Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [241,2,Mod(1,241)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(241, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("241.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 241.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: | \(1.92439468871\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | 7.7.31056073.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.369356\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 241.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.630644 | −0.445933 | −0.222966 | − | 0.974826i | \(-0.571574\pi\) | ||||
−0.222966 | + | 0.974826i | \(0.571574\pi\) | |||||||
\(3\) | 2.33806 | 1.34988 | 0.674940 | − | 0.737872i | \(-0.264169\pi\) | ||||
0.674940 | + | 0.737872i | \(0.264169\pi\) | |||||||
\(4\) | −1.60229 | −0.801144 | ||||||||
\(5\) | −3.89634 | −1.74250 | −0.871249 | − | 0.490842i | \(-0.836689\pi\) | ||||
−0.871249 | + | 0.490842i | \(0.836689\pi\) | |||||||
\(6\) | −1.47449 | −0.601956 | ||||||||
\(7\) | −3.68231 | −1.39178 | −0.695892 | − | 0.718146i | \(-0.744991\pi\) | ||||
−0.695892 | + | 0.718146i | \(0.744991\pi\) | |||||||
\(8\) | 2.27176 | 0.803189 | ||||||||
\(9\) | 2.46654 | 0.822178 | ||||||||
\(10\) | 2.45721 | 0.777037 | ||||||||
\(11\) | −4.96431 | −1.49679 | −0.748397 | − | 0.663250i | \(-0.769176\pi\) | ||||
−0.748397 | + | 0.663250i | \(0.769176\pi\) | |||||||
\(12\) | −3.74625 | −1.08145 | ||||||||
\(13\) | −1.69048 | −0.468855 | −0.234428 | − | 0.972134i | \(-0.575322\pi\) | ||||
−0.234428 | + | 0.972134i | \(0.575322\pi\) | |||||||
\(14\) | 2.32223 | 0.620642 | ||||||||
\(15\) | −9.10989 | −2.35216 | ||||||||
\(16\) | 1.77190 | 0.442975 | ||||||||
\(17\) | 5.52260 | 1.33943 | 0.669714 | − | 0.742619i | \(-0.266417\pi\) | ||||
0.669714 | + | 0.742619i | \(0.266417\pi\) | |||||||
\(18\) | −1.55551 | −0.366636 | ||||||||
\(19\) | 4.21489 | 0.966961 | 0.483481 | − | 0.875355i | \(-0.339372\pi\) | ||||
0.483481 | + | 0.875355i | \(0.339372\pi\) | |||||||
\(20\) | 6.24306 | 1.39599 | ||||||||
\(21\) | −8.60948 | −1.87874 | ||||||||
\(22\) | 3.13071 | 0.667470 | ||||||||
\(23\) | −2.77495 | −0.578617 | −0.289308 | − | 0.957236i | \(-0.593425\pi\) | ||||
−0.289308 | + | 0.957236i | \(0.593425\pi\) | |||||||
\(24\) | 5.31152 | 1.08421 | ||||||||
\(25\) | 10.1815 | 2.03630 | ||||||||
\(26\) | 1.06609 | 0.209078 | ||||||||
\(27\) | −1.24727 | −0.240038 | ||||||||
\(28\) | 5.90013 | 1.11502 | ||||||||
\(29\) | −2.31253 | −0.429425 | −0.214713 | − | 0.976677i | \(-0.568881\pi\) | ||||
−0.214713 | + | 0.976677i | \(0.568881\pi\) | |||||||
\(30\) | 5.74510 | 1.04891 | ||||||||
\(31\) | −0.199515 | −0.0358340 | −0.0179170 | − | 0.999839i | \(-0.505703\pi\) | ||||
−0.0179170 | + | 0.999839i | \(0.505703\pi\) | |||||||
\(32\) | −5.66096 | −1.00073 | ||||||||
\(33\) | −11.6069 | −2.02049 | ||||||||
\(34\) | −3.48280 | −0.597295 | ||||||||
\(35\) | 14.3476 | 2.42518 | ||||||||
\(36\) | −3.95210 | −0.658683 | ||||||||
\(37\) | 1.79089 | 0.294420 | 0.147210 | − | 0.989105i | \(-0.452971\pi\) | ||||
0.147210 | + | 0.989105i | \(0.452971\pi\) | |||||||
\(38\) | −2.65809 | −0.431200 | ||||||||
\(39\) | −3.95245 | −0.632899 | ||||||||
\(40\) | −8.85157 | −1.39956 | ||||||||
\(41\) | −12.1960 | −1.90470 | −0.952351 | − | 0.305003i | \(-0.901343\pi\) | ||||
−0.952351 | + | 0.305003i | \(0.901343\pi\) | |||||||
\(42\) | 5.42952 | 0.837793 | ||||||||
\(43\) | −5.34523 | −0.815139 | −0.407570 | − | 0.913174i | \(-0.633624\pi\) | ||||
−0.407570 | + | 0.913174i | \(0.633624\pi\) | |||||||
\(44\) | 7.95425 | 1.19915 | ||||||||
\(45\) | −9.61047 | −1.43264 | ||||||||
\(46\) | 1.75001 | 0.258024 | ||||||||
\(47\) | −10.7345 | −1.56579 | −0.782893 | − | 0.622157i | \(-0.786257\pi\) | ||||
−0.782893 | + | 0.622157i | \(0.786257\pi\) | |||||||
\(48\) | 4.14282 | 0.597964 | ||||||||
\(49\) | 6.55944 | 0.937063 | ||||||||
\(50\) | −6.42090 | −0.908052 | ||||||||
\(51\) | 12.9122 | 1.80807 | ||||||||
\(52\) | 2.70864 | 0.375621 | ||||||||
\(53\) | 1.32229 | 0.181631 | 0.0908154 | − | 0.995868i | \(-0.471053\pi\) | ||||
0.0908154 | + | 0.995868i | \(0.471053\pi\) | |||||||
\(54\) | 0.786587 | 0.107041 | ||||||||
\(55\) | 19.3426 | 2.60816 | ||||||||
\(56\) | −8.36534 | −1.11787 | ||||||||
\(57\) | 9.85467 | 1.30528 | ||||||||
\(58\) | 1.45838 | 0.191495 | ||||||||
\(59\) | 5.78578 | 0.753244 | 0.376622 | − | 0.926367i | \(-0.377086\pi\) | ||||
0.376622 | + | 0.926367i | \(0.377086\pi\) | |||||||
\(60\) | 14.5967 | 1.88442 | ||||||||
\(61\) | −0.0766435 | −0.00981320 | −0.00490660 | − | 0.999988i | \(-0.501562\pi\) | ||||
−0.00490660 | + | 0.999988i | \(0.501562\pi\) | |||||||
\(62\) | 0.125823 | 0.0159795 | ||||||||
\(63\) | −9.08256 | −1.14429 | ||||||||
\(64\) | 0.0262532 | 0.00328165 | ||||||||
\(65\) | 6.58670 | 0.816979 | ||||||||
\(66\) | 7.31980 | 0.901005 | ||||||||
\(67\) | 12.6166 | 1.54136 | 0.770681 | − | 0.637221i | \(-0.219916\pi\) | ||||
0.770681 | + | 0.637221i | \(0.219916\pi\) | |||||||
\(68\) | −8.84880 | −1.07307 | ||||||||
\(69\) | −6.48800 | −0.781064 | ||||||||
\(70\) | −9.04821 | −1.08147 | ||||||||
\(71\) | −5.20391 | −0.617591 | −0.308796 | − | 0.951128i | \(-0.599926\pi\) | ||||
−0.308796 | + | 0.951128i | \(0.599926\pi\) | |||||||
\(72\) | 5.60338 | 0.660365 | ||||||||
\(73\) | −14.0733 | −1.64715 | −0.823577 | − | 0.567204i | \(-0.808025\pi\) | ||||
