Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2225,2,Mod(1,2225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2225, 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("2225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2225 = 5^{2} \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2225.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: | \(17.7667144497\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 445) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.737640\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2225.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.45589 | −1.02947 | −0.514734 | − | 0.857350i | \(-0.672109\pi\) | ||||
−0.514734 | + | 0.857350i | \(0.672109\pi\) | |||||||
\(3\) | 2.19353 | 1.26643 | 0.633217 | − | 0.773975i | \(-0.281734\pi\) | ||||
0.633217 | + | 0.773975i | \(0.281734\pi\) | |||||||
\(4\) | 0.119606 | 0.0598032 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.19353 | −1.30375 | ||||||||
\(7\) | −3.71135 | −1.40276 | −0.701379 | − | 0.712789i | \(-0.747432\pi\) | ||||
−0.701379 | + | 0.712789i | \(0.747432\pi\) | |||||||
\(8\) | 2.73764 | 0.967902 | ||||||||
\(9\) | 1.81156 | 0.603854 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.80647 | −0.544672 | −0.272336 | − | 0.962202i | \(-0.587796\pi\) | ||||
−0.272336 | + | 0.962202i | \(0.587796\pi\) | |||||||
\(12\) | 0.262360 | 0.0757367 | ||||||||
\(13\) | 6.78527 | 1.88190 | 0.940948 | − | 0.338552i | \(-0.109937\pi\) | ||||
0.940948 | + | 0.338552i | \(0.109937\pi\) | |||||||
\(14\) | 5.40330 | 1.44409 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.22491 | −1.05623 | ||||||||
\(17\) | 1.92293 | 0.466380 | 0.233190 | − | 0.972431i | \(-0.425084\pi\) | ||||
0.233190 | + | 0.972431i | \(0.425084\pi\) | |||||||
\(18\) | −2.63743 | −0.621648 | ||||||||
\(19\) | −6.21801 | −1.42651 | −0.713255 | − | 0.700905i | \(-0.752780\pi\) | ||||
−0.713255 | + | 0.700905i | \(0.752780\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.14094 | −1.77650 | ||||||||
\(22\) | 2.63002 | 0.560722 | ||||||||
\(23\) | −1.39822 | −0.291548 | −0.145774 | − | 0.989318i | \(-0.546567\pi\) | ||||
−0.145774 | + | 0.989318i | \(0.546567\pi\) | |||||||
\(24\) | 6.00509 | 1.22578 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.87858 | −1.93735 | ||||||||
\(27\) | −2.60687 | −0.501693 | ||||||||
\(28\) | −0.443901 | −0.0838894 | ||||||||
\(29\) | −4.99310 | −0.927196 | −0.463598 | − | 0.886046i | \(-0.653442\pi\) | ||||
−0.463598 | + | 0.886046i | \(0.653442\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.92427 | 0.345609 | 0.172805 | − | 0.984956i | \(-0.444717\pi\) | ||||
0.172805 | + | 0.984956i | \(0.444717\pi\) | |||||||
\(32\) | 0.675706 | 0.119449 | ||||||||
\(33\) | −3.96255 | −0.689791 | ||||||||
\(34\) | −2.79958 | −0.480123 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.216674 | 0.0361124 | ||||||||
\(37\) | −2.70709 | −0.445042 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(38\) | 9.05272 | 1.46854 | ||||||||
\(39\) | 14.8837 | 2.38329 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.91604 | 0.455408 | 0.227704 | − | 0.973730i | \(-0.426878\pi\) | ||||
0.227704 | + | 0.973730i | \(0.426878\pi\) | |||||||
\(42\) | 11.8523 | 1.82885 | ||||||||
\(43\) | −0.211586 | −0.0322666 | −0.0161333 | − | 0.999870i | \(-0.505136\pi\) | ||||
−0.0161333 | + | 0.999870i | \(0.505136\pi\) | |||||||
\(44\) | −0.216066 | −0.0325731 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.03564 | 0.300139 | ||||||||
\(47\) | 9.61114 | 1.40193 | 0.700964 | − | 0.713197i | \(-0.252753\pi\) | ||||
0.700964 | + | 0.713197i | \(0.252753\pi\) | |||||||
\(48\) | −9.26745 | −1.33764 | ||||||||
\(49\) | 6.77411 | 0.967730 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.21801 | 0.590639 | ||||||||
\(52\) | 0.811561 | 0.112543 | ||||||||
\(53\) | −10.9331 | −1.50178 | −0.750889 | − | 0.660428i | \(-0.770375\pi\) | ||||
−0.750889 | + | 0.660428i | \(0.770375\pi\) | |||||||
\(54\) | 3.79531 | 0.516477 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −10.1603 | −1.35773 | ||||||||
\(57\) | −13.6394 | −1.80658 | ||||||||
\(58\) | 7.26939 | 0.954518 | ||||||||
\(59\) | −12.0984 | −1.57508 | −0.787539 | − | 0.616265i | \(-0.788645\pi\) | ||||
−0.787539 | + | 0.616265i | \(0.788645\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1997 | 1.30594 | 0.652971 | − | 0.757383i | \(-0.273522\pi\) | ||||
0.652971 | + | 0.757383i | \(0.273522\pi\) | |||||||
\(62\) | −2.80152 | −0.355793 | ||||||||
\(63\) | −6.72333 | −0.847061 | ||||||||
\(64\) | 7.46606 | 0.933258 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.76902 | 0.710117 | ||||||||
\(67\) | −2.88548 | −0.352518 | −0.176259 | − | 0.984344i | \(-0.556400\pi\) | ||||
−0.176259 | + | 0.984344i | \(0.556400\pi\) | |||||||
\(68\) | 0.229995 | 0.0278910 | ||||||||
\(69\) | −3.06702 | −0.369226 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.85919 | −0.458002 | −0.229001 | − | 0.973426i | \(-0.573546\pi\) | ||||
−0.229001 | + | 0.973426i | \(0.573546\pi\) | |||||||
\(72\) | 4.95940 | 0.584471 | ||||||||
\(73\) | −11.5899 | −1.35650 | −0.678250 | − | 0.734832i | \(-0.737261\pi\) | ||||
−0.678250 | + | 0.734832i | \(0.737261\pi\) | |||||||
\(74\) | 3.94121 | 0.458156 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.743713 | −0.0853098 | ||||||||
\(77\) | 6.70445 | 0.764043 | ||||||||
\(78\) | −21.6689 | −2.45352 | ||||||||
\(79\) | −10.8158 | −1.21688 | −0.608438 | − | 0.793602i | \(-0.708203\pi\) | ||||
−0.608438 | + | 0.793602i | \(0.708203\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1529 | −1.23921 | ||||||||
\(82\) | −4.24542 | −0.468828 | ||||||||
\(83\) | 5.59257 | 0.613864 | 0.306932 | − | 0.951731i | \(-0.400698\pi\) | ||||
0.306932 | + | 0.951731i | \(0.400698\pi\) | |||||||
\(84\) | −0.973708 | −0.106240 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.308045 | 0.0332174 | ||||||||
\(87\) | −10.9525 | −1.17423 | ||||||||
\(88\) | −4.94547 | −0.527189 | ||||||||
\(89\) | −1.00000 | −0.106000 | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25.1825 | −2.63984 | ||||||||
\(92\) | −0.167235 | −0.0174355 | ||||||||
\(93\) | 4.22094 | 0.437691 | ||||||||
\(94\) | −13.9927 | −1.44324 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.48218 | 0.151274 | ||||||||
\(97\) | −1.07064 | −0.108707 | −0.0543536 | − | 0.998522i | \(-0.517310\pi\) | ||||
−0.0543536 | + | 0.998522i | \(0.517310\pi\) | |||||||
\(98\) | −9.86233 | −0.996246 | ||||||||
\(99\) | −3.27254 | −0.328902 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.8603 | −1.37915 | −0.689576 | − | 0.724213i | \(-0.742203\pi\) | ||||
−0.689576 | + | 0.724213i | \(0.742203\pi\) | |||||||
\(102\) | −6.14094 | −0.608044 | ||||||||
\(103\) | −2.85216 | −0.281032 | −0.140516 | − | 0.990078i | \(-0.544876\pi\) | ||||
−0.140516 | + | 0.990078i | \(0.544876\pi\) | |||||||
\(104\) | 18.5756 | 1.82149 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.9174 | 1.54603 | ||||||||
