723 | − | 0.679449i | \(-0.762219\pi\) | ||||
−0.733723 | + | 0.679449i | \(0.762219\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.34175 | 0.474546 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.0241 | 1.64580 | 0.822902 | − | 0.568183i | \(-0.192353\pi\) | ||||
0.822902 | + | 0.568183i | \(0.192353\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.26466 | 0.0714829 | 0.0357415 | − | 0.999361i | \(-0.488621\pi\) | ||||
0.0357415 | + | 0.999361i | \(0.488621\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.903758 | 0.0509210 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.1536 | 1.24427 | 0.622136 | − | 0.782909i | \(-0.286265\pi\) | ||||
0.622136 | + | 0.782909i | \(0.286265\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.09107 | 0.117077 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.7546 | −0.990966 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.690134 | 0.0384001 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.39860 | −0.243991 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.3708 | 0.684105 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.7698 | 0.704022 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.4869 | 1.89557 | 0.947785 | − | 0.318909i | \(-0.103316\pi\) | ||||
0.947785 | + | 0.318909i | \(0.103316\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.00000 | −0.219199 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.0146 | −0.820334 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.1022 | 0.768198 | 0.384099 | − | 0.923292i | \(-0.374512\pi\) | ||||
0.384099 | + | 0.923292i | \(0.374512\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.2399 | 1.04497 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.19253 | −0.281191 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4737 | 0.835499 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.05622 | −0.487570 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.82662 | 0.0980581 | 0.0490290 | − | 0.998797i | \(-0.484387\pi\) | ||||
0.0490290 | + | 0.998797i | \(0.484387\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.7964 | −1.48791 | −0.743954 | − | 0.668231i | \(-0.767052\pi\) | ||||
−0.743954 | + | 0.668231i | \(0.767052\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.65269 | −0.301719 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.6245 | −0.991282 | −0.495641 | − | 0.868527i | \(-0.665067\pi\) | ||||
−0.495641 | + | 0.868527i | \(0.665067\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.4115 | 0.552586 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.62707 | 0.0861135 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.8766 | 0.837933 | 0.418967 | − | 0.908002i | \(-0.362392\pi\) | ||||
0.418967 | + | 0.908002i | \(0.362392\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.89799 | 0.0996186 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.11903 | 0.424969 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.497768 | 0.0259833 | 0.0129916 | − | 0.999916i | \(-0.495865\pi\) | ||||
0.0129916 | + | 0.999916i | \(0.495865\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.82381 | 0.199060 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.61902 | −0.447477 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.47904 | 0.231916 | 0.115958 | − | 0.993254i | \(-0.463006\pi\) | ||||
0.115958 | + | 0.993254i | \(0.463006\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.5804 | 1.01113 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.59744 | −0.133775 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.2849 | −1.45290 | −0.726449 | − | 0.687220i | \(-0.758831\pi\) | ||||
−0.726449 | + | 0.687220i | \(0.758831\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.4282 | −0.636717 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −36.8401 | −1.88244 | −0.941220 | − | 0.337795i | \(-0.890319\pi\) | ||||
−0.941220 | + | 0.337795i | \(0.890319\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.50035 | −0.0764651 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.57265 | −0.334107 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −28.1779 | −1.42868 | −0.714339 | − | 0.699800i | \(-0.753272\pi\) | ||||
−0.714339 | + | 0.699800i | \(0.753272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.72628 | −0.137874 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.03193 | 0.405157 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.8704 | 0.597267 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.4847 | −0.626590 | −0.313295 | − | 0.949656i | \(-0.601433\pi\) | ||||
−0.313295 | + | 0.949656i | \(0.601433\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.35761 | 0.118028 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.5902 | 1.02822 | 0.514112 | − | 0.857723i | \(-0.328122\pi\) | ||||
0.514112 | + | 0.857723i | \(0.328122\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.44997 | 0.321296 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.6151 | 0.626852 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.64051 | 0.329158 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.94974 | 0.442536 | 0.221268 | − | 0.975213i | \(-0.428980\pi\) | ||||
0.221268 | + | 0.975213i | \(0.428980\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.75649 | −0.382600 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.2949 | 0.801822 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.8139 | 0.874452 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.8024 | −0.969728 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.8590 | 0.677057 | 0.338528 | − | 0.940956i | \(-0.390071\pi\) | ||||
0.338528 | + | 0.940956i | \(0.390071\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0707 | 1.66051 | 0.830253 | − | 0.557387i | \(-0.188196\pi\) | ||||