−0.823577 | + | 0.567204i | \(0.808025\pi\) | |||||||
\(74\) | −1.12941 | −0.131291 | ||||||||
\(75\) | 23.8050 | 2.74876 | ||||||||
\(76\) | −6.75346 | −0.774675 | ||||||||
\(77\) | 18.2801 | 2.08322 | ||||||||
\(78\) | 2.49259 | 0.282230 | ||||||||
\(79\) | 7.82844 | 0.880769 | 0.440384 | − | 0.897809i | \(-0.354842\pi\) | ||||
0.440384 | + | 0.897809i | \(0.354842\pi\) | |||||||
\(80\) | −6.90393 | −0.771883 | ||||||||
\(81\) | −10.3158 | −1.14620 | ||||||||
\(82\) | 7.69137 | 0.849370 | ||||||||
\(83\) | 2.55372 | 0.280307 | 0.140153 | − | 0.990130i | \(-0.455240\pi\) | ||||
0.140153 | + | 0.990130i | \(0.455240\pi\) | |||||||
\(84\) | 13.7949 | 1.50514 | ||||||||
\(85\) | −21.5180 | −2.33395 | ||||||||
\(86\) | 3.37094 | 0.363497 | ||||||||
\(87\) | −5.40683 | −0.579673 | ||||||||
\(88\) | −11.2777 | −1.20221 | ||||||||
\(89\) | −4.35327 | −0.461446 | −0.230723 | − | 0.973019i | \(-0.574109\pi\) | ||||
−0.230723 | + | 0.973019i | \(0.574109\pi\) | |||||||
\(90\) | 6.06079 | 0.638863 | ||||||||
\(91\) | 6.22489 | 0.652546 | ||||||||
\(92\) | 4.44627 | 0.463555 | ||||||||
\(93\) | −0.466479 | −0.0483716 | ||||||||
\(94\) | 6.76964 | 0.698235 | ||||||||
\(95\) | −16.4226 | −1.68493 | ||||||||
\(96\) | −13.2357 | −1.35086 | ||||||||
\(97\) | 9.02693 | 0.916546 | 0.458273 | − | 0.888811i | \(-0.348468\pi\) | ||||
0.458273 | + | 0.888811i | \(0.348468\pi\) | |||||||
\(98\) | −4.13668 | −0.417867 | ||||||||
\(99\) | −12.2446 | −1.23063 | ||||||||
\(100\) | −16.3137 | −1.63137 | ||||||||
\(101\) | 6.94323 | 0.690877 | 0.345439 | − | 0.938441i | \(-0.387730\pi\) | ||||
0.345439 | + | 0.938441i | \(0.387730\pi\) | |||||||
\(102\) | −8.14300 | −0.806277 | ||||||||
\(103\) | −0.105009 | −0.0103469 | −0.00517343 | − | 0.999987i | \(-0.501647\pi\) | ||||
−0.00517343 | + | 0.999987i | \(0.501647\pi\) | |||||||
\(104\) | −3.84037 | −0.376580 | ||||||||
\(105\) | 33.5455 | 3.27371 | ||||||||
\(106\) | −0.833897 | −0.0809952 | ||||||||
\(107\) | −18.1842 | −1.75793 | −0.878966 | − | 0.476885i | \(-0.841766\pi\) | ||||
−0.878966 | + | 0.476885i | \(0.841766\pi\) | |||||||
\(108\) | 1.99849 | 0.192305 | ||||||||
\(109\) | 14.6576 | 1.40394 | 0.701972 | − | 0.712205i | \(-0.252303\pi\) | ||||
0.701972 | + | 0.712205i | \(0.252303\pi\) | |||||||
\(110\) | −12.1983 | −1.16307 | ||||||||
\(111\) | 4.18720 | 0.397432 | ||||||||
\(112\) | −6.52470 | −0.616526 | ||||||||
\(113\) | 1.08836 | 0.102384 | 0.0511922 | − | 0.998689i | \(-0.483698\pi\) | ||||
0.0511922 | + | 0.998689i | \(0.483698\pi\) | |||||||
\(114\) | −6.21479 | −0.582068 | ||||||||
\(115\) | 10.8122 | 1.00824 | ||||||||
\(116\) | 3.70533 | 0.344031 | ||||||||
\(117\) | −4.16963 | −0.385483 | ||||||||
\(118\) | −3.64877 | −0.335896 | ||||||||
\(119\) | −20.3360 | −1.86420 | ||||||||
\(120\) | −20.6955 | −1.88923 | ||||||||
\(121\) | 13.6443 | 1.24040 | ||||||||
\(122\) | 0.0483348 | 0.00437603 | ||||||||
\(123\) | −28.5151 | −2.57112 | ||||||||
\(124\) | 0.319681 | 0.0287082 | ||||||||
\(125\) | −20.1889 | −1.80575 | ||||||||
\(126\) | 5.72786 | 0.510279 | ||||||||
\(127\) | 0.364538 | 0.0323475 | 0.0161737 | − | 0.999869i | \(-0.494852\pi\) | ||||
0.0161737 | + | 0.999869i | \(0.494852\pi\) | |||||||
\(128\) | 11.3054 | 0.999263 | ||||||||
\(129\) | −12.4975 | −1.10034 | ||||||||
\(130\) | −4.15386 | −0.364318 | ||||||||
\(131\) | 5.48865 | 0.479546 | 0.239773 | − | 0.970829i | \(-0.422927\pi\) | ||||
0.239773 | + | 0.970829i | \(0.422927\pi\) | |||||||
\(132\) | 18.5975 | 1.61871 | ||||||||
\(133\) | −15.5205 | −1.34580 | ||||||||
\(134\) | −7.95658 | −0.687344 | ||||||||
\(135\) | 4.85981 | 0.418266 | ||||||||
\(136\) | 12.5460 | 1.07581 | ||||||||
\(137\) | −17.1533 | −1.46551 | −0.732754 | − | 0.680493i | \(-0.761766\pi\) | ||||
−0.732754 | + | 0.680493i | \(0.761766\pi\) | |||||||
\(138\) | 4.09162 | 0.348302 | ||||||||
\(139\) | −19.6074 | −1.66308 | −0.831539 | − | 0.555467i | \(-0.812540\pi\) | ||||
−0.831539 | + | 0.555467i | \(0.812540\pi\) | |||||||
\(140\) | −22.9889 | −1.94292 | ||||||||
\(141\) | −25.0979 | −2.11362 | ||||||||
\(142\) | 3.28182 | 0.275404 | ||||||||
\(143\) | 8.39207 | 0.701780 | ||||||||
\(144\) | 4.37046 | 0.364205 | ||||||||
\(145\) | 9.01039 | 0.748272 | ||||||||
\(146\) | 8.87525 | 0.734521 | ||||||||
\(147\) | 15.3364 | 1.26492 | ||||||||
\(148\) | −2.86951 | −0.235873 | ||||||||
\(149\) | 19.0508 | 1.56070 | 0.780350 | − | 0.625343i | \(-0.215041\pi\) | ||||
0.780350 | + | 0.625343i | \(0.215041\pi\) | |||||||
\(150\) | −15.0125 | −1.22576 | ||||||||
\(151\) | −4.76802 | −0.388016 | −0.194008 | − | 0.981000i | \(-0.562149\pi\) | ||||
−0.194008 | + | 0.981000i | \(0.562149\pi\) | |||||||
\(152\) | 9.57522 | 0.776653 | ||||||||
\(153\) | 13.6217 | 1.10125 | ||||||||
\(154\) | −11.5283 | −0.928974 | ||||||||
\(155\) | 0.777379 | 0.0624406 | ||||||||
\(156\) | 6.33297 | 0.507043 | ||||||||
\(157\) | 6.12724 | 0.489007 | 0.244503 | − | 0.969648i | \(-0.421375\pi\) | ||||
0.244503 | + | 0.969648i | \(0.421375\pi\) | |||||||
\(158\) | −4.93696 | −0.392764 | ||||||||
\(159\) | 3.09160 | 0.245180 | ||||||||
\(160\) | 22.0571 | 1.74376 | ||||||||
\(161\) | 10.2182 | 0.805310 | ||||||||
\(162\) | 6.50561 | 0.511129 | ||||||||
\(163\) | −1.20414 | −0.0943159 | −0.0471579 | − | 0.998887i | \(-0.515016\pi\) | ||||
−0.0471579 | + | 0.998887i | \(0.515016\pi\) | |||||||
\(164\) | 19.5416 | 1.52594 | ||||||||