\(107\) | 1.48908 | 0.143954 | 0.0719772 | − | 0.997406i | \(-0.477069\pi\) | ||||
0.0719772 | + | 0.997406i | \(0.477069\pi\) | |||||||
\(108\) | −0.311798 | −0.0300028 | ||||||||
\(109\) | 9.40330 | 0.900673 | 0.450337 | − | 0.892859i | \(-0.351304\pi\) | ||||
0.450337 | + | 0.892859i | \(0.351304\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.93807 | −0.563616 | ||||||||
\(112\) | 15.6801 | 1.48163 | ||||||||
\(113\) | −12.6841 | −1.19322 | −0.596609 | − | 0.802532i | \(-0.703485\pi\) | ||||
−0.596609 | + | 0.802532i | \(0.703485\pi\) | |||||||
\(114\) | 19.8574 | 1.85981 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.597207 | −0.0554492 | ||||||||
\(117\) | 12.2919 | 1.13639 | ||||||||
\(118\) | 17.6139 | 1.62149 | ||||||||
\(119\) | −7.13668 | −0.654218 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.73666 | −0.703332 | ||||||||
\(122\) | −14.8497 | −1.34442 | ||||||||
\(123\) | 6.39641 | 0.576744 | ||||||||
\(124\) | 0.230155 | 0.0206685 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 9.78841 | 0.872021 | ||||||||
\(127\) | −1.25413 | −0.111286 | −0.0556429 | − | 0.998451i | \(-0.517721\pi\) | ||||
−0.0556429 | + | 0.998451i | \(0.517721\pi\) | |||||||
\(128\) | −12.2212 | −1.08021 | ||||||||
\(129\) | −0.464120 | −0.0408635 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.27240 | −0.198541 | −0.0992704 | − | 0.995060i | \(-0.531651\pi\) | ||||
−0.0992704 | + | 0.995060i | \(0.531651\pi\) | |||||||
\(132\) | −0.473946 | −0.0412517 | ||||||||
\(133\) | 23.0772 | 2.00105 | ||||||||
\(134\) | 4.20093 | 0.362905 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.26430 | 0.451410 | ||||||||
\(137\) | 15.5836 | 1.33140 | 0.665700 | − | 0.746219i | \(-0.268133\pi\) | ||||
0.665700 | + | 0.746219i | \(0.268133\pi\) | |||||||
\(138\) | 4.46524 | 0.380106 | ||||||||
\(139\) | −21.5004 | −1.82364 | −0.911819 | − | 0.410593i | \(-0.865322\pi\) | ||||
−0.911819 | + | 0.410593i | \(0.865322\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.0823 | 1.77545 | ||||||||
\(142\) | 5.61854 | 0.471498 | ||||||||
\(143\) | −12.2574 | −1.02502 | ||||||||
\(144\) | −7.65368 | −0.637806 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.8736 | 1.39647 | ||||||||
\(147\) | 14.8592 | 1.22557 | ||||||||
\(148\) | −0.323785 | −0.0266149 | ||||||||
\(149\) | −17.0028 | −1.39292 | −0.696461 | − | 0.717595i | \(-0.745243\pi\) | ||||
−0.696461 | + | 0.717595i | \(0.745243\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.7866 | −1.44745 | −0.723727 | − | 0.690087i | \(-0.757572\pi\) | ||||
−0.723727 | + | 0.690087i | \(0.757572\pi\) | |||||||
\(152\) | −17.0227 | −1.38072 | ||||||||
\(153\) | 3.48351 | 0.281625 | ||||||||
\(154\) | −9.76092 | −0.786557 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.78018 | 0.142529 | ||||||||
\(157\) | 8.13061 | 0.648893 | 0.324447 | − | 0.945904i | \(-0.394822\pi\) | ||||
0.324447 | + | 0.945904i | \(0.394822\pi\) | |||||||
\(158\) | 15.7466 | 1.25273 | ||||||||
\(159\) | −23.9821 | −1.90190 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.18926 | 0.408971 | ||||||||
\(162\) | 16.2374 | 1.27573 | ||||||||
\(163\) | −23.0135 | −1.80255 | −0.901276 | − | 0.433244i | \(-0.857369\pi\) | ||||
−0.901276 | + | 0.433244i | \(0.857369\pi\) | |||||||
\(164\) | 0.348776 | 0.0272349 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.14214 | −0.631953 | ||||||||
\(167\) | −5.88974 | −0.455762 | −0.227881 | − | 0.973689i | \(-0.573180\pi\) | ||||
−0.227881 | + | 0.973689i | \(0.573180\pi\) | |||||||
\(168\) | −22.2870 | −1.71948 | ||||||||
\(169\) | 33.0399 | 2.54153 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.2643 | −0.861403 | ||||||||
\(172\) | −0.0253070 | −0.00192964 | ||||||||
\(173\) | 15.0723 | 1.14593 | 0.572964 | − | 0.819581i | \(-0.305794\pi\) | ||||
0.572964 | + | 0.819581i | \(0.305794\pi\) | |||||||
\(174\) | 15.9456 | 1.20883 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.63218 | 0.575297 | ||||||||
\(177\) | −26.5382 | −1.99473 | ||||||||
\(178\) | 1.45589 | 0.109123 | ||||||||
\(179\) | 4.65562 | 0.347977 | 0.173989 | − | 0.984748i | \(-0.444334\pi\) | ||||
0.173989 | + | 0.984748i | \(0.444334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.62070 | 0.715101 | 0.357551 | − | 0.933894i | \(-0.383612\pi\) | ||||
0.357551 | + | 0.933894i | \(0.383612\pi\) | |||||||
\(182\) | 36.6629 | 2.71763 | ||||||||
\(183\) | 22.3734 | 1.65389 | ||||||||
\(184\) | −3.82781 | −0.282190 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.14521 | −0.450588 | ||||||||
\(187\) | −3.47373 | −0.254024 | ||||||||
\(188\) | 1.14955 | 0.0838397 | ||||||||
\(189\) | 9.67501 | 0.703754 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.3629 | 0.966907 | 0.483454 | − | 0.875370i | \(-0.339382\pi\) | ||||
0.483454 | + | 0.875370i | \(0.339382\pi\) | |||||||
\(192\) | 16.3770 | 1.18191 | ||||||||
\(193\) | −0.449680 | −0.0323687 | −0.0161843 | − | 0.999869i | \(-0.505152\pi\) | ||||
−0.0161843 | + | 0.999869i | \(0.505152\pi\) | |||||||
\(194\) | 1.55873 | 0.111911 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.810226 | 0.0578733 | ||||||||
\(197\) | −8.56942 | −0.610546 | −0.305273 | − | 0.952265i | \(-0.598748\pi\) | ||||
−0.305273 | + | 0.952265i | \(0.598748\pi\) | |||||||
\(198\) | 4.76444 | 0.338594 | ||||||||
\(199\) | −8.67704 | −0.615099 | −0.307550 | − | 0.951532i | \(-0.599509\pi\) | ||||
−0.307550 | + | 0.951532i | \(0.599509\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.32938 | −0.446440 | ||||||||
\(202\) | 20.1790 | 1.41979 | ||||||||
\(203\) | 18.5311 | 1.30063 | ||||||||
\(204\) | 0.504501 | 0.0353221 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.15242 | 0.289313 | ||||||||
\(207\) | −2.53295 | −0.176052 | ||||||||
\(208\) | −28.6671 | −1.98771 | ||||||||
\(209\) | 11.2327 | 0.776980 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.1953 | 1.73452 | 0.867258 | − | 0.497858i | \(-0.165880\pi\) | ||||
0.867258 | + | 0.497858i | \(0.165880\pi\) | |||||||
\(212\) | −1.30767 | −0.0898111 | ||||||||
\(213\) | −8.46524 | −0.580029 | ||||||||
\(214\) | −2.16793 | −0.148196 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.13668 | −0.485590 | ||||||||
\(217\) | −7.14163 | −0.484806 | ||||||||
\(218\) | −13.6901 | −0.927214 | ||||||||
\(219\) | −25.4228 | −1.71792 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.0476 | 0.877679 | ||||||||
\(222\) | 8.64515 | 0.580225 | ||||||||
\(223\) | −16.2438 | −1.08777 | −0.543884 | − | 0.839161i | \(-0.683047\pi\) | ||||
−0.543884 | + | 0.839161i | \(0.683047\pi\) | |||||||
\(224\) | −2.50778 | −0.167558 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.4666 | 1.22838 | ||||||||
\(227\) | 13.1941 | 0.875726 | 0.437863 | − | 0.899042i | \(-0.355736\pi\) | ||||
0.437863 | + | 0.899042i | \(0.355736\pi\) | |||||||
\(228\) | −1.63135 | −0.108039 | ||||||||
\(229\) | 2.36998 | 0.156613 | 0.0783063 | − | 0.996929i | \(-0.475049\pi\) | ||||