0.830253 | + | 0.557387i | \(0.188196\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.19248 | −0.301089 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.44382 | 0.118543 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.1345 | −0.538837 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.35761 | −0.113827 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.2036 | 0.635997 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.74315 | −0.372112 | −0.186056 | − | 0.982539i | \(-0.559571\pi\) | ||||
−0.186056 | + | 0.982539i | \(0.559571\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.79376 | 0.229843 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.95037 | −0.188972 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.56801 | 0.265747 | 0.132873 | − | 0.991133i | \(-0.457580\pi\) | ||||
0.132873 | + | 0.991133i | \(0.457580\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.28712 | −0.156529 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.4542 | −0.971807 | −0.485904 | − | 0.874012i | \(-0.661509\pi\) | ||||
−0.485904 | + | 0.874012i | \(0.661509\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.23280 | 0.390272 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.5665 | 1.30385 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.8802 | 1.03259 | 0.516295 | − | 0.856411i | \(-0.327311\pi\) | ||||
0.516295 | + | 0.856411i | \(0.327311\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.34801 | −0.298916 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −34.5558 | −1.62357 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.86368 | 0.0873708 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.8243 | −1.02090 | −0.510449 | − | 0.859908i | \(-0.670521\pi\) | ||||
−0.510449 | + | 0.859908i | \(0.670521\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.14058 | 0.146590 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.1526 | −0.752300 | −0.376150 | − | 0.926559i | \(-0.622752\pi\) | ||||
−0.376150 | + | 0.926559i | \(0.622752\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.9853 | −0.742899 | −0.371450 | − | 0.928453i | \(-0.621139\pi\) | ||||
−0.371450 | + | 0.928453i | \(0.621139\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.9039 | −0.552029 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.504024 | −0.0233234 | −0.0116617 | − | 0.999932i | \(-0.503712\pi\) | ||||
−0.0116617 | + | 0.999932i | \(0.503712\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.4410 | −0.713001 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.3433 | −0.937371 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.9114 | 0.501708 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.54108 | 0.162476 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.17963 | 0.191372 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.39563 | 0.246533 | 0.123266 | − | 0.992374i | \(-0.460663\pi\) | ||||
0.123266 | + | 0.992374i | \(0.460663\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.24859 | −0.376103 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.31344 | −0.423776 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.58883 | −0.299184 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.2897 | 0.466270 | 0.233135 | − | 0.972444i | \(-0.425102\pi\) | ||||
0.233135 | + | 0.972444i | \(0.425102\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −37.4325 | −1.69276 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.1413 | −1.31513 | −0.657563 | − | 0.753399i | \(-0.728413\pi\) | ||||
−0.657563 | + | 0.753399i | \(0.728413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.44312 | 0.0649946 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.727569 | 0.0327018 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.7072 | 0.480285 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.2496 | −0.503603 | −0.251801 | − | 0.967779i | \(-0.581023\pi\) | ||||
−0.251801 | + | 0.967779i | \(0.581023\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 29.1537 | 1.30249 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.8290 | −0.839542 | −0.419771 | − | 0.907630i | \(-0.637890\pi\) | ||||
−0.419771 | + | 0.907630i | \(0.637890\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.24199 | 0.277765 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.7453 | −0.965744 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.4338 | 0.817064 | 0.408532 | − | 0.912744i | \(-0.366041\pi\) | ||||
0.408532 | + | 0.912744i | \(0.366041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.34963 | 0.369366 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.55069 | 0.200918 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.30858 | −0.233924 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.2803 | 0.452127 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 42.4626 | 1.86390 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.55309 | 0.111853 | 0.0559265 | − | 0.998435i | \(-0.482189\pi\) | ||||
0.0559265 | + | 0.998435i | \(0.482189\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.5592 | 0.724082 | 0.362041 | − | 0.932162i | \(-0.382080\pi\) | ||||
0.362041 | + | 0.932162i | \(0.382080\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.34850 | 0.364358 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.58354 | −0.156102 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.39456 | −0.321503 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.90193 | −0.342915 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.88526 | 0.341548 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.2988 | 0.488490 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −45.5069 | −1.96377 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.45703 | 0.235051 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.2044 | −0.653688 | −0.326844 | − | 0.945078i | \(-0.605985\pi\) | ||||