\(165\) | 45.2243 | 3.52071 | ||||||||
\(166\) | −1.61049 | −0.124998 | ||||||||
\(167\) | −0.900391 | −0.0696744 | −0.0348372 | − | 0.999393i | \(-0.511091\pi\) | ||||
−0.0348372 | + | 0.999393i | \(0.511091\pi\) | |||||||
\(168\) | −19.5587 | −1.50899 | ||||||||
\(169\) | −10.1423 | −0.780175 | ||||||||
\(170\) | 13.5702 | 1.04079 | ||||||||
\(171\) | 10.3962 | 0.795015 | ||||||||
\(172\) | 8.56459 | 0.653044 | ||||||||
\(173\) | 12.3564 | 0.939436 | 0.469718 | − | 0.882817i | \(-0.344356\pi\) | ||||
0.469718 | + | 0.882817i | \(0.344356\pi\) | |||||||
\(174\) | 3.40979 | 0.258495 | ||||||||
\(175\) | −37.4915 | −2.83409 | ||||||||
\(176\) | −8.79626 | −0.663043 | ||||||||
\(177\) | 13.5275 | 1.01679 | ||||||||
\(178\) | 2.74537 | 0.205774 | ||||||||
\(179\) | −10.0258 | −0.749367 | −0.374683 | − | 0.927153i | \(-0.622249\pi\) | ||||
−0.374683 | + | 0.927153i | \(0.622249\pi\) | |||||||
\(180\) | 15.3987 | 1.14775 | ||||||||
\(181\) | −17.0491 | −1.26725 | −0.633623 | − | 0.773642i | \(-0.718433\pi\) | ||||
−0.633623 | + | 0.773642i | \(0.718433\pi\) | |||||||
\(182\) | −3.92569 | −0.290992 | ||||||||
\(183\) | −0.179197 | −0.0132467 | ||||||||
\(184\) | −6.30402 | −0.464739 | ||||||||
\(185\) | −6.97790 | −0.513026 | ||||||||
\(186\) | 0.294182 | 0.0215705 | ||||||||
\(187\) | −27.4159 | −2.00485 | ||||||||
\(188\) | 17.1997 | 1.25442 | ||||||||
\(189\) | 4.59286 | 0.334081 | ||||||||
\(190\) | 10.3568 | 0.751365 | ||||||||
\(191\) | −23.7744 | −1.72026 | −0.860129 | − | 0.510077i | \(-0.829617\pi\) | ||||
−0.860129 | + | 0.510077i | \(0.829617\pi\) | |||||||
\(192\) | 0.0613816 | 0.00442984 | ||||||||
\(193\) | 7.49373 | 0.539411 | 0.269705 | − | 0.962943i | \(-0.413074\pi\) | ||||
0.269705 | + | 0.962943i | \(0.413074\pi\) | |||||||
\(194\) | −5.69278 | −0.408718 | ||||||||
\(195\) | 15.4001 | 1.10282 | ||||||||
\(196\) | −10.5101 | −0.750723 | ||||||||
\(197\) | 1.85647 | 0.132268 | 0.0661339 | − | 0.997811i | \(-0.478934\pi\) | ||||
0.0661339 | + | 0.997811i | \(0.478934\pi\) | |||||||
\(198\) | 7.72201 | 0.548779 | ||||||||
\(199\) | 3.46667 | 0.245746 | 0.122873 | − | 0.992422i | \(-0.460789\pi\) | ||||
0.122873 | + | 0.992422i | \(0.460789\pi\) | |||||||
\(200\) | 23.1299 | 1.63553 | ||||||||
\(201\) | 29.4984 | 2.08066 | ||||||||
\(202\) | −4.37871 | −0.308085 | ||||||||
\(203\) | 8.51545 | 0.597667 | ||||||||
\(204\) | −20.6890 | −1.44852 | ||||||||
\(205\) | 47.5200 | 3.31894 | ||||||||
\(206\) | 0.0662234 | 0.00461400 | ||||||||
\(207\) | −6.84451 | −0.475726 | ||||||||
\(208\) | −2.99537 | −0.207691 | ||||||||
\(209\) | −20.9240 | −1.44734 | ||||||||
\(210\) | −21.1553 | −1.45985 | ||||||||
\(211\) | −2.33201 | −0.160542 | −0.0802711 | − | 0.996773i | \(-0.525579\pi\) | ||||
−0.0802711 | + | 0.996773i | \(0.525579\pi\) | |||||||
\(212\) | −2.11869 | −0.145512 | ||||||||
\(213\) | −12.1671 | −0.833674 | ||||||||
\(214\) | 11.4678 | 0.783919 | ||||||||
\(215\) | 20.8268 | 1.42038 | ||||||||
\(216\) | −2.83351 | −0.192796 | ||||||||
\(217\) | 0.734678 | 0.0498732 | ||||||||
\(218\) | −9.24373 | −0.626065 | ||||||||
\(219\) | −32.9042 | −2.22346 | ||||||||
\(220\) | −30.9925 | −2.08951 | ||||||||
\(221\) | −9.33587 | −0.627998 | ||||||||
\(222\) | −2.64063 | −0.177228 | ||||||||
\(223\) | −1.75535 | −0.117547 | −0.0587734 | − | 0.998271i | \(-0.518719\pi\) | ||||
−0.0587734 | + | 0.998271i | \(0.518719\pi\) | |||||||
\(224\) | 20.8455 | 1.39280 | ||||||||
\(225\) | 25.1130 | 1.67420 | ||||||||
\(226\) | −0.686369 | −0.0456566 | ||||||||
\(227\) | 4.35631 | 0.289139 | 0.144569 | − | 0.989495i | \(-0.453820\pi\) | ||||
0.144569 | + | 0.989495i | \(0.453820\pi\) | |||||||
\(228\) | −15.7900 | −1.04572 | ||||||||
\(229\) | 6.24160 | 0.412457 | 0.206228 | − | 0.978504i | \(-0.433881\pi\) | ||||
0.206228 | + | 0.978504i | \(0.433881\pi\) | |||||||
\(230\) | −6.81862 | −0.449607 | ||||||||
\(231\) | 42.7401 | 2.81209 | ||||||||
\(232\) | −5.25351 | −0.344910 | ||||||||
\(233\) | 13.8315 | 0.906135 | 0.453067 | − | 0.891476i | \(-0.350330\pi\) | ||||
0.453067 | + | 0.891476i | \(0.350330\pi\) | |||||||
\(234\) | 2.62956 | 0.171899 | ||||||||
\(235\) | 41.8252 | 2.72838 | ||||||||
\(236\) | −9.27048 | −0.603457 | ||||||||
\(237\) | 18.3034 | 1.18893 | ||||||||
\(238\) | 12.8248 | 0.831306 | ||||||||
\(239\) | −19.3924 | −1.25439 | −0.627194 | − | 0.778863i | \(-0.715797\pi\) | ||||
−0.627194 | + | 0.778863i | \(0.715797\pi\) | |||||||
\(240\) | −16.1418 | −1.04195 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | −8.60473 | −0.553133 | ||||||||
\(243\) | −20.3772 | −1.30720 | ||||||||
\(244\) | 0.122805 | 0.00786178 | ||||||||
\(245\) | −25.5578 | −1.63283 | ||||||||
\(246\) | 17.9829 | 1.14655 | ||||||||
\(247\) | −7.12519 | −0.453365 | ||||||||
\(248\) | −0.453251 | −0.0287815 | ||||||||
\(249\) | 5.97075 | 0.378381 | ||||||||
\(250\) | 12.7320 | 0.805242 | ||||||||
\(251\) | −14.4441 | −0.911705 | −0.455852 | − | 0.890055i | \(-0.650666\pi\) | ||||
−0.455852 | + | 0.890055i | \(0.650666\pi\) | |||||||
\(252\) | 14.5529 | 0.916745 | ||||||||
\(253\) | 13.7757 | 0.866071 | ||||||||
\(254\) | −0.229894 | −0.0144248 | ||||||||
\(255\) | −50.3103 | −3.15056 | ||||||||
\(256\) | −7.18218 | −0.448886 | ||||||||
\(257\) | 28.9004 | 1.80276 | 0.901379 | − | 0.433031i | \(-0.142556\pi\) | ||||
0.901379 | + | 0.433031i | \(0.142556\pi\) | |||||||
\(258\) | 7.88146 | 0.490678 | ||||||||