0.0783063 | + | 0.996929i | \(0.475049\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.7064 | 0.967610 | ||||||||
\(232\) | −13.6693 | −0.897435 | ||||||||
\(233\) | 9.67877 | 0.634077 | 0.317039 | − | 0.948413i | \(-0.397312\pi\) | ||||
0.317039 | + | 0.948413i | \(0.397312\pi\) | |||||||
\(234\) | −17.8957 | −1.16988 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.44705 | −0.0941946 | ||||||||
\(237\) | −23.7248 | −1.54109 | ||||||||
\(238\) | 10.3902 | 0.673497 | ||||||||
\(239\) | −23.8871 | −1.54513 | −0.772564 | − | 0.634936i | \(-0.781026\pi\) | ||||
−0.772564 | + | 0.634936i | \(0.781026\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.7221 | −1.01275 | −0.506376 | − | 0.862313i | \(-0.669015\pi\) | ||||
−0.506376 | + | 0.862313i | \(0.669015\pi\) | |||||||
\(242\) | 11.2637 | 0.724058 | ||||||||
\(243\) | −16.6436 | −1.06769 | ||||||||
\(244\) | 1.21995 | 0.0780995 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.31244 | −0.593740 | ||||||||
\(247\) | −42.1909 | −2.68454 | ||||||||
\(248\) | 5.26796 | 0.334516 | ||||||||
\(249\) | 12.2674 | 0.777418 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.2933 | 0.902183 | 0.451091 | − | 0.892478i | \(-0.351035\pi\) | ||||
0.451091 | + | 0.892478i | \(0.351035\pi\) | |||||||
\(252\) | −0.804153 | −0.0506569 | ||||||||
\(253\) | 2.52584 | 0.158798 | ||||||||
\(254\) | 1.82587 | 0.114565 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.86049 | 0.178781 | ||||||||
\(257\) | 8.51369 | 0.531070 | 0.265535 | − | 0.964101i | \(-0.414451\pi\) | ||||
0.265535 | + | 0.964101i | \(0.414451\pi\) | |||||||
\(258\) | 0.675706 | 0.0420676 | ||||||||
\(259\) | 10.0469 | 0.624286 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.04531 | −0.559891 | ||||||||
\(262\) | 3.30836 | 0.204391 | ||||||||
\(263\) | 19.3754 | 1.19474 | 0.597370 | − | 0.801966i | \(-0.296212\pi\) | ||||
0.597370 | + | 0.801966i | \(0.296212\pi\) | |||||||
\(264\) | −10.8480 | −0.667650 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −33.5978 | −2.06001 | ||||||||
\(267\) | −2.19353 | −0.134242 | ||||||||
\(268\) | −0.345122 | −0.0210817 | ||||||||
\(269\) | −7.39853 | −0.451096 | −0.225548 | − | 0.974232i | \(-0.572417\pi\) | ||||
−0.225548 | + | 0.974232i | \(0.572417\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.2477 | −1.65518 | −0.827590 | − | 0.561333i | \(-0.810289\pi\) | ||||
−0.827590 | + | 0.561333i | \(0.810289\pi\) | |||||||
\(272\) | −8.12422 | −0.492603 | ||||||||
\(273\) | −55.2385 | −3.34319 | ||||||||
\(274\) | −22.6880 | −1.37063 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.366835 | −0.0220809 | ||||||||
\(277\) | −28.4582 | −1.70989 | −0.854943 | − | 0.518722i | \(-0.826408\pi\) | ||||
−0.854943 | + | 0.518722i | \(0.826408\pi\) | |||||||
\(278\) | 31.3021 | 1.87738 | ||||||||
\(279\) | 3.48593 | 0.208697 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.1815 | 1.32323 | 0.661617 | − | 0.749842i | \(-0.269870\pi\) | ||||
0.661617 | + | 0.749842i | \(0.269870\pi\) | |||||||
\(282\) | −30.6934 | −1.82777 | ||||||||
\(283\) | −0.247445 | −0.0147091 | −0.00735455 | − | 0.999973i | \(-0.502341\pi\) | ||||
−0.00735455 | + | 0.999973i | \(0.502341\pi\) | |||||||
\(284\) | −0.461584 | −0.0273899 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 17.8454 | 1.05522 | ||||||||
\(287\) | −10.8224 | −0.638828 | ||||||||
\(288\) | 1.22408 | 0.0721297 | ||||||||
\(289\) | −13.3023 | −0.782490 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.34848 | −0.137671 | ||||||||
\(292\) | −1.38623 | −0.0811229 | ||||||||
\(293\) | 11.3844 | 0.665085 | 0.332542 | − | 0.943088i | \(-0.392094\pi\) | ||||
0.332542 | + | 0.943088i | \(0.392094\pi\) | |||||||
\(294\) | −21.6333 | −1.26168 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.41103 | −0.430757 | ||||||||
\(297\) | 4.70925 | 0.273258 | ||||||||
\(298\) | 24.7541 | 1.43397 | ||||||||
\(299\) | −9.48727 | −0.548663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.785269 | 0.0452622 | ||||||||
\(302\) | 25.8953 | 1.49011 | ||||||||
\(303\) | −30.4030 | −1.74660 | ||||||||
\(304\) | 26.2705 | 1.50672 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.07160 | −0.289924 | ||||||||
\(307\) | 6.37110 | 0.363618 | 0.181809 | − | 0.983334i | \(-0.441805\pi\) | ||||
0.181809 | + | 0.983334i | \(0.441805\pi\) | |||||||
\(308\) | 0.801895 | 0.0456922 | ||||||||
\(309\) | −6.25629 | −0.355908 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.5996 | −1.73514 | −0.867572 | − | 0.497312i | \(-0.834321\pi\) | ||||
−0.867572 | + | 0.497312i | \(0.834321\pi\) | |||||||
\(312\) | 40.7461 | 2.30680 | ||||||||
\(313\) | 19.2316 | 1.08704 | 0.543518 | − | 0.839398i | \(-0.317092\pi\) | ||||
0.543518 | + | 0.839398i | \(0.317092\pi\) | |||||||
\(314\) | −11.8372 | −0.668014 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.29364 | −0.0727730 | ||||||||
\(317\) | 9.70429 | 0.545047 | 0.272524 | − | 0.962149i | \(-0.412142\pi\) | ||||
0.272524 | + | 0.962149i | \(0.412142\pi\) | |||||||
\(318\) | 34.9152 | 1.95795 | ||||||||
\(319\) | 9.01990 | 0.505018 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.26633 | 0.182309 | ||||||||
\(322\) | −7.55498 | −0.421023 | ||||||||
\(323\) | −11.9568 | −0.665296 | ||||||||
\(324\) | −1.33396 | −0.0741089 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 33.5050 | 1.85567 | ||||||||
\(327\) | 20.6264 | 1.14064 | ||||||||
\(328\) | 7.98306 | 0.440791 | ||||||||
\(329\) | −35.6703 | −1.96657 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.9275 | −1.59000 | −0.795001 | − | 0.606608i | \(-0.792530\pi\) | ||||
−0.795001 | + | 0.606608i | \(0.792530\pi\) | |||||||
\(332\) | 0.668906 | 0.0367110 | ||||||||
\(333\) | −4.90405 | −0.268740 | ||||||||
\(334\) | 8.57480 | 0.469192 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 34.3947 | 1.87639 | ||||||||
\(337\) | −2.30865 | −0.125760 | −0.0628802 | − | 0.998021i | \(-0.520029\pi\) | ||||
−0.0628802 | + | 0.998021i | \(0.520029\pi\) | |||||||
\(338\) | −48.1023 | −2.61642 | ||||||||
\(339\) | −27.8229 | −1.51113 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.47614 | −0.188244 | ||||||||
\(342\) | 16.3996 | 0.886786 | ||||||||
\(343\) | 0.838363 | 0.0452673 | ||||||||
\(344\) | −0.579246 | −0.0312309 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −21.9436 | −1.17970 | ||||||||
\(347\) | 34.4649 | 1.85017 | 0.925085 | − | 0.379759i | \(-0.123993\pi\) | ||||
0.925085 | + | 0.379759i | \(0.123993\pi\) | |||||||
\(348\) | −1.30999 | −0.0702228 | ||||||||
\(349\) | 19.3154 | 1.03393 | 0.516965 | − | 0.856007i | \(-0.327062\pi\) | ||||
0.516965 | + | 0.856007i | \(0.327062\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.6883 | −0.944133 | ||||||||
\(352\) | −1.22064 | −0.0650605 | ||||||||
\(353\) | −1.41183 | −0.0751441 | −0.0375721 | − | 0.999294i | \(-0.511962\pi\) | ||||
−0.0375721 | + | 0.999294i | \(0.511962\pi\) | |||||||
\(354\) | 38.6366 | 2.05351 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.119606 | −0.00633912 | ||||||||