−0.326844 | + | 0.945078i | \(0.605985\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.1479 | −1.12211 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.87260 | −0.337225 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.4098 | 0.530604 | 0.265302 | − | 0.964165i | \(-0.414528\pi\) | ||||
0.265302 | + | 0.964165i | \(0.414528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.39947 | 0.230444 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.09107 | 0.0890824 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.2076 | 0.519120 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.2233 | 0.646195 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.5846 | −1.04168 | −0.520841 | − | 0.853654i | \(-0.674382\pi\) | ||||
−0.520841 | + | 0.853654i | \(0.674382\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.5538 | −0.573263 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.30987 | 0.0553026 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.33678 | 0.393498 | 0.196749 | − | 0.980454i | \(-0.436962\pi\) | ||||
0.196749 | + | 0.980454i | \(0.436962\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.2440 | −0.515109 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.9735 | 0.544834 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.4314 | 1.77882 | 0.889409 | − | 0.457112i | \(-0.151116\pi\) | ||||
0.889409 | + | 0.457112i | \(0.151116\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.9246 | −1.04306 | −0.521531 | − | 0.853232i | \(-0.674639\pi\) | ||||
−0.521531 | + | 0.853232i | \(0.674639\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.0990 | 1.38273 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.9886 | −0.583365 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.0685 | 1.29340 | 0.646700 | − | 0.762745i | \(-0.276149\pi\) | ||||
0.646700 | + | 0.762745i | \(0.276149\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.7088 | 1.23465 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.3199 | 0.760038 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.93872 | −0.287372 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.903758 | −0.0373658 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.06575 | 0.291635 | 0.145817 | − | 0.989312i | \(-0.453419\pi\) | ||||
0.145817 | + | 0.989312i | \(0.453419\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.19253 | −0.213955 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.8638 | 0.529145 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.6153 | 0.805502 | 0.402751 | − | 0.915310i | \(-0.368054\pi\) | ||||
0.402751 | + | 0.915310i | \(0.368054\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.03544 | −0.0424491 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.4788 | −0.592577 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.0560 | 0.901182 | 0.450591 | − | 0.892731i | \(-0.351213\pi\) | ||||
0.450591 | + | 0.892731i | \(0.351213\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.57976 | −0.268394 | −0.134197 | − | 0.990955i | \(-0.542846\pi\) | ||||
−0.134197 | + | 0.990955i | \(0.542846\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.48784 | 0.304929 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.20786 | −0.0491063 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.5127 | −0.954350 | −0.477175 | − | 0.878808i | \(-0.658339\pi\) | ||||
−0.477175 | + | 0.878808i | \(0.658339\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.92992 | 0.199770 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.7698 | −0.516611 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.17119 | −0.0473040 | −0.0236520 | − | 0.999720i | \(-0.507529\pi\) | ||||
−0.0236520 | + | 0.999720i | \(0.507529\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.5528 | −0.586825 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.2649 | −0.815836 | −0.407918 | − | 0.913019i | \(-0.633745\pi\) | ||||
−0.407918 | + | 0.913019i | \(0.633745\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −48.3884 | −1.94489 | −0.972447 | − | 0.233125i | \(-0.925105\pi\) | ||||
−0.972447 | + | 0.233125i | \(0.925105\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.9769 | −0.721389 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.46664 | 0.339209 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.24470 | 0.209788 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.89799 | 0.0757984 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.58284 | 0.182730 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.5857 | 1.21760 | 0.608799 | − | 0.793325i | \(-0.291652\pi\) | ||||
0.608799 | + | 0.793325i | \(0.291652\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 27.0974 | 1.07703 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.90916 | 0.313865 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.77852 | −0.268575 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.19228 | −0.205403 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.7378 | 0.463615 | 0.231807 | − | 0.972762i | \(-0.425536\pi\) | ||||
0.231807 | + | 0.972762i | \(0.425536\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.4233 | −1.23921 | −0.619606 | − | 0.784913i | \(-0.712708\pi\) | ||||
−0.619606 | + | 0.784913i | \(0.712708\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.0144 | 0.984942 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.0169 | 0.826260 | 0.413130 | − | 0.910672i | \(-0.364436\pi\) | ||||
0.413130 | + | 0.910672i | \(0.364436\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.1182 | 0.514934 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.2420 | −0.479801 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.5247 | −0.959726 | −0.479863 | − | 0.877343i | \(-0.659314\pi\) | ||||