\(259\) | −6.59460 | −0.409769 | ||||||||
\(260\) | −10.5538 | −0.654518 | ||||||||
\(261\) | −5.70393 | −0.353064 | ||||||||
\(262\) | −3.46139 | −0.213845 | ||||||||
\(263\) | 26.3078 | 1.62221 | 0.811103 | − | 0.584903i | \(-0.198867\pi\) | ||||
0.811103 | + | 0.584903i | \(0.198867\pi\) | |||||||
\(264\) | −26.3680 | −1.62284 | ||||||||
\(265\) | −5.15211 | −0.316491 | ||||||||
\(266\) | 9.78794 | 0.600137 | ||||||||
\(267\) | −10.1782 | −0.622897 | ||||||||
\(268\) | −20.2154 | −1.23485 | ||||||||
\(269\) | −9.42450 | −0.574622 | −0.287311 | − | 0.957837i | \(-0.592761\pi\) | ||||
−0.287311 | + | 0.957837i | \(0.592761\pi\) | |||||||
\(270\) | −3.06481 | −0.186518 | ||||||||
\(271\) | −5.86519 | −0.356285 | −0.178142 | − | 0.984005i | \(-0.557009\pi\) | ||||
−0.178142 | + | 0.984005i | \(0.557009\pi\) | |||||||
\(272\) | 9.78551 | 0.593334 | ||||||||
\(273\) | 14.5542 | 0.880859 | ||||||||
\(274\) | 10.8177 | 0.653519 | ||||||||
\(275\) | −50.5440 | −3.04792 | ||||||||
\(276\) | 10.3956 | 0.625744 | ||||||||
\(277\) | 5.60395 | 0.336708 | 0.168354 | − | 0.985727i | \(-0.446155\pi\) | ||||
0.168354 | + | 0.985727i | \(0.446155\pi\) | |||||||
\(278\) | 12.3653 | 0.741621 | ||||||||
\(279\) | −0.492111 | −0.0294619 | ||||||||
\(280\) | 32.5943 | 1.94788 | ||||||||
\(281\) | −4.71669 | −0.281374 | −0.140687 | − | 0.990054i | \(-0.544931\pi\) | ||||
−0.140687 | + | 0.990054i | \(0.544931\pi\) | |||||||
\(282\) | 15.8278 | 0.942534 | ||||||||
\(283\) | 19.2068 | 1.14173 | 0.570864 | − | 0.821044i | \(-0.306608\pi\) | ||||
0.570864 | + | 0.821044i | \(0.306608\pi\) | |||||||
\(284\) | 8.33817 | 0.494779 | ||||||||
\(285\) | −38.3972 | −2.27445 | ||||||||
\(286\) | −5.29241 | −0.312947 | ||||||||
\(287\) | 44.9097 | 2.65094 | ||||||||
\(288\) | −13.9630 | −0.822776 | ||||||||
\(289\) | 13.4992 | 0.794069 | ||||||||
\(290\) | −5.68235 | −0.333679 | ||||||||
\(291\) | 21.1055 | 1.23723 | ||||||||
\(292\) | 22.5495 | 1.31961 | ||||||||
\(293\) | 13.0140 | 0.760289 | 0.380144 | − | 0.924927i | \(-0.375874\pi\) | ||||
0.380144 | + | 0.924927i | \(0.375874\pi\) | |||||||
\(294\) | −9.67181 | −0.564071 | ||||||||
\(295\) | −22.5434 | −1.31253 | ||||||||
\(296\) | 4.06847 | 0.236475 | ||||||||
\(297\) | 6.19185 | 0.359288 | ||||||||
\(298\) | −12.0143 | −0.695968 | ||||||||
\(299\) | 4.69100 | 0.271288 | ||||||||
\(300\) | −38.1424 | −2.20215 | ||||||||
\(301\) | 19.6828 | 1.13450 | ||||||||
\(302\) | 3.00692 | 0.173029 | ||||||||
\(303\) | 16.2337 | 0.932602 | ||||||||
\(304\) | 7.46836 | 0.428340 | ||||||||
\(305\) | 0.298630 | 0.0170995 | ||||||||
\(306\) | −8.59045 | −0.491083 | ||||||||
\(307\) | −11.5372 | −0.658463 | −0.329232 | − | 0.944249i | \(-0.606790\pi\) | ||||
−0.329232 | + | 0.944249i | \(0.606790\pi\) | |||||||
\(308\) | −29.2900 | −1.66896 | ||||||||
\(309\) | −0.245518 | −0.0139670 | ||||||||
\(310\) | −0.490250 | −0.0278443 | ||||||||
\(311\) | −23.1542 | −1.31296 | −0.656478 | − | 0.754345i | \(-0.727955\pi\) | ||||
−0.656478 | + | 0.754345i | \(0.727955\pi\) | |||||||
\(312\) | −8.97903 | −0.508338 | ||||||||
\(313\) | −7.88902 | −0.445914 | −0.222957 | − | 0.974828i | \(-0.571571\pi\) | ||||
−0.222957 | + | 0.974828i | \(0.571571\pi\) | |||||||
\(314\) | −3.86411 | −0.218064 | ||||||||
\(315\) | 35.3888 | 1.99393 | ||||||||
\(316\) | −12.5434 | −0.705623 | ||||||||
\(317\) | −2.38325 | −0.133857 | −0.0669283 | − | 0.997758i | \(-0.521320\pi\) | ||||
−0.0669283 | + | 0.997758i | \(0.521320\pi\) | |||||||
\(318\) | −1.94970 | −0.109334 | ||||||||
\(319\) | 11.4801 | 0.642761 | ||||||||
\(320\) | −0.102292 | −0.00571827 | ||||||||
\(321\) | −42.5157 | −2.37300 | ||||||||
\(322\) | −6.44407 | −0.359114 | ||||||||
\(323\) | 23.2772 | 1.29518 | ||||||||
\(324\) | 16.5289 | 0.918272 | ||||||||
\(325\) | −17.2116 | −0.954729 | ||||||||
\(326\) | 0.759387 | 0.0420585 | ||||||||
\(327\) | 34.2704 | 1.89516 | ||||||||
\(328\) | −27.7065 | −1.52984 | ||||||||
\(329\) | 39.5278 | 2.17924 | ||||||||
\(330\) | −28.5205 | −1.57000 | ||||||||
\(331\) | −3.05598 | −0.167972 | −0.0839860 | − | 0.996467i | \(-0.526765\pi\) | ||||
−0.0839860 | + | 0.996467i | \(0.526765\pi\) | |||||||
\(332\) | −4.09179 | −0.224566 | ||||||||
\(333\) | 4.41728 | 0.242066 | ||||||||
\(334\) | 0.567827 | 0.0310701 | ||||||||
\(335\) | −49.1586 | −2.68582 | ||||||||
\(336\) | −15.2551 | −0.832237 | ||||||||
\(337\) | −16.1755 | −0.881134 | −0.440567 | − | 0.897720i | \(-0.645223\pi\) | ||||
−0.440567 | + | 0.897720i | \(0.645223\pi\) | |||||||
\(338\) | 6.39617 | 0.347906 | ||||||||
\(339\) | 2.54466 | 0.138207 | ||||||||
\(340\) | 34.4780 | 1.86983 | ||||||||
\(341\) | 0.990454 | 0.0536361 | ||||||||
\(342\) | −6.55628 | −0.354523 | ||||||||
\(343\) | 1.62227 | 0.0875943 | ||||||||
\(344\) | −12.1431 | −0.654711 | ||||||||
\(345\) | 25.2795 | 1.36100 | ||||||||
\(346\) | −7.79246 | −0.418925 | ||||||||
\(347\) | 24.4716 | 1.31370 | 0.656851 | − | 0.754020i | \(-0.271888\pi\) | ||||
0.656851 | + | 0.754020i | \(0.271888\pi\) | |||||||
\(348\) | 8.66329 | 0.464401 | ||||||||
\(349\) | −13.0468 | −0.698380 | −0.349190 | − | 0.937052i | \(-0.613543\pi\) | ||||
−0.349190 | + | 0.937052i | \(0.613543\pi\) | |||||||
\(350\) | 23.6438 | 1.26381 | ||||||||
\(351\) | 2.10849 | 0.112543 | ||||||||
\(352\) | 28.1028 | 1.49788 | ||||||||
\(353\) | 23.6788 | 1.26029 | 0.630147 | − | 0.776476i | \(-0.282995\pi\) | ||||