\(357\) | −15.6545 | −0.828524 | ||||||||
\(358\) | −6.77806 | −0.358231 | ||||||||
\(359\) | −17.2200 | −0.908834 | −0.454417 | − | 0.890789i | \(-0.650152\pi\) | ||||
−0.454417 | + | 0.890789i | \(0.650152\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.6636 | 1.03493 | ||||||||
\(362\) | −14.0067 | −0.736173 | ||||||||
\(363\) | −16.9706 | −0.890724 | ||||||||
\(364\) | −3.01199 | −0.157871 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −32.5731 | −1.70262 | ||||||||
\(367\) | 20.4193 | 1.06588 | 0.532939 | − | 0.846154i | \(-0.321087\pi\) | ||||
0.532939 | + | 0.846154i | \(0.321087\pi\) | |||||||
\(368\) | 5.90733 | 0.307941 | ||||||||
\(369\) | 5.28258 | 0.275000 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 40.5766 | 2.10663 | ||||||||
\(372\) | 0.504851 | 0.0261753 | ||||||||
\(373\) | 0.00410346 | 0.000212469 0 | 0.000106235 | − | 1.00000i | \(-0.499966\pi\) | ||||
0.000106235 | 1.00000i | \(0.499966\pi\) | ||||||||
\(374\) | 5.05736 | 0.261510 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 26.3118 | 1.35693 | ||||||||
\(377\) | −33.8795 | −1.74489 | ||||||||
\(378\) | −14.0857 | −0.724492 | ||||||||
\(379\) | 33.3456 | 1.71285 | 0.856424 | − | 0.516273i | \(-0.172681\pi\) | ||||
0.856424 | + | 0.516273i | \(0.172681\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.75096 | −0.140936 | ||||||||
\(382\) | −19.4549 | −0.995399 | ||||||||
\(383\) | −34.6473 | −1.77039 | −0.885196 | − | 0.465218i | \(-0.845976\pi\) | ||||
−0.885196 | + | 0.465218i | \(0.845976\pi\) | |||||||
\(384\) | −26.8074 | −1.36801 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.654683 | 0.0333225 | ||||||||
\(387\) | −0.383301 | −0.0194843 | ||||||||
\(388\) | −0.128056 | −0.00650104 | ||||||||
\(389\) | 30.7954 | 1.56139 | 0.780696 | − | 0.624912i | \(-0.214865\pi\) | ||||
0.780696 | + | 0.624912i | \(0.214865\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.68868 | −0.135972 | ||||||||
\(392\) | 18.5451 | 0.936668 | ||||||||
\(393\) | −4.98458 | −0.251439 | ||||||||
\(394\) | 12.4761 | 0.628537 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.391416 | −0.0196694 | ||||||||
\(397\) | −30.1664 | −1.51401 | −0.757004 | − | 0.653411i | \(-0.773338\pi\) | ||||
−0.757004 | + | 0.653411i | \(0.773338\pi\) | |||||||
\(398\) | 12.6328 | 0.633224 | ||||||||
\(399\) | 50.6205 | 2.53419 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.51947 | −0.375504 | −0.187752 | − | 0.982216i | \(-0.560120\pi\) | ||||
−0.187752 | + | 0.982216i | \(0.560120\pi\) | |||||||
\(402\) | 9.21486 | 0.459596 | ||||||||
\(403\) | 13.0567 | 0.650400 | ||||||||
\(404\) | −1.65778 | −0.0824777 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −26.9792 | −1.33896 | ||||||||
\(407\) | 4.89028 | 0.242402 | ||||||||
\(408\) | 11.5474 | 0.571681 | ||||||||
\(409\) | 32.8936 | 1.62648 | 0.813241 | − | 0.581927i | \(-0.197701\pi\) | ||||
0.813241 | + | 0.581927i | \(0.197701\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 34.1831 | 1.68613 | ||||||||
\(412\) | −0.341136 | −0.0168066 | ||||||||
\(413\) | 44.9014 | 2.20945 | ||||||||
\(414\) | 3.68769 | 0.181240 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.58484 | 0.224790 | ||||||||
\(417\) | −47.1616 | −2.30952 | ||||||||
\(418\) | −16.3535 | −0.799875 | ||||||||
\(419\) | 15.0851 | 0.736957 | 0.368479 | − | 0.929636i | \(-0.379879\pi\) | ||||
0.368479 | + | 0.929636i | \(0.379879\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.0575 | −1.12375 | −0.561876 | − | 0.827221i | \(-0.689920\pi\) | ||||
−0.561876 | + | 0.827221i | \(0.689920\pi\) | |||||||
\(422\) | −36.6815 | −1.78563 | ||||||||
\(423\) | 17.4112 | 0.846560 | ||||||||
\(424\) | −29.9309 | −1.45357 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.3244 | 0.597120 | ||||||||
\(427\) | −37.8548 | −1.83192 | ||||||||
\(428\) | 0.178103 | 0.00860893 | ||||||||
\(429\) | −26.8870 | −1.29811 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.8238 | −0.617703 | −0.308851 | − | 0.951110i | \(-0.599945\pi\) | ||||
−0.308851 | + | 0.951110i | \(0.599945\pi\) | |||||||
\(432\) | 11.0138 | 0.529901 | ||||||||
\(433\) | 28.7231 | 1.38034 | 0.690171 | − | 0.723646i | \(-0.257535\pi\) | ||||
0.690171 | + | 0.723646i | \(0.257535\pi\) | |||||||
\(434\) | 10.3974 | 0.499092 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.12469 | 0.0538631 | ||||||||
\(437\) | 8.69411 | 0.415896 | ||||||||
\(438\) | 37.0128 | 1.76854 | ||||||||
\(439\) | −23.6489 | −1.12870 | −0.564349 | − | 0.825536i | \(-0.690873\pi\) | ||||
−0.564349 | + | 0.825536i | \(0.690873\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.2717 | 0.584367 | ||||||||
\(442\) | −18.9959 | −0.903541 | ||||||||
\(443\) | 35.5043 | 1.68686 | 0.843430 | − | 0.537239i | \(-0.180533\pi\) | ||||
0.843430 | + | 0.537239i | \(0.180533\pi\) | |||||||
\(444\) | −0.710230 | −0.0337060 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 23.6492 | 1.11982 | ||||||||
\(447\) | −37.2960 | −1.76404 | ||||||||
\(448\) | −27.7092 | −1.30913 | ||||||||
\(449\) | 32.7779 | 1.54688 | 0.773442 | − | 0.633867i | \(-0.218533\pi\) | ||||
0.773442 | + | 0.633867i | \(0.218533\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.26774 | −0.248048 | ||||||||
\(452\) | −1.51710 | −0.0713582 | ||||||||
\(453\) | −39.0154 | −1.83310 | ||||||||
\(454\) | −19.2092 | −0.901531 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −37.3397 | −1.74859 | ||||||||
\(457\) | −28.7506 | −1.34490 | −0.672448 | − | 0.740145i | \(-0.734757\pi\) | ||||
−0.672448 | + | 0.740145i | \(0.734757\pi\) | |||||||
\(458\) | −3.45042 | −0.161228 | ||||||||
\(459\) | −5.01285 | −0.233980 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.6097 | −0.540717 | −0.270358 | − | 0.962760i | \(-0.587142\pi\) | ||||
−0.270358 | + | 0.962760i | \(0.587142\pi\) | |||||||
\(462\) | −21.4108 | −0.996123 | ||||||||
\(463\) | 18.7448 | 0.871145 | 0.435573 | − | 0.900154i | \(-0.356546\pi\) | ||||
0.435573 | + | 0.900154i | \(0.356546\pi\) | |||||||
\(464\) | 21.0954 | 0.979329 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.0912 | −0.652762 | ||||||||
\(467\) | 0.634016 | 0.0293387 | 0.0146694 | − | 0.999892i | \(-0.495330\pi\) | ||||
0.0146694 | + | 0.999892i | \(0.495330\pi\) | |||||||
\(468\) | 1.47019 | 0.0679597 | ||||||||
\(469\) | 10.7090 | 0.494497 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.8347 | 0.821780 | ||||||||
\(472\) | −33.1211 | −1.52452 | ||||||||
\(473\) | 0.382224 | 0.0175747 | ||||||||
\(474\) | 34.5406 | 1.58650 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.853592 | −0.0391243 | ||||||||
\(477\) | −19.8060 | −0.906854 | ||||||||
\(478\) | 34.7769 | 1.59066 | ||||||||
\(479\) | 29.2698 | 1.33737 | 0.668686 | − | 0.743545i | \(-0.266857\pi\) | ||||
0.668686 | + | 0.743545i | \(0.266857\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.3683 | −0.837523 | ||||||||
\(482\) | 22.8896 | 1.04259 | ||||||||