−0.479863 | + | 0.877343i | \(0.659314\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.11141 | −0.199719 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.04900 | −0.157967 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.6883 | −1.35126 | −0.675632 | − | 0.737239i | \(-0.736129\pi\) | ||||
−0.675632 | + | 0.737239i | \(0.736129\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.13503 | −0.199730 | −0.0998648 | − | 0.995001i | \(-0.531841\pi\) | ||||
−0.0998648 | + | 0.995001i | \(0.531841\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.62707 | −0.0631900 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.50035 | −0.0581812 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.26049 | −0.319847 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.9817 | 0.927187 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.96381 | −0.346044 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.9611 | −0.692350 | −0.346175 | − | 0.938170i | \(-0.612520\pi\) | ||||
−0.346175 | + | 0.938170i | \(0.612520\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.1144 | 0.620242 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.95618 | 0.382647 | 0.191324 | − | 0.981527i | \(-0.438722\pi\) | ||||
0.191324 | + | 0.981527i | \(0.438722\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.77598 | −0.260038 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.8952 | 1.45215 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −37.3100 | −1.42763 | −0.713815 | − | 0.700335i | \(-0.753034\pi\) | ||||
−0.713815 | + | 0.700335i | \(0.753034\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.93613 | 0.188600 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.3968 | −0.778186 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.61902 | 0.328358 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.8278 | 1.28687 | 0.643434 | − | 0.765501i | \(-0.277509\pi\) | ||||
0.643434 | + | 0.765501i | \(0.277509\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.748234 | 0.0284231 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.6020 | 0.478021 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.38097 | −0.165941 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.8638 | 0.675673 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.3402 | −1.82578 | −0.912892 | − | 0.408201i | \(-0.866156\pi\) | ||||
−0.912892 | + | 0.408201i | \(0.866156\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.64051 | 0.250451 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.5676 | 0.887606 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.41929 | 0.241422 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.6851 | −0.814400 | −0.407200 | − | 0.913339i | \(-0.633495\pi\) | ||||
−0.407200 | + | 0.913339i | \(0.633495\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.91985 | −0.222012 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.5124 | 0.768197 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.50035 | 0.0561100 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28.8345 | 1.07684 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.43335 | 0.202630 | 0.101315 | − | 0.994854i | \(-0.467695\pi\) | ||||
0.101315 | + | 0.994854i | \(0.467695\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.45936 | −0.203317 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.93014 | −0.0717828 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.40464 | 0.275001 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.0709 | −1.30071 | −0.650355 | − | 0.759631i | \(-0.725380\pi\) | ||||
−0.650355 | + | 0.759631i | \(0.725380\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.6202 | 0.726675 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.53034 | 0.278520 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.41787 | −0.0893061 | −0.0446530 | − | 0.999003i | \(-0.514218\pi\) | ||||
−0.0446530 | + | 0.999003i | \(0.514218\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.5102 | 0.461447 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.4308 | −0.457893 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.2381 | 1.22268 | 0.611342 | − | 0.791367i | \(-0.290630\pi\) | ||||
0.611342 | + | 0.791367i | \(0.290630\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.35761 | −0.0866090 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.7003 | 1.74995 | 0.874977 | − | 0.484165i | \(-0.160876\pi\) | ||||
0.874977 | + | 0.484165i | \(0.160876\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.5430 | −0.642724 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.88390 | −0.325045 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.6197 | 0.424576 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.3385 | −0.413747 | −0.206873 | − | 0.978368i | \(-0.566329\pi\) | ||||
−0.206873 | + | 0.978368i | \(0.566329\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.1698 | 0.735027 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.9908 | 0.800329 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.67982 | 0.133745 | 0.0668727 | − | 0.997762i | \(-0.478698\pi\) | ||||
0.0668727 | + | 0.997762i | \(0.478698\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.49776 | −0.272152 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.9899 | 1.70338 | 0.851691 | − | 0.524045i | \(-0.175578\pi\) | ||||
0.851691 | + | 0.524045i | \(0.175578\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.09620 | −0.293102 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.502120 | 0.0181542 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.2949 | −0.588376 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.1449 | −1.59190 | −0.795952 | − | 0.605360i | \(-0.793029\pi\) | ||||