0.630147 | + | 0.776476i | \(0.282995\pi\) | |||||||
\(354\) | −8.53104 | −0.453420 | ||||||||
\(355\) | 20.2762 | 1.07615 | ||||||||
\(356\) | 6.97519 | 0.369685 | ||||||||
\(357\) | −47.5468 | −2.51644 | ||||||||
\(358\) | 6.32274 | 0.334167 | ||||||||
\(359\) | −25.5499 | −1.34847 | −0.674236 | − | 0.738516i | \(-0.735527\pi\) | ||||
−0.674236 | + | 0.738516i | \(0.735527\pi\) | |||||||
\(360\) | −21.8327 | −1.15068 | ||||||||
\(361\) | −1.23473 | −0.0649857 | ||||||||
\(362\) | 10.7519 | 0.565107 | ||||||||
\(363\) | 31.9013 | 1.67439 | ||||||||
\(364\) | −9.97406 | −0.522783 | ||||||||
\(365\) | 54.8344 | 2.87016 | ||||||||
\(366\) | 0.113010 | 0.00590712 | ||||||||
\(367\) | 8.35766 | 0.436266 | 0.218133 | − | 0.975919i | \(-0.430003\pi\) | ||||
0.218133 | + | 0.975919i | \(0.430003\pi\) | |||||||
\(368\) | −4.91693 | −0.256313 | ||||||||
\(369\) | −30.0820 | −1.56601 | ||||||||
\(370\) | 4.40058 | 0.228775 | ||||||||
\(371\) | −4.86910 | −0.252791 | ||||||||
\(372\) | 0.747433 | 0.0387526 | ||||||||
\(373\) | −24.6934 | −1.27858 | −0.639288 | − | 0.768968i | \(-0.720771\pi\) | ||||
−0.639288 | + | 0.768968i | \(0.720771\pi\) | |||||||
\(374\) | 17.2897 | 0.894028 | ||||||||
\(375\) | −47.2028 | −2.43754 | ||||||||
\(376\) | −24.3862 | −1.25762 | ||||||||
\(377\) | 3.90928 | 0.201338 | ||||||||
\(378\) | −2.89646 | −0.148978 | ||||||||
\(379\) | 18.6593 | 0.958465 | 0.479232 | − | 0.877688i | \(-0.340915\pi\) | ||||
0.479232 | + | 0.877688i | \(0.340915\pi\) | |||||||
\(380\) | 26.3138 | 1.34987 | ||||||||
\(381\) | 0.852312 | 0.0436652 | ||||||||
\(382\) | 14.9932 | 0.767119 | ||||||||
\(383\) | 11.9780 | 0.612049 | 0.306025 | − | 0.952024i | \(-0.401001\pi\) | ||||
0.306025 | + | 0.952024i | \(0.401001\pi\) | |||||||
\(384\) | 26.4327 | 1.34889 | ||||||||
\(385\) | −71.2257 | −3.63000 | ||||||||
\(386\) | −4.72588 | −0.240541 | ||||||||
\(387\) | −13.1842 | −0.670190 | ||||||||
\(388\) | −14.4637 | −0.734285 | ||||||||
\(389\) | −7.62670 | −0.386689 | −0.193344 | − | 0.981131i | \(-0.561933\pi\) | ||||
−0.193344 | + | 0.981131i | \(0.561933\pi\) | |||||||
\(390\) | −9.71199 | −0.491786 | ||||||||
\(391\) | −15.3249 | −0.775016 | ||||||||
\(392\) | 14.9015 | 0.752639 | ||||||||
\(393\) | 12.8328 | 0.647330 | ||||||||
\(394\) | −1.17077 | −0.0589826 | ||||||||
\(395\) | −30.5023 | −1.53474 | ||||||||
\(396\) | 19.6194 | 0.985914 | ||||||||
\(397\) | −33.4013 | −1.67636 | −0.838181 | − | 0.545392i | \(-0.816381\pi\) | ||||
−0.838181 | + | 0.545392i | \(0.816381\pi\) | |||||||
\(398\) | −2.18624 | −0.109586 | ||||||||
\(399\) | −36.2880 | −1.81667 | ||||||||
\(400\) | 18.0406 | 0.902030 | ||||||||
\(401\) | −1.73530 | −0.0866566 | −0.0433283 | − | 0.999061i | \(-0.513796\pi\) | ||||
−0.0433283 | + | 0.999061i | \(0.513796\pi\) | |||||||
\(402\) | −18.6030 | −0.927833 | ||||||||
\(403\) | 0.337277 | 0.0168010 | ||||||||
\(404\) | −11.1251 | −0.553492 | ||||||||
\(405\) | 40.1939 | 1.99725 | ||||||||
\(406\) | −5.37022 | −0.266519 | ||||||||
\(407\) | −8.89050 | −0.440686 | ||||||||
\(408\) | 29.3334 | 1.45222 | ||||||||
\(409\) | −3.81908 | −0.188841 | −0.0944207 | − | 0.995532i | \(-0.530100\pi\) | ||||
−0.0944207 | + | 0.995532i | \(0.530100\pi\) | |||||||
\(410\) | −29.9682 | −1.48002 | ||||||||
\(411\) | −40.1056 | −1.97826 | ||||||||
\(412\) | 0.168255 | 0.00828932 | ||||||||
\(413\) | −21.3050 | −1.04835 | ||||||||
\(414\) | 4.31645 | 0.212142 | ||||||||
\(415\) | −9.95015 | −0.488434 | ||||||||
\(416\) | 9.56976 | 0.469196 | ||||||||
\(417\) | −45.8433 | −2.24496 | ||||||||
\(418\) | 13.1956 | 0.645418 | ||||||||
\(419\) | 0.640088 | 0.0312703 | 0.0156352 | − | 0.999878i | \(-0.495023\pi\) | ||||
0.0156352 | + | 0.999878i | \(0.495023\pi\) | |||||||
\(420\) | −53.7495 | −2.62271 | ||||||||
\(421\) | 13.2765 | 0.647057 | 0.323528 | − | 0.946218i | \(-0.395131\pi\) | ||||
0.323528 | + | 0.946218i | \(0.395131\pi\) | |||||||
\(422\) | 1.47067 | 0.0715910 | ||||||||
\(423\) | −26.4770 | −1.28735 | ||||||||
\(424\) | 3.00394 | 0.145884 | ||||||||
\(425\) | 56.2283 | 2.72748 | ||||||||
\(426\) | 7.67310 | 0.371763 | ||||||||
\(427\) | 0.282226 | 0.0136579 | ||||||||
\(428\) | 29.1363 | 1.40836 | ||||||||
\(429\) | 19.6212 | 0.947320 | ||||||||
\(430\) | −13.1343 | −0.633393 | ||||||||
\(431\) | −26.8180 | −1.29178 | −0.645888 | − | 0.763432i | \(-0.723513\pi\) | ||||
−0.645888 | + | 0.763432i | \(0.723513\pi\) | |||||||
\(432\) | −2.21005 | −0.106331 | ||||||||
\(433\) | −20.7392 | −0.996664 | −0.498332 | − | 0.866986i | \(-0.666054\pi\) | ||||
−0.498332 | + | 0.866986i | \(0.666054\pi\) | |||||||
\(434\) | −0.463320 | −0.0222401 | ||||||||
\(435\) | 21.0669 | 1.01008 | ||||||||
\(436\) | −23.4857 | −1.12476 | ||||||||
\(437\) | −11.6961 | −0.559500 | ||||||||
\(438\) | 20.7509 | 0.991515 | ||||||||
\(439\) | −12.7382 | −0.607960 | −0.303980 | − | 0.952678i | \(-0.598316\pi\) | ||||
−0.303980 | + | 0.952678i | \(0.598316\pi\) | |||||||
\(440\) | 43.9419 | 2.09485 | ||||||||
\(441\) | 16.1791 | 0.770433 | ||||||||
\(442\) | 5.88761 | 0.280045 | ||||||||
\(443\) | 23.4058 | 1.11204 | 0.556022 | − | 0.831167i | \(-0.312327\pi\) | ||||
0.556022 | + | 0.831167i | \(0.312327\pi\) | |||||||
\(444\) | −6.70910 | −0.318400 | ||||||||
\(445\) | 16.9618 | 0.804068 | ||||||||
\(446\) | 1.10700 | 0.0524180 | ||||||||
\(447\) | 44.5419 | 2.10676 | ||||||||
\(448\) | −0.0966726 | −0.00456735 | ||||||||