\(483\) | 11.3828 | 0.517935 | ||||||||
\(484\) | −0.925353 | −0.0420615 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 24.2312 | 1.09915 | ||||||||
\(487\) | −8.96526 | −0.406255 | −0.203127 | − | 0.979152i | \(-0.565111\pi\) | ||||
−0.203127 | + | 0.979152i | \(0.565111\pi\) | |||||||
\(488\) | 27.9232 | 1.26402 | ||||||||
\(489\) | −50.4806 | −2.28281 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.4601 | 0.968479 | 0.484240 | − | 0.874935i | \(-0.339096\pi\) | ||||
0.484240 | + | 0.874935i | \(0.339096\pi\) | |||||||
\(492\) | 0.765050 | 0.0344911 | ||||||||
\(493\) | −9.60141 | −0.432426 | ||||||||
\(494\) | 61.4251 | 2.76365 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.12986 | −0.365041 | ||||||||
\(497\) | 14.3228 | 0.642465 | ||||||||
\(498\) | −17.8600 | −0.800326 | ||||||||
\(499\) | 21.8821 | 0.979576 | 0.489788 | − | 0.871841i | \(-0.337074\pi\) | ||||
0.489788 | + | 0.871841i | \(0.337074\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.9193 | −0.577192 | ||||||||
\(502\) | −20.8094 | −0.928768 | ||||||||
\(503\) | 8.91940 | 0.397696 | 0.198848 | − | 0.980030i | \(-0.436280\pi\) | ||||
0.198848 | + | 0.980030i | \(0.436280\pi\) | |||||||
\(504\) | −18.4061 | −0.819872 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.67733 | −0.163477 | ||||||||
\(507\) | 72.4739 | 3.21868 | ||||||||
\(508\) | −0.150001 | −0.00665524 | ||||||||
\(509\) | −5.76572 | −0.255561 | −0.127780 | − | 0.991802i | \(-0.540785\pi\) | ||||
−0.127780 | + | 0.991802i | \(0.540785\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43.0143 | 1.90284 | ||||||||
\(512\) | 20.2778 | 0.896159 | ||||||||
\(513\) | 16.2096 | 0.715670 | ||||||||
\(514\) | −12.3950 | −0.546719 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.0555116 | −0.00244376 | ||||||||
\(517\) | −17.3623 | −0.763591 | ||||||||
\(518\) | −14.6272 | −0.642682 | ||||||||
\(519\) | 33.0616 | 1.45124 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.8063 | 0.648676 | 0.324338 | − | 0.945941i | \(-0.394858\pi\) | ||||
0.324338 | + | 0.945941i | \(0.394858\pi\) | |||||||
\(522\) | 13.1689 | 0.576389 | ||||||||
\(523\) | −34.3182 | −1.50063 | −0.750315 | − | 0.661081i | \(-0.770098\pi\) | ||||
−0.750315 | + | 0.661081i | \(0.770098\pi\) | |||||||
\(524\) | −0.271794 | −0.0118734 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.2084 | −1.22995 | ||||||||
\(527\) | 3.70024 | 0.161185 | ||||||||
\(528\) | 16.7414 | 0.728576 | ||||||||
\(529\) | −21.0450 | −0.915000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.9170 | −0.951117 | ||||||||
\(532\) | 2.76018 | 0.119669 | ||||||||
\(533\) | 19.7861 | 0.857031 | ||||||||
\(534\) | 3.19353 | 0.138197 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.89941 | −0.341203 | ||||||||
\(537\) | 10.2122 | 0.440690 | ||||||||
\(538\) | 10.7714 | 0.464389 | ||||||||
\(539\) | −12.2372 | −0.527095 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.0816 | −0.820384 | −0.410192 | − | 0.911999i | \(-0.634538\pi\) | ||||
−0.410192 | + | 0.911999i | \(0.634538\pi\) | |||||||
\(542\) | 39.6696 | 1.70395 | ||||||||
\(543\) | 21.1033 | 0.905628 | ||||||||
\(544\) | 1.29934 | 0.0557086 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 80.4210 | 3.44170 | ||||||||
\(547\) | 16.2497 | 0.694789 | 0.347394 | − | 0.937719i | \(-0.387067\pi\) | ||||
0.347394 | + | 0.937719i | \(0.387067\pi\) | |||||||
\(548\) | 1.86390 | 0.0796220 | ||||||||
\(549\) | 18.4774 | 0.788598 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.0472 | 1.32265 | ||||||||
\(552\) | −8.39641 | −0.357375 | ||||||||
\(553\) | 40.1413 | 1.70698 | ||||||||
\(554\) | 41.4319 | 1.76027 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.57158 | −0.109059 | ||||||||
\(557\) | −34.7023 | −1.47038 | −0.735191 | − | 0.677860i | \(-0.762908\pi\) | ||||
−0.735191 | + | 0.677860i | \(0.762908\pi\) | |||||||
\(558\) | −5.07512 | −0.214847 | ||||||||
\(559\) | −1.43567 | −0.0607223 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.61972 | −0.321705 | ||||||||
\(562\) | −32.2937 | −1.36223 | ||||||||
\(563\) | −11.6228 | −0.489842 | −0.244921 | − | 0.969543i | \(-0.578762\pi\) | ||||
−0.244921 | + | 0.969543i | \(0.578762\pi\) | |||||||
\(564\) | 2.52157 | 0.106177 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.360253 | 0.0151425 | ||||||||
\(567\) | 41.3924 | 1.73832 | ||||||||
\(568\) | −10.5651 | −0.443301 | ||||||||
\(569\) | 42.6106 | 1.78633 | 0.893164 | − | 0.449732i | \(-0.148480\pi\) | ||||
0.893164 | + | 0.449732i | \(0.148480\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.41985 | −0.143116 | −0.0715582 | − | 0.997436i | \(-0.522797\pi\) | ||||
−0.0715582 | + | 0.997436i | \(0.522797\pi\) | |||||||
\(572\) | −1.46606 | −0.0612992 | ||||||||
\(573\) | 29.3119 | 1.22452 | ||||||||
\(574\) | 15.7562 | 0.657652 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 13.5252 | 0.563551 | ||||||||
\(577\) | −6.58744 | −0.274239 | −0.137119 | − | 0.990555i | \(-0.543784\pi\) | ||||
−0.137119 | + | 0.990555i | \(0.543784\pi\) | |||||||
\(578\) | 19.3667 | 0.805548 | ||||||||
\(579\) | −0.986386 | −0.0409928 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.7560 | −0.861103 | ||||||||
\(582\) | 3.41913 | 0.141727 | ||||||||
\(583\) | 19.7504 | 0.817977 | ||||||||
\(584\) | −31.7291 | −1.31296 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.5744 | −0.684683 | ||||||||
\(587\) | 3.93893 | 0.162577 | 0.0812884 | − | 0.996691i | \(-0.474097\pi\) | ||||
0.0812884 | + | 0.996691i | \(0.474097\pi\) | |||||||
\(588\) | 1.77725 | 0.0732927 | ||||||||
\(589\) | −11.9651 | −0.493014 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.7973 | −0.773216 | ||||||||
\(592\) | 11.4372 | 0.470065 | ||||||||
\(593\) | 20.9067 | 0.858537 | 0.429269 | − | 0.903177i | \(-0.358771\pi\) | ||||
0.429269 | + | 0.903177i | \(0.358771\pi\) | |||||||
\(594\) | −6.85613 | −0.281310 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.03364 | −0.0833011 | ||||||||
\(597\) | −19.0333 | −0.778982 | ||||||||
\(598\) | 13.8124 | 0.564830 | ||||||||
\(599\) | 8.80091 | 0.359595 | 0.179798 | − | 0.983704i | \(-0.442456\pi\) | ||||
0.179798 | + | 0.983704i | \(0.442456\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.04731 | 0.124303 | 0.0621513 | − | 0.998067i | \(-0.480204\pi\) | ||||
0.0621513 | + | 0.998067i | \(0.480204\pi\) | |||||||
\(602\) | −1.14326 | −0.0465959 | ||||||||
\(603\) | −5.22723 | −0.212869 | ||||||||
\(604\) | −2.12739 | −0.0865623 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 44.2633 | 1.79807 | ||||||||
\(607\) | 37.2207 | 1.51074 | 0.755371 | − | 0.655298i | \(-0.227457\pi\) | ||||
0.755371 | + | 0.655298i | \(0.227457\pi\) | |||||||
\(608\) | −4.20154 | −0.170395 | ||||||||
\(609\) | 40.6486 | 1.64716 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 65.2141 | 2.63828 | ||||||||
\(612\) | 0.416650 | 0.0168421 | ||||||||
\(613\) | −7.03831 | −0.284275 | −0.142137 | − | 0.989847i | \(-0.545397\pi\) | ||||