−0.795952 | + | 0.605360i | \(0.793029\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.7842 | −0.532439 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.15592 | −0.329315 | −0.164658 | − | 0.986351i | \(-0.552652\pi\) | ||||
−0.164658 | + | 0.986351i | \(0.552652\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.3872 | −0.660488 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.6557 | 0.561646 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.34801 | −0.227441 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.61984 | 0.308442 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.51579 | 0.340067 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.9462 | 0.462070 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.9487 | 1.78048 | 0.890240 | − | 0.455492i | \(-0.150537\pi\) | ||||
0.890240 | + | 0.455492i | \(0.150537\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −59.8630 | −2.13118 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.5918 | −0.447712 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.1345 | 0.395398 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.9070 | −0.564163 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.4356 | −0.405071 | −0.202536 | − | 0.979275i | \(-0.564918\pi\) | ||||
−0.202536 | + | 0.979275i | \(0.564918\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.09478 | 0.250995 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.10574 | −0.145069 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.72185 | 0.237209 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.92695 | 0.208898 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.7525 | −0.730521 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.0943 | 1.69090 | 0.845452 | − | 0.534051i | \(-0.179331\pi\) | ||||
0.845452 | + | 0.534051i | \(0.179331\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.41754 | −0.120006 | −0.0600030 | − | 0.998198i | \(-0.519111\pi\) | ||||
−0.0600030 | + | 0.998198i | \(0.519111\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.4940 | 1.06947 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.8216 | 0.834433 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.9114 | 0.381743 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.929428 | −0.0324768 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.63856 | −0.0571863 | −0.0285931 | − | 0.999591i | \(-0.509103\pi\) | ||||
−0.0285931 | + | 0.999591i | \(0.509103\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.1955 | −0.738827 | −0.369414 | − | 0.929265i | \(-0.620441\pi\) | ||||
−0.369414 | + | 0.929265i | \(0.620441\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.72094 | 0.233993 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.7585 | 1.48686 | 0.743429 | − | 0.668815i | \(-0.233198\pi\) | ||||
0.743429 | + | 0.668815i | \(0.233198\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.3896 | −0.673430 | −0.336715 | − | 0.941607i | \(-0.609316\pi\) | ||||
−0.336715 | + | 0.941607i | \(0.609316\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.9275 | 1.48914 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.76608 | 0.130487 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.5530 | −0.642055 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.6296 | −0.816759 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.49519 | 0.189715 | 0.0948574 | − | 0.995491i | \(-0.469760\pi\) | ||||
0.0948574 | + | 0.995491i | \(0.469760\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.6274 | −0.849222 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 48.6713 | 1.67633 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.8384 | 0.476057 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.24216 | −0.0426812 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.18386 | 0.0749500 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.2325 | −0.899237 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.1766 | 1.17018 | 0.585092 | − | 0.810967i | \(-0.301058\pi\) | ||||
0.585092 | + | 0.810967i | \(0.301058\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.727569 | 0.0248823 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.9699 | 0.989593 | 0.494796 | − | 0.869009i | \(-0.335243\pi\) | ||||
0.494796 | + | 0.869009i | \(0.335243\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.9817 | −0.408811 | −0.204405 | − | 0.978886i | \(-0.565526\pi\) | ||||
−0.204405 | + | 0.978886i | \(0.565526\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.9661 | −0.510045 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.5276 | −1.03917 | −0.519585 | − | 0.854419i | \(-0.673914\pi\) | ||||
−0.519585 | + | 0.854419i | \(0.673914\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.0226 | −0.918798 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −31.3618 | −1.06510 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.82770 | 0.333382 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.4410 | 0.523199 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.28589 | 0.111210 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.8146 | −0.433214 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.8775 | 0.806287 | 0.403144 | − | 0.915137i | \(-0.367917\pi\) | ||||
0.403144 | + | 0.915137i | \(0.367917\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.05471 | −0.305408 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.69730 | −0.225638 | −0.112819 | − | 0.993616i | \(-0.535988\pi\) | ||||
−0.112819 | + | 0.993616i | \(0.535988\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.0580 | −1.65093 | −0.825467 | − | 0.564451i | \(-0.809088\pi\) | ||||