\(449\) | 35.8887 | 1.69369 | 0.846846 | − | 0.531838i | \(-0.178498\pi\) | ||||
0.846846 | + | 0.531838i | \(0.178498\pi\) | |||||||
\(450\) | −15.8374 | −0.746581 | ||||||||
\(451\) | 60.5449 | 2.85095 | ||||||||
\(452\) | −1.74387 | −0.0820247 | ||||||||
\(453\) | −11.1479 | −0.523775 | ||||||||
\(454\) | −2.74728 | −0.128936 | ||||||||
\(455\) | −24.2543 | −1.13706 | ||||||||
\(456\) | 22.3875 | 1.04839 | ||||||||
\(457\) | −23.4014 | −1.09467 | −0.547336 | − | 0.836913i | \(-0.684358\pi\) | ||||
−0.547336 | + | 0.836913i | \(0.684358\pi\) | |||||||
\(458\) | −3.93623 | −0.183928 | ||||||||
\(459\) | −6.88820 | −0.321514 | ||||||||
\(460\) | −17.3242 | −0.807744 | ||||||||
\(461\) | 17.9146 | 0.834366 | 0.417183 | − | 0.908822i | \(-0.363017\pi\) | ||||
0.417183 | + | 0.908822i | \(0.363017\pi\) | |||||||
\(462\) | −26.9538 | −1.25400 | ||||||||
\(463\) | −32.0159 | −1.48790 | −0.743952 | − | 0.668233i | \(-0.767051\pi\) | ||||
−0.743952 | + | 0.668233i | \(0.767051\pi\) | |||||||
\(464\) | −4.09757 | −0.190225 | ||||||||
\(465\) | 1.81756 | 0.0842874 | ||||||||
\(466\) | −8.72279 | −0.404075 | ||||||||
\(467\) | −12.2949 | −0.568940 | −0.284470 | − | 0.958685i | \(-0.591818\pi\) | ||||
−0.284470 | + | 0.958685i | \(0.591818\pi\) | |||||||
\(468\) | 6.68095 | 0.308827 | ||||||||
\(469\) | −46.4583 | −2.14524 | ||||||||
\(470\) | −26.3768 | −1.21667 | ||||||||
\(471\) | 14.3259 | 0.660101 | ||||||||
\(472\) | 13.1439 | 0.604997 | ||||||||
\(473\) | 26.5353 | 1.22010 | ||||||||
\(474\) | −11.5429 | −0.530184 | ||||||||
\(475\) | 42.9138 | 1.96902 | ||||||||
\(476\) | 32.5841 | 1.49349 | ||||||||
\(477\) | 3.26148 | 0.149333 | ||||||||
\(478\) | 12.2297 | 0.559373 | ||||||||
\(479\) | 15.1555 | 0.692472 | 0.346236 | − | 0.938148i | \(-0.387460\pi\) | ||||
0.346236 | + | 0.938148i | \(0.387460\pi\) | |||||||
\(480\) | 51.5708 | 2.35387 | ||||||||
\(481\) | −3.02746 | −0.138040 | ||||||||
\(482\) | 0.630644 | 0.0287251 | ||||||||
\(483\) | 23.8909 | 1.08707 | ||||||||
\(484\) | −21.8622 | −0.993735 | ||||||||
\(485\) | −35.1720 | −1.59708 | ||||||||
\(486\) | 12.8508 | 0.582922 | ||||||||
\(487\) | −15.5008 | −0.702407 | −0.351204 | − | 0.936299i | \(-0.614227\pi\) | ||||
−0.351204 | + | 0.936299i | \(0.614227\pi\) | |||||||
\(488\) | −0.174116 | −0.00788186 | ||||||||
\(489\) | −2.81536 | −0.127315 | ||||||||
\(490\) | 16.1179 | 0.728133 | ||||||||
\(491\) | 12.5838 | 0.567901 | 0.283950 | − | 0.958839i | \(-0.408355\pi\) | ||||
0.283950 | + | 0.958839i | \(0.408355\pi\) | |||||||
\(492\) | 45.6894 | 2.05984 | ||||||||
\(493\) | −12.7712 | −0.575184 | ||||||||
\(494\) | 4.49346 | 0.202170 | ||||||||
\(495\) | 47.7093 | 2.14437 | ||||||||
\(496\) | −0.353521 | −0.0158736 | ||||||||
\(497\) | 19.1625 | 0.859553 | ||||||||
\(498\) | −3.76542 | −0.168732 | ||||||||
\(499\) | −41.9638 | −1.87856 | −0.939280 | − | 0.343152i | \(-0.888505\pi\) | ||||
−0.939280 | + | 0.343152i | \(0.888505\pi\) | |||||||
\(500\) | 32.3484 | 1.44666 | ||||||||
\(501\) | −2.10517 | −0.0940521 | ||||||||
\(502\) | 9.10910 | 0.406559 | ||||||||
\(503\) | 7.23458 | 0.322574 | 0.161287 | − | 0.986908i | \(-0.448436\pi\) | ||||
0.161287 | + | 0.986908i | \(0.448436\pi\) | |||||||
\(504\) | −20.6334 | −0.919085 | ||||||||
\(505\) | −27.0532 | −1.20385 | ||||||||
\(506\) | −8.68756 | −0.386209 | ||||||||
\(507\) | −23.7133 | −1.05314 | ||||||||
\(508\) | −0.584094 | −0.0259150 | ||||||||
\(509\) | 43.2945 | 1.91899 | 0.959497 | − | 0.281718i | \(-0.0909041\pi\) | ||||
0.959497 | + | 0.281718i | \(0.0909041\pi\) | |||||||
\(510\) | 31.7279 | 1.40494 | ||||||||
\(511\) | 51.8223 | 2.29248 | ||||||||
\(512\) | −18.0813 | −0.799090 | ||||||||
\(513\) | −5.25712 | −0.232108 | ||||||||
\(514\) | −18.2259 | −0.803909 | ||||||||
\(515\) | 0.409152 | 0.0180294 | ||||||||
\(516\) | 20.0245 | 0.881531 | ||||||||
\(517\) | 53.2893 | 2.34366 | ||||||||
\(518\) | 4.15885 | 0.182729 | ||||||||
\(519\) | 28.8899 | 1.26813 | ||||||||
\(520\) | 14.9634 | 0.656189 | ||||||||
\(521\) | −22.7560 | −0.996961 | −0.498480 | − | 0.866901i | \(-0.666108\pi\) | ||||
−0.498480 | + | 0.866901i | \(0.666108\pi\) | |||||||
\(522\) | 3.59715 | 0.157443 | ||||||||
\(523\) | 36.7529 | 1.60709 | 0.803547 | − | 0.595241i | \(-0.202944\pi\) | ||||
0.803547 | + | 0.595241i | \(0.202944\pi\) | |||||||
\(524\) | −8.79440 | −0.384185 | ||||||||
\(525\) | −87.6573 | −3.82568 | ||||||||
\(526\) | −16.5908 | −0.723395 | ||||||||
\(527\) | −1.10184 | −0.0479970 | ||||||||
\(528\) | −20.5662 | −0.895029 | ||||||||
\(529\) | −15.2997 | −0.665203 | ||||||||
\(530\) | 3.24915 | 0.141134 | ||||||||
\(531\) | 14.2708 | 0.619301 | ||||||||
\(532\) | 24.8684 | 1.07818 | ||||||||
\(533\) | 20.6172 | 0.893030 | ||||||||
\(534\) | 6.41884 | 0.277770 | ||||||||
\(535\) | 70.8518 | 3.06319 | ||||||||
\(536\) | 28.6619 | 1.23801 | ||||||||
\(537\) | −23.4410 | −1.01156 | ||||||||
\(538\) | 5.94351 | 0.256243 | ||||||||
\(539\) | −32.5631 | −1.40259 | ||||||||
\(540\) | −7.78681 | −0.335091 | ||||||||
\(541\) | −19.7726 | −0.850089 | −0.425045 | − | 0.905172i | \(-0.639742\pi\) | ||||
−0.425045 | + | 0.905172i | \(0.639742\pi\) | |||||||
\(542\) | 3.69885 | 0.158879 | ||||||||
\(543\) | −39.8617 | −1.71063 | ||||||||
\(544\) | −31.2633 | −1.34040 | ||||||||
\(545\) | −57.1110 | −2.44637 | ||||||||
\(546\) | −9.17851 | −0.392804 | ||||||||
\(547\) | −9.94319 | −0.425140 | −0.212570 | − | 0.977146i | \(-0.568183\pi\) | ||||