−0.142137 | + | 0.989847i | \(0.545397\pi\) | |||||||
\(614\) | −9.27560 | −0.374333 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18.3544 | 0.739519 | ||||||||
\(617\) | 41.9256 | 1.68786 | 0.843931 | − | 0.536452i | \(-0.180236\pi\) | ||||
0.843931 | + | 0.536452i | \(0.180236\pi\) | |||||||
\(618\) | 9.10845 | 0.366395 | ||||||||
\(619\) | −7.92233 | −0.318425 | −0.159213 | − | 0.987244i | \(-0.550896\pi\) | ||||
−0.159213 | + | 0.987244i | \(0.550896\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.64497 | 0.146268 | ||||||||
\(622\) | 44.5496 | 1.78627 | ||||||||
\(623\) | 3.71135 | 0.148692 | ||||||||
\(624\) | −62.8821 | −2.51730 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −27.9991 | −1.11907 | ||||||||
\(627\) | 24.6392 | 0.983993 | ||||||||
\(628\) | 0.972472 | 0.0388059 | ||||||||
\(629\) | −5.20555 | −0.207559 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.9812 | 1.11391 | 0.556956 | − | 0.830542i | \(-0.311969\pi\) | ||||
0.556956 | + | 0.830542i | \(0.311969\pi\) | |||||||
\(632\) | −29.6098 | −1.17782 | ||||||||
\(633\) | 55.2666 | 2.19665 | ||||||||
\(634\) | −14.1283 | −0.561108 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.86841 | −0.113740 | ||||||||
\(637\) | 45.9641 | 1.82117 | ||||||||
\(638\) | −13.1320 | −0.519899 | ||||||||
\(639\) | −6.99116 | −0.276566 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.8328 | −0.427868 | −0.213934 | − | 0.976848i | \(-0.568628\pi\) | ||||
−0.213934 | + | 0.976848i | \(0.568628\pi\) | |||||||
\(642\) | −4.75541 | −0.187681 | ||||||||
\(643\) | −33.1604 | −1.30772 | −0.653859 | − | 0.756616i | \(-0.726851\pi\) | ||||
−0.653859 | + | 0.756616i | \(0.726851\pi\) | |||||||
\(644\) | 0.620669 | 0.0244578 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.4078 | 0.684900 | ||||||||
\(647\) | −7.80677 | −0.306916 | −0.153458 | − | 0.988155i | \(-0.549041\pi\) | ||||
−0.153458 | + | 0.988155i | \(0.549041\pi\) | |||||||
\(648\) | −30.5327 | −1.19944 | ||||||||
\(649\) | 21.8554 | 0.857901 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.6654 | −0.613974 | ||||||||
\(652\) | −2.75255 | −0.107798 | ||||||||
\(653\) | 9.79178 | 0.383182 | 0.191591 | − | 0.981475i | \(-0.438635\pi\) | ||||
0.191591 | + | 0.981475i | \(0.438635\pi\) | |||||||
\(654\) | −30.0297 | −1.17425 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −12.3200 | −0.481015 | ||||||||
\(657\) | −20.9959 | −0.819127 | ||||||||
\(658\) | 51.9319 | 2.02452 | ||||||||
\(659\) | −33.0449 | −1.28725 | −0.643623 | − | 0.765342i | \(-0.722570\pi\) | ||||
−0.643623 | + | 0.765342i | \(0.722570\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.9348 | 0.853165 | 0.426582 | − | 0.904449i | \(-0.359717\pi\) | ||||
0.426582 | + | 0.904449i | \(0.359717\pi\) | |||||||
\(662\) | 42.1152 | 1.63686 | ||||||||
\(663\) | 28.6203 | 1.11152 | ||||||||
\(664\) | 15.3104 | 0.594160 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.13974 | 0.276659 | ||||||||
\(667\) | 6.98143 | 0.270322 | ||||||||
\(668\) | −0.704451 | −0.0272560 | ||||||||
\(669\) | −35.6313 | −1.37758 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.4255 | −0.711310 | ||||||||
\(672\) | −5.50088 | −0.212201 | ||||||||
\(673\) | −12.6202 | −0.486472 | −0.243236 | − | 0.969967i | \(-0.578209\pi\) | ||||
−0.243236 | + | 0.969967i | \(0.578209\pi\) | |||||||
\(674\) | 3.36114 | 0.129466 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.95178 | 0.151991 | ||||||||
\(677\) | 43.1296 | 1.65761 | 0.828803 | − | 0.559541i | \(-0.189023\pi\) | ||||
0.828803 | + | 0.559541i | \(0.189023\pi\) | |||||||
\(678\) | 40.5069 | 1.55566 | ||||||||
\(679\) | 3.97353 | 0.152490 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.9417 | 1.10905 | ||||||||
\(682\) | 5.06087 | 0.193791 | ||||||||
\(683\) | 33.1031 | 1.26666 | 0.633328 | − | 0.773884i | \(-0.281689\pi\) | ||||
0.633328 | + | 0.773884i | \(0.281689\pi\) | |||||||
\(684\) | −1.34728 | −0.0515146 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.22056 | −0.0466012 | ||||||||
\(687\) | 5.19862 | 0.198340 | ||||||||
\(688\) | 0.893931 | 0.0340808 | ||||||||
\(689\) | −74.1841 | −2.82619 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.4778 | 0.436637 | 0.218319 | − | 0.975878i | \(-0.429943\pi\) | ||||
0.218319 | + | 0.975878i | \(0.429943\pi\) | |||||||
\(692\) | 1.80275 | 0.0685301 | ||||||||
\(693\) | 12.1455 | 0.461370 | ||||||||
\(694\) | −50.1769 | −1.90469 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −29.9840 | −1.13654 | ||||||||
\(697\) | 5.60735 | 0.212393 | ||||||||
\(698\) | −28.1210 | −1.06440 | ||||||||
\(699\) | 21.2306 | 0.803017 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.7156 | 1.04680 | 0.523401 | − | 0.852087i | \(-0.324663\pi\) | ||||
0.523401 | + | 0.852087i | \(0.324663\pi\) | |||||||
\(702\) | 25.7522 | 0.971955 | ||||||||
\(703\) | 16.8327 | 0.634857 | ||||||||
\(704\) | −13.4872 | −0.508320 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.05546 | 0.0773584 | ||||||||
\(707\) | 51.4404 | 1.93462 | ||||||||
\(708\) | −3.17413 | −0.119291 | ||||||||
\(709\) | 21.6735 | 0.813965 | 0.406983 | − | 0.913436i | \(-0.366581\pi\) | ||||
0.406983 | + | 0.913436i | \(0.366581\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.5935 | −0.734815 | ||||||||
\(712\) | −2.73764 | −0.102597 | ||||||||
\(713\) | −2.69054 | −0.100762 | ||||||||
\(714\) | 22.7912 | 0.852939 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.556842 | 0.0208101 | ||||||||
\(717\) | −52.3970 | −1.95680 | ||||||||
\(718\) | 25.0703 | 0.935615 | ||||||||
\(719\) | 13.5991 | 0.507160 | 0.253580 | − | 0.967314i | \(-0.418392\pi\) | ||||
0.253580 | + | 0.967314i | \(0.418392\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.5854 | 0.394219 | ||||||||
\(722\) | −28.6280 | −1.06542 | ||||||||
\(723\) | −34.4869 | −1.28258 | ||||||||
\(724\) | 1.15070 | 0.0427653 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 24.7072 | 0.916971 | ||||||||
\(727\) | −22.5512 | −0.836379 | −0.418189 | − | 0.908360i | \(-0.637335\pi\) | ||||
−0.418189 | + | 0.908360i | \(0.637335\pi\) | |||||||
\(728\) | −68.9406 | −2.55511 | ||||||||
\(729\) | −3.04947 | −0.112943 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.406866 | −0.0150485 | ||||||||
\(732\) | 2.67600 | 0.0989078 | ||||||||
\(733\) | −11.3716 | −0.420019 | −0.210009 | − | 0.977699i | \(-0.567349\pi\) | ||||
−0.210009 | + | 0.977699i | \(0.567349\pi\) | |||||||
\(734\) | −29.7282 | −1.09729 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.944782 | −0.0348251 | ||||||||
\(737\) | 5.21254 | 0.192007 | ||||||||
\(738\) | −7.69084 | −0.283104 | ||||||||
\(739\) | −51.8437 | −1.90710 | −0.953551 | − | 0.301232i | \(-0.902602\pi\) | ||||
−0.953551 | + | 0.301232i | \(0.902602\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −92.5468 | −3.39979 | ||||||||
\(742\) | −59.0749 | −2.16871 | ||||||||
\(743\) | −20.9239 | −0.767623 | −0.383812 | − | 0.923411i | \(-0.625389\pi\) | ||||