−0.825467 | + | 0.564451i | \(0.809088\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 30.0734 | 1.01091 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.05578 | 0.136180 | 0.0680898 | − | 0.997679i | \(-0.478310\pi\) | ||||
0.0680898 | + | 0.997679i | \(0.478310\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.13380 | 0.272799 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.4442 | 0.349896 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.2803 | 0.344017 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.9600 | 0.968026 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.31344 | 0.310967 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.8579 | −0.362132 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.78864 | −0.159533 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.7249 | 0.856071 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.6402 | 0.553138 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.9954 | −0.531119 | −0.265560 | − | 0.964094i | \(-0.585557\pi\) | ||||
−0.265560 | + | 0.964094i | \(0.585557\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.11291 | −0.103249 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.84554 | −0.0942770 | −0.0471385 | − | 0.998888i | \(-0.515010\pi\) | ||||
−0.0471385 | + | 0.998888i | \(0.515010\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.7484 | 0.488101 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20.5495 | −0.679346 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.25659 | −0.173588 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.9831 | 1.35191 | 0.675955 | − | 0.736943i | \(-0.263732\pi\) | ||||
0.675955 | + | 0.736943i | \(0.263732\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −48.8006 | −1.60803 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.7072 | −0.352433 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.5146 | 0.773155 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.64742 | 0.0869526 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.7454 | −0.647824 | −0.323912 | − | 0.946087i | \(-0.604998\pi\) | ||||
−0.323912 | + | 0.946087i | \(0.604998\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.45703 | 0.178847 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 55.0874 | 1.80348 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.833582 | −0.0272610 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.5669 | 0.802567 | 0.401283 | − | 0.915954i | \(-0.368564\pi\) | ||||
0.401283 | + | 0.915954i | \(0.368564\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.40031 | 0.0783313 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.6233 | −0.509305 | −0.254653 | − | 0.967033i | \(-0.581961\pi\) | ||||
−0.254653 | + | 0.967033i | \(0.581961\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.0770 | 0.816619 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.82764 | −0.222103 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.37770 | 0.272239 | 0.136119 | − | 0.990692i | \(-0.456537\pi\) | ||||
0.136119 | + | 0.990692i | \(0.456537\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.34963 | −0.271040 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 42.0474 | 1.36348 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50.7519 | 1.64402 | 0.822008 | − | 0.569476i | \(-0.192854\pi\) | ||||
0.822008 | + | 0.569476i | \(0.192854\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.0638 | −0.681608 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.96882 | 0.128294 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.07633 | 0.163923 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.03759 | −0.130245 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.63477 | −0.181578 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.9063 | −0.608614 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.3207 | 1.55389 | 0.776944 | − | 0.629569i | \(-0.216769\pi\) | ||||
0.776944 | + | 0.629569i | \(0.216769\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.30987 | 0.0420790 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.0788 | 1.02946 | 0.514729 | − | 0.857353i | \(-0.327893\pi\) | ||||
0.514729 | + | 0.857353i | \(0.327893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.9599 | 0.415476 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.34850 | −0.267366 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.3545 | −0.619207 | −0.309603 | − | 0.950866i | \(-0.600196\pi\) | ||||
−0.309603 | + | 0.950866i | \(0.600196\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.81604 | 0.217842 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.92610 | 0.125351 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.1841 | 1.53683 | 0.768417 | − | 0.639950i | \(-0.221045\pi\) | ||||
0.768417 | + | 0.639950i | \(0.221045\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.18634 | −0.260839 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.2370 | 0.771471 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −43.1042 | −1.37063 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.3376 | 1.44020 | 0.720098 | − | 0.693872i | \(-0.244097\pi\) | ||||
0.720098 | + | 0.693872i | \(0.244097\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 65.4557 | 2.07718 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.21410 | 0.292107 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.6016 | −0.557447 | −0.278724 | − | 0.960371i | \(-0.589911\pi\) | ||||
−0.278724 | + | 0.960371i | \(0.589911\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 30.2189 | 0.956083 |
(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 | 3344.2.a.v.1.6 | 6 | ||
4.3 | odd | 2 | 1672.2.a.j.1.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.j.1.1 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.v.1.6 | 6 | 1.1 | even | 1 | trivial |