−0.212570 | + | 0.977146i | \(0.568183\pi\) | |||||||
\(548\) | 27.4846 | 1.17408 | ||||||||
\(549\) | −0.189044 | −0.00806820 | ||||||||
\(550\) | 31.8753 | 1.35917 | ||||||||
\(551\) | −9.74703 | −0.415238 | ||||||||
\(552\) | −14.7392 | −0.627342 | ||||||||
\(553\) | −28.8268 | −1.22584 | ||||||||
\(554\) | −3.53410 | −0.150149 | ||||||||
\(555\) | −16.3148 | −0.692524 | ||||||||
\(556\) | 31.4167 | 1.33236 | ||||||||
\(557\) | −7.84163 | −0.332260 | −0.166130 | − | 0.986104i | \(-0.553127\pi\) | ||||
−0.166130 | + | 0.986104i | \(0.553127\pi\) | |||||||
\(558\) | 0.310347 | 0.0131380 | ||||||||
\(559\) | 9.03601 | 0.382182 | ||||||||
\(560\) | 25.4225 | 1.07430 | ||||||||
\(561\) | −64.1001 | −2.70631 | ||||||||
\(562\) | 2.97455 | 0.125474 | ||||||||
\(563\) | −19.2105 | −0.809625 | −0.404813 | − | 0.914400i | \(-0.632663\pi\) | ||||
−0.404813 | + | 0.914400i | \(0.632663\pi\) | |||||||
\(564\) | 40.2140 | 1.69332 | ||||||||
\(565\) | −4.24063 | −0.178405 | ||||||||
\(566\) | −12.1127 | −0.509134 | ||||||||
\(567\) | 37.9861 | 1.59526 | ||||||||
\(568\) | −11.8221 | −0.496043 | ||||||||
\(569\) | 25.1338 | 1.05366 | 0.526831 | − | 0.849970i | \(-0.323380\pi\) | ||||
0.526831 | + | 0.849970i | \(0.323380\pi\) | |||||||
\(570\) | 24.2150 | 1.01425 | ||||||||
\(571\) | −18.1912 | −0.761277 | −0.380638 | − | 0.924724i | \(-0.624296\pi\) | ||||
−0.380638 | + | 0.924724i | \(0.624296\pi\) | |||||||
\(572\) | −13.4465 | −0.562227 | ||||||||
\(573\) | −55.5861 | −2.32214 | ||||||||
\(574\) | −28.3220 | −1.18214 | ||||||||
\(575\) | −28.2531 | −1.17824 | ||||||||
\(576\) | 0.0647545 | 0.00269810 | ||||||||
\(577\) | 28.9417 | 1.20486 | 0.602429 | − | 0.798172i | \(-0.294200\pi\) | ||||
0.602429 | + | 0.798172i | \(0.294200\pi\) | |||||||
\(578\) | −8.51317 | −0.354101 | ||||||||
\(579\) | 17.5208 | 0.728140 | ||||||||
\(580\) | −14.4372 | −0.599474 | ||||||||
\(581\) | −9.40358 | −0.390126 | ||||||||
\(582\) | −13.3101 | −0.551721 | ||||||||
\(583\) | −6.56427 | −0.271864 | ||||||||
\(584\) | −31.9712 | −1.32298 | ||||||||
\(585\) | 16.2463 | 0.671703 | ||||||||
\(586\) | −8.20724 | −0.339038 | ||||||||
\(587\) | −21.9772 | −0.907098 | −0.453549 | − | 0.891231i | \(-0.649842\pi\) | ||||
−0.453549 | + | 0.891231i | \(0.649842\pi\) | |||||||
\(588\) | −24.5733 | −1.01339 | ||||||||
\(589\) | −0.840934 | −0.0346501 | ||||||||
\(590\) | 14.2168 | 0.585298 | ||||||||
\(591\) | 4.34054 | 0.178546 | ||||||||
\(592\) | 3.17327 | 0.130421 | ||||||||
\(593\) | 15.0138 | 0.616544 | 0.308272 | − | 0.951298i | \(-0.400249\pi\) | ||||
0.308272 | + | 0.951298i | \(0.400249\pi\) | |||||||
\(594\) | −3.90486 | −0.160218 | ||||||||
\(595\) | 79.2359 | 3.24836 | ||||||||
\(596\) | −30.5248 | −1.25035 | ||||||||
\(597\) | 8.10529 | 0.331728 | ||||||||
\(598\) | −2.95835 | −0.120976 | ||||||||
\(599\) | −31.7086 | −1.29558 | −0.647789 | − | 0.761820i | \(-0.724306\pi\) | ||||
−0.647789 | + | 0.761820i | \(0.724306\pi\) | |||||||
\(600\) | 54.0792 | 2.20777 | ||||||||
\(601\) | 5.63682 | 0.229931 | 0.114965 | − | 0.993369i | \(-0.463324\pi\) | ||||
0.114965 | + | 0.993369i | \(0.463324\pi\) | |||||||
\(602\) | −12.4129 | −0.505910 | ||||||||
\(603\) | 31.1193 | 1.26727 | ||||||||
\(604\) | 7.63973 | 0.310856 | ||||||||
\(605\) | −53.1631 | −2.16139 | ||||||||
\(606\) | −10.2377 | −0.415878 | ||||||||
\(607\) | 39.7534 | 1.61354 | 0.806770 | − | 0.590866i | \(-0.201214\pi\) | ||||
0.806770 | + | 0.590866i | \(0.201214\pi\) | |||||||
\(608\) | −23.8603 | −0.967664 | ||||||||
\(609\) | 19.9096 | 0.806780 | ||||||||
\(610\) | −0.188329 | −0.00762522 | ||||||||
\(611\) | 18.1465 | 0.734127 | ||||||||
\(612\) | −21.8259 | −0.882259 | ||||||||
\(613\) | 30.3066 | 1.22407 | 0.612035 | − | 0.790831i | \(-0.290351\pi\) | ||||
0.612035 | + | 0.790831i | \(0.290351\pi\) | |||||||
\(614\) | 7.27588 | 0.293631 | ||||||||
\(615\) | 111.105 | 4.48017 | ||||||||
\(616\) | 41.5281 | 1.67322 | ||||||||
\(617\) | 18.2240 | 0.733670 | 0.366835 | − | 0.930286i | \(-0.380441\pi\) | ||||
0.366835 | + | 0.930286i | \(0.380441\pi\) | |||||||
\(618\) | 0.154834 | 0.00622836 | ||||||||
\(619\) | −26.3431 | −1.05882 | −0.529409 | − | 0.848366i | \(-0.677586\pi\) | ||||
−0.529409 | + | 0.848366i | \(0.677586\pi\) | |||||||
\(620\) | −1.24559 | −0.0500239 | ||||||||
\(621\) | 3.46112 | 0.138890 | ||||||||
\(622\) | 14.6021 | 0.585491 | ||||||||
\(623\) | 16.0301 | 0.642233 | ||||||||
\(624\) | −7.00335 | −0.280359 | ||||||||
\(625\) | 27.7553 | 1.11021 | ||||||||
\(626\) | 4.97516 | 0.198848 | ||||||||
\(627\) | −48.9216 | −1.95374 | ||||||||
\(628\) | −9.81759 | −0.391765 | ||||||||
\(629\) | 9.89035 | 0.394354 | ||||||||
\(630\) | −22.3177 | −0.889160 | ||||||||
\(631\) | 18.4187 | 0.733236 | 0.366618 | − | 0.930372i | \(-0.380516\pi\) | ||||
0.366618 | + | 0.930372i | \(0.380516\pi\) | |||||||
\(632\) | 17.7844 | 0.707424 | ||||||||
\(633\) | −5.45238 | −0.216713 | ||||||||
\(634\) | 1.50298 | 0.0596910 | ||||||||
\(635\) | −1.42036 | −0.0563654 | ||||||||
\(636\) | −4.95364 | −0.196425 | ||||||||
\(637\) | −11.0886 | −0.439347 | ||||||||
\(638\) | −7.23985 | −0.286629 | ||||||||
\(639\) | −12.8356 | −0.507770 | ||||||||
\(640\) | −44.0496 | −1.74121 | ||||||||
\(641\) | −12.6956 | −0.501446 | −0.250723 | − | 0.968059i | \(-0.580668\pi\) | ||||
−0.250723 | + | 0.968059i | \(0.580668\pi\) | |||||||