−0.383812 | + | 0.923411i | \(0.625389\pi\) | |||||||
\(744\) | 11.5554 | 0.423642 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.00597418 | −0.000218730 0 | ||||||||
\(747\) | 10.1313 | 0.370684 | ||||||||
\(748\) | −0.415480 | −0.0151915 | ||||||||
\(749\) | −5.52648 | −0.201933 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.2392 | 0.993972 | 0.496986 | − | 0.867759i | \(-0.334440\pi\) | ||||
0.496986 | + | 0.867759i | \(0.334440\pi\) | |||||||
\(752\) | −40.6062 | −1.48075 | ||||||||
\(753\) | 31.3527 | 1.14255 | ||||||||
\(754\) | 49.3248 | 1.79630 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.15719 | 0.0420867 | ||||||||
\(757\) | 18.6306 | 0.677142 | 0.338571 | − | 0.940941i | \(-0.390057\pi\) | ||||
0.338571 | + | 0.940941i | \(0.390057\pi\) | |||||||
\(758\) | −48.5474 | −1.76332 | ||||||||
\(759\) | 5.54049 | 0.201107 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.06378 | −0.147312 | −0.0736559 | − | 0.997284i | \(-0.523467\pi\) | ||||
−0.0736559 | + | 0.997284i | \(0.523467\pi\) | |||||||
\(762\) | 4.00509 | 0.145089 | ||||||||
\(763\) | −34.8989 | −1.26343 | ||||||||
\(764\) | 1.59829 | 0.0578241 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 50.4425 | 1.82256 | ||||||||
\(767\) | −82.0909 | −2.96413 | ||||||||
\(768\) | 6.27456 | 0.226414 | ||||||||
\(769\) | −32.7396 | −1.18062 | −0.590310 | − | 0.807177i | \(-0.700994\pi\) | ||||
−0.590310 | + | 0.807177i | \(0.700994\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.6750 | 0.672564 | ||||||||
\(772\) | −0.0537846 | −0.00193575 | ||||||||
\(773\) | −19.0463 | −0.685049 | −0.342524 | − | 0.939509i | \(-0.611282\pi\) | ||||
−0.342524 | + | 0.939509i | \(0.611282\pi\) | |||||||
\(774\) | 0.558043 | 0.0200584 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.93103 | −0.105218 | ||||||||
\(777\) | 22.0382 | 0.790617 | ||||||||
\(778\) | −44.8347 | −1.60740 | ||||||||
\(779\) | −18.1319 | −0.649644 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.97152 | 0.249461 | ||||||||
\(782\) | 3.91441 | 0.139979 | ||||||||
\(783\) | 13.0164 | 0.465168 | ||||||||
\(784\) | −28.6200 | −1.02214 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7.25698 | 0.258848 | ||||||||
\(787\) | −36.9703 | −1.31785 | −0.658924 | − | 0.752210i | \(-0.728988\pi\) | ||||
−0.658924 | + | 0.752210i | \(0.728988\pi\) | |||||||
\(788\) | −1.02496 | −0.0365126 | ||||||||
\(789\) | 42.5005 | 1.51306 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 47.0750 | 1.67379 | ||||||||
\(792\) | −8.95903 | −0.318345 | ||||||||
\(793\) | 69.2079 | 2.45765 | ||||||||
\(794\) | 43.9188 | 1.55862 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.03783 | −0.0367849 | ||||||||
\(797\) | 10.1404 | 0.359191 | 0.179596 | − | 0.983741i | \(-0.442521\pi\) | ||||
0.179596 | + | 0.983741i | \(0.442521\pi\) | |||||||
\(798\) | −73.6977 | −2.60887 | ||||||||
\(799\) | 18.4816 | 0.653832 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.81156 | −0.0640084 | ||||||||
\(802\) | 10.9475 | 0.386570 | ||||||||
\(803\) | 20.9369 | 0.738847 | ||||||||
\(804\) | −0.757034 | −0.0266985 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19.0091 | −0.669566 | ||||||||
\(807\) | −16.2289 | −0.571284 | ||||||||
\(808\) | −37.9445 | −1.33488 | ||||||||
\(809\) | 0.167200 | 0.00587845 | 0.00293922 | − | 0.999996i | \(-0.499064\pi\) | ||||
0.00293922 | + | 0.999996i | \(0.499064\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.1102 | −1.44357 | −0.721787 | − | 0.692115i | \(-0.756679\pi\) | ||||
−0.721787 | + | 0.692115i | \(0.756679\pi\) | |||||||
\(812\) | 2.21644 | 0.0777819 | ||||||||
\(813\) | −59.7686 | −2.09618 | ||||||||
\(814\) | −7.11969 | −0.249545 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −17.8207 | −0.623849 | ||||||||
\(817\) | 1.31564 | 0.0460285 | ||||||||
\(818\) | −47.8893 | −1.67441 | ||||||||
\(819\) | −45.6196 | −1.59408 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.1698 | −1.50664 | −0.753318 | − | 0.657656i | \(-0.771548\pi\) | ||||
−0.753318 | + | 0.657656i | \(0.771548\pi\) | |||||||
\(822\) | −49.7668 | −1.73582 | ||||||||
\(823\) | 8.46445 | 0.295052 | 0.147526 | − | 0.989058i | \(-0.452869\pi\) | ||||
0.147526 | + | 0.989058i | \(0.452869\pi\) | |||||||
\(824\) | −7.80818 | −0.272011 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −65.3713 | −2.27456 | ||||||||
\(827\) | −6.41763 | −0.223163 | −0.111581 | − | 0.993755i | \(-0.535592\pi\) | ||||
−0.111581 | + | 0.993755i | \(0.535592\pi\) | |||||||
\(828\) | −0.302957 | −0.0105285 | ||||||||
\(829\) | −16.7935 | −0.583261 | −0.291631 | − | 0.956531i | \(-0.594198\pi\) | ||||
−0.291631 | + | 0.956531i | \(0.594198\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −62.4238 | −2.16546 | ||||||||
\(832\) | 50.6592 | 1.75629 | ||||||||
\(833\) | 13.0262 | 0.451330 | ||||||||
\(834\) | 68.6620 | 2.37757 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.34350 | 0.0464658 | ||||||||
\(837\) | −5.01633 | −0.173390 | ||||||||
\(838\) | −21.9623 | −0.758673 | ||||||||
\(839\) | −7.92834 | −0.273717 | −0.136858 | − | 0.990591i | \(-0.543701\pi\) | ||||
−0.136858 | + | 0.990591i | \(0.543701\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.06893 | −0.140308 | ||||||||
\(842\) | 33.5691 | 1.15687 | ||||||||
\(843\) | 48.6556 | 1.67579 | ||||||||
\(844\) | 3.01352 | 0.103730 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −25.3487 | −0.871505 | ||||||||
\(847\) | 28.7134 | 0.986605 | ||||||||
\(848\) | 46.1914 | 1.58622 | ||||||||
\(849\) | −0.542778 | −0.0186281 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.78509 | 0.129751 | ||||||||
\(852\) | −1.01250 | −0.0346875 | ||||||||
\(853\) | 27.1727 | 0.930375 | 0.465187 | − | 0.885212i | \(-0.345987\pi\) | ||||
0.465187 | + | 0.885212i | \(0.345987\pi\) | |||||||
\(854\) | 55.1123 | 1.88590 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.07656 | 0.139334 | ||||||||
\(857\) | 43.2642 | 1.47788 | 0.738938 | − | 0.673773i | \(-0.235328\pi\) | ||||
0.738938 | + | 0.673773i | \(0.235328\pi\) | |||||||
\(858\) | 39.1444 | 1.33637 | ||||||||
\(859\) | 18.4487 | 0.629463 | 0.314731 | − | 0.949181i | \(-0.398086\pi\) | ||||
0.314731 | + | 0.949181i | \(0.398086\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.7393 | −0.809033 | ||||||||
\(862\) | 18.6701 | 0.635905 | ||||||||
\(863\) | −1.54533 | −0.0526037 | −0.0263018 | − | 0.999654i | \(-0.508373\pi\) | ||||
−0.0263018 | + | 0.999654i | \(0.508373\pi\) | |||||||
\(864\) | −1.76148 | −0.0599267 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −41.8175 | −1.42102 | ||||||||
\(867\) | −29.1790 | −0.990971 | ||||||||
\(868\) | −0.854185 | −0.0289929 | ||||||||
\(869\) | 19.5385 | 0.662798 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.5788 | −0.663401 | ||||||||
\(872\) | 25.7429 | 0.871763 | ||||||||
\(873\) | −1.93953 | −0.0656433 | ||||||||
\(874\) | −12.6576 | −0.428151 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.04073 | −0.102737 | ||||||||
\(877\) | −47.7230 | −1.61149 | −0.805745 | − | 0.592262i | \(-0.798235\pi\) | ||||
−0.805745 | + | 0.592262i | \(0.798235\pi\) | |||||||
\(878\) | 34.4301 | 1.16196 | ||||||||
\(879\) | 24.9720 | 0.842286 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.2004 | 0.950095 | 0.475047 | − | 0.879960i | \(-0.342431\pi\) | ||||
0.475047 | + | 0.879960i | \(0.342431\pi\) | |||||||
\(882\) | −17.8662 | −0.601587 | ||||||||
\(883\) | 11.2269 | 0.377816 | 0.188908 | − | 0.981995i | \(-0.439505\pi\) | ||||
0.188908 | + | 0.981995i | \(0.439505\pi\) | |||||||
\(884\) | 1.56058 | 0.0524879 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −51.6902 | −1.73657 | ||||||||
\(887\) | −12.8249 | −0.430619 | −0.215309 | − | 0.976546i | \(-0.569076\pi\) | ||||
−0.215309 | + | 0.976546i | \(0.569076\pi\) | |||||||
\(888\) | −16.2563 | −0.545525 | ||||||||
\(889\) | 4.65450 | 0.156107 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.1475 | 0.674965 | ||||||||
\(892\) | −1.94286 | −0.0650519 | ||||||||
\(893\) | −59.7621 | −1.99986 | ||||||||
\(894\) | 54.2988 | 1.81602 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 45.3570 | 1.51527 | ||||||||
\(897\) | −20.8106 | −0.694845 | ||||||||
\(898\) | −47.7209 | −1.59247 | ||||||||
\(899\) | −9.60807 | −0.320447 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.0237 | −0.700400 | ||||||||
\(902\) | 7.66923 | 0.255358 | ||||||||
\(903\) | 1.72251 | 0.0573215 | ||||||||
\(904\) | −34.7244 | −1.15492 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 56.8020 | 1.88712 | ||||||||
\(907\) | 45.9112 | 1.52446 | 0.762229 | − | 0.647308i | \(-0.224105\pi\) | ||||
0.762229 | + | 0.647308i | \(0.224105\pi\) | |||||||
\(908\) | 1.57810 | 0.0523712 | ||||||||
\(909\) | −25.1088 | −0.832806 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.7475 | 1.84700 | 0.923499 | − | 0.383600i | \(-0.125316\pi\) | ||||
0.923499 | + | 0.383600i | \(0.125316\pi\) | |||||||
\(912\) | 57.6251 | 1.90816 | ||||||||
\(913\) | −10.1028 | −0.334355 | ||||||||
\(914\) | 41.8576 | 1.38453 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.283465 | 0.00936593 | ||||||||
\(917\) | 8.43368 | 0.278505 | ||||||||
\(918\) | 7.29814 | 0.240874 | ||||||||
\(919\) | −49.0675 | −1.61859 | −0.809293 | − | 0.587405i | \(-0.800150\pi\) | ||||
−0.809293 | + | 0.587405i | \(0.800150\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.9752 | 0.460498 | ||||||||
\(922\) | 16.9024 | 0.556650 | ||||||||
\(923\) | −26.1856 | −0.861911 | ||||||||
\(924\) | 1.75898 | 0.0578661 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −27.2903 | −0.896815 | ||||||||
\(927\) | −5.16686 | −0.169702 | ||||||||
\(928\) | −3.37387 | −0.110753 | ||||||||
\(929\) | −0.564626 | −0.0185248 | −0.00926238 | − | 0.999957i | \(-0.502948\pi\) | ||||
−0.00926238 | + | 0.999957i | \(0.502948\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.1215 | −1.38048 | ||||||||
\(932\) | 1.15764 | 0.0379198 | ||||||||
\(933\) | −67.1210 | −2.19744 | ||||||||
\(934\) | −0.923055 | −0.0302033 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 33.6509 | 1.09991 | ||||||||
\(937\) | −21.4710 | −0.701426 | −0.350713 | − | 0.936483i | \(-0.614061\pi\) | ||||
−0.350713 | + | 0.936483i | \(0.614061\pi\) | |||||||
\(938\) | −15.5911 | −0.509069 | ||||||||
\(939\) | 42.1851 | 1.37666 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.9258 | 1.07335 | 0.536676 | − | 0.843789i | \(-0.319680\pi\) | ||||
0.536676 | + | 0.843789i | \(0.319680\pi\) | |||||||
\(942\) | −25.9653 | −0.845996 | ||||||||
\(943\) | −4.07725 | −0.132773 | ||||||||
\(944\) | 51.1146 | 1.66364 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.556475 | −0.0180926 | ||||||||
\(947\) | 46.4200 | 1.50845 | 0.754224 | − | 0.656617i | \(-0.228013\pi\) | ||||
0.754224 | + | 0.656617i | \(0.228013\pi\) | |||||||
\(948\) | −2.83764 | −0.0921621 | ||||||||
\(949\) | −78.6408 | −2.55279 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.2866 | 0.690266 | ||||||||
\(952\) | −19.5377 | −0.633219 | ||||||||
\(953\) | −40.6651 | −1.31727 | −0.658636 | − | 0.752462i | \(-0.728866\pi\) | ||||
−0.658636 | + | 0.752462i | \(0.728866\pi\) | |||||||
\(954\) | 28.8353 | 0.933577 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.85705 | −0.0924036 | ||||||||
\(957\) | 19.7854 | 0.639571 | ||||||||
\(958\) | −42.6135 | −1.37678 | ||||||||
\(959\) | −57.8363 | −1.86763 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.2972 | −0.880554 | ||||||||
\(962\) | 26.7422 | 0.862202 | ||||||||
\(963\) | 2.69755 | 0.0869274 | ||||||||
\(964\) | −1.88047 | −0.0605657 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −16.5721 | −0.533197 | ||||||||
\(967\) | −13.7463 | −0.442051 | −0.221026 | − | 0.975268i | \(-0.570940\pi\) | ||||
−0.221026 | + | 0.975268i | \(0.570940\pi\) | |||||||
\(968\) | −21.1802 | −0.680757 | ||||||||
\(969\) | −26.2276 | −0.842553 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.4871 | −0.336548 | −0.168274 | − | 0.985740i | \(-0.553819\pi\) | ||||
−0.168274 | + | 0.985740i | \(0.553819\pi\) | |||||||
\(972\) | −1.99068 | −0.0638512 | ||||||||
\(973\) | 79.7954 | 2.55812 | ||||||||
\(974\) | 13.0524 | 0.418226 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −43.0929 | −1.37937 | ||||||||
\(977\) | −26.8721 | −0.859716 | −0.429858 | − | 0.902897i | \(-0.641436\pi\) | ||||
−0.429858 | + | 0.902897i | \(0.641436\pi\) | |||||||
\(978\) | 73.4941 | 2.35008 | ||||||||
\(979\) | 1.80647 | 0.0577351 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.0347 | 0.543875 | ||||||||
\(982\) | −31.2434 | −0.997018 | ||||||||
\(983\) | −5.47408 | −0.174596 | −0.0872980 | − | 0.996182i | \(-0.527823\pi\) | ||||
−0.0872980 | + | 0.996182i | \(0.527823\pi\) | |||||||
\(984\) | 17.5111 | 0.558232 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 13.9786 | 0.445168 | ||||||||
\(987\) | −78.2437 | −2.49052 | ||||||||
\(988\) | −5.04629 | −0.160544 | ||||||||
\(989\) | 0.295843 | 0.00940725 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.1620 | 0.799296 | 0.399648 | − | 0.916669i | \(-0.369132\pi\) | ||||
0.399648 | + | 0.916669i | \(0.369132\pi\) | |||||||
\(992\) | 1.30024 | 0.0412827 | ||||||||
\(993\) | −63.4534 | −2.01363 | ||||||||
\(994\) | −20.8524 | −0.661397 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.46726 | 0.0464920 | ||||||||
\(997\) | −11.3414 | −0.359186 | −0.179593 | − | 0.983741i | \(-0.557478\pi\) | ||||
−0.179593 | + | 0.983741i | \(0.557478\pi\) | |||||||
\(998\) | −31.8578 | −1.00844 | ||||||||
\(999\) | 7.05703 | 0.223274 |
(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 | 2225.2.a.i.1.2 | 4 | ||
5.4 | even | 2 | 445.2.a.d.1.3 | ✓ | 4 | ||
15.14 | odd | 2 | 4005.2.a.l.1.2 | 4 | |||
20.19 | odd | 2 | 7120.2.a.bc.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
445.2.a.d.1.3 | ✓ | 4 | 5.4 | even | 2 | ||
2225.2.a.i.1.2 | 4 | 1.1 | even | 1 | trivial | ||
4005.2.a.l.1.2 | 4 | 15.14 | odd | 2 | |||
7120.2.a.bc.1.4 | 4 | 20.19 | odd | 2 |