\(642\) | 26.8123 | 1.05820 | ||||||||
\(643\) | −35.1591 | −1.38654 | −0.693270 | − | 0.720678i | \(-0.743831\pi\) | ||||
−0.693270 | + | 0.720678i | \(0.743831\pi\) | |||||||
\(644\) | −16.3725 | −0.645169 | ||||||||
\(645\) | 48.6944 | 1.91734 | ||||||||
\(646\) | −14.6796 | −0.577561 | ||||||||
\(647\) | 19.7535 | 0.776588 | 0.388294 | − | 0.921535i | \(-0.373064\pi\) | ||||
0.388294 | + | 0.921535i | \(0.373064\pi\) | |||||||
\(648\) | −23.4351 | −0.920616 | ||||||||
\(649\) | −28.7224 | −1.12745 | ||||||||
\(650\) | 10.8544 | 0.425745 | ||||||||
\(651\) | 1.71772 | 0.0673228 | ||||||||
\(652\) | 1.92939 | 0.0755606 | ||||||||
\(653\) | −44.0129 | −1.72236 | −0.861178 | − | 0.508303i | \(-0.830273\pi\) | ||||
−0.861178 | + | 0.508303i | \(0.830273\pi\) | |||||||
\(654\) | −21.6124 | −0.845113 | ||||||||
\(655\) | −21.3857 | −0.835608 | ||||||||
\(656\) | −21.6102 | −0.843736 | ||||||||
\(657\) | −34.7123 | −1.35426 | ||||||||
\(658\) | −24.9280 | −0.971793 | ||||||||
\(659\) | −32.2032 | −1.25446 | −0.627229 | − | 0.778835i | \(-0.715811\pi\) | ||||
−0.627229 | + | 0.778835i | \(0.715811\pi\) | |||||||
\(660\) | −72.4623 | −2.82059 | ||||||||
\(661\) | 29.5485 | 1.14930 | 0.574651 | − | 0.818398i | \(-0.305138\pi\) | ||||
0.574651 | + | 0.818398i | \(0.305138\pi\) | |||||||
\(662\) | 1.92724 | 0.0749043 | ||||||||
\(663\) | −21.8278 | −0.847723 | ||||||||
\(664\) | 5.80143 | 0.225139 | ||||||||
\(665\) | 60.4734 | 2.34506 | ||||||||
\(666\) | −2.78573 | −0.107945 | ||||||||
\(667\) | 6.41714 | 0.248473 | ||||||||
\(668\) | 1.44269 | 0.0558192 | ||||||||
\(669\) | −4.10412 | −0.158674 | ||||||||
\(670\) | 31.0016 | 1.19770 | ||||||||
\(671\) | 0.380482 | 0.0146883 | ||||||||
\(672\) | 48.7380 | 1.88011 | ||||||||
\(673\) | 28.4424 | 1.09637 | 0.548186 | − | 0.836356i | \(-0.315319\pi\) | ||||
0.548186 | + | 0.836356i | \(0.315319\pi\) | |||||||
\(674\) | 10.2010 | 0.392927 | ||||||||
\(675\) | −12.6991 | −0.488789 | ||||||||
\(676\) | 16.2508 | 0.625032 | ||||||||
\(677\) | 16.9259 | 0.650514 | 0.325257 | − | 0.945626i | \(-0.394549\pi\) | ||||
0.325257 | + | 0.945626i | \(0.394549\pi\) | |||||||
\(678\) | −1.60477 | −0.0616310 | ||||||||
\(679\) | −33.2400 | −1.27563 | ||||||||
\(680\) | −48.8837 | −1.87460 | ||||||||
\(681\) | 10.1853 | 0.390303 | ||||||||
\(682\) | −0.624625 | −0.0239181 | ||||||||
\(683\) | −29.0324 | −1.11090 | −0.555448 | − | 0.831551i | \(-0.687453\pi\) | ||||
−0.555448 | + | 0.831551i | \(0.687453\pi\) | |||||||
\(684\) | −16.6576 | −0.636921 | ||||||||
\(685\) | 66.8353 | 2.55365 | ||||||||
\(686\) | −1.02307 | −0.0390612 | ||||||||
\(687\) | 14.5933 | 0.556767 | ||||||||
\(688\) | −9.47121 | −0.361087 | ||||||||
\(689\) | −2.23531 | −0.0851586 | ||||||||
\(690\) | −15.9424 | −0.606915 | ||||||||
\(691\) | −21.5798 | −0.820935 | −0.410467 | − | 0.911875i | \(-0.634634\pi\) | ||||
−0.410467 | + | 0.911875i | \(0.634634\pi\) | |||||||
\(692\) | −19.7984 | −0.752623 | ||||||||
\(693\) | 45.0886 | 1.71277 | ||||||||
\(694\) | −15.4329 | −0.585823 | ||||||||
\(695\) | 76.3972 | 2.89791 | ||||||||
\(696\) | −12.2830 | −0.465587 | ||||||||
\(697\) | −67.3540 | −2.55121 | ||||||||
\(698\) | 8.22790 | 0.311431 | ||||||||
\(699\) | 32.3390 | 1.22317 | ||||||||
\(700\) | 60.0721 | 2.27051 | ||||||||
\(701\) | −13.2247 | −0.499489 | −0.249744 | − | 0.968312i | \(-0.580347\pi\) | ||||
−0.249744 | + | 0.968312i | \(0.580347\pi\) | |||||||
\(702\) | −1.32971 | −0.0501867 | ||||||||
\(703\) | 7.54838 | 0.284692 | ||||||||
\(704\) | −0.130329 | −0.00491196 | ||||||||
\(705\) | 97.7900 | 3.68298 | ||||||||
\(706\) | −14.9329 | −0.562006 | ||||||||
\(707\) | −25.5672 | −0.961552 | ||||||||
\(708\) | −21.6750 | −0.814595 | ||||||||
\(709\) | 18.8314 | 0.707228 | 0.353614 | − | 0.935391i | \(-0.384953\pi\) | ||||
0.353614 | + | 0.935391i | \(0.384953\pi\) | |||||||
\(710\) | −12.7871 | −0.479891 | ||||||||
\(711\) | 19.3091 | 0.724149 | ||||||||
\(712\) | −9.88960 | −0.370628 | ||||||||
\(713\) | 0.553644 | 0.0207341 | ||||||||
\(714\) | 29.9851 | 1.12216 | ||||||||
\(715\) | −32.6984 | −1.22285 | ||||||||
\(716\) | 16.0643 | 0.600351 | ||||||||
\(717\) | −45.3406 | −1.69328 | ||||||||
\(718\) | 16.1129 | 0.601328 | ||||||||
\(719\) | −37.7936 | −1.40946 | −0.704731 | − | 0.709475i | \(-0.748932\pi\) | ||||
−0.704731 | + | 0.709475i | \(0.748932\pi\) | |||||||
\(720\) | −17.0288 | −0.634626 | ||||||||
\(721\) | 0.386677 | 0.0144006 | ||||||||
\(722\) | 0.778675 | 0.0289793 | ||||||||
\(723\) | −2.33806 | −0.0869535 | ||||||||
\(724\) | 27.3175 | 1.01525 | ||||||||
\(725\) | −23.5450 | −0.874438 | ||||||||
\(726\) | −20.1184 | −0.746664 | ||||||||
\(727\) | −9.96692 | −0.369653 | −0.184826 | − | 0.982771i | \(-0.559172\pi\) | ||||
−0.184826 | + | 0.982771i | \(0.559172\pi\) | |||||||
\(728\) | 14.1415 | 0.524118 | ||||||||
\(729\) | −16.6957 | −0.618359 | ||||||||
\(730\) | −34.5810 | −1.27990 | ||||||||
\(731\) | −29.5196 | −1.09182 | ||||||||
\(732\) | 0.287126 | 0.0106125 | ||||||||
\(733\) | 46.8282 | 1.72964 | 0.864819 | − | 0.502083i | \(-0.167433\pi\) | ||||
0.864819 | + | 0.502083i | \(0.167433\pi\) | |||||||
\(734\) | −5.27071 | −0.194546 | ||||||||
\(735\) | −59.7558 | −2.20413 | ||||||||
\(736\) | 15.7089 | 0.579037 | ||||||||
\(737\) | −62.6326 | −2.30710 | ||||||||
\(738\) | 18.9710 | 0.698333 | ||||||||
\(739\) | 31.1213 | 1.14482 | 0.572408 | − | 0.819969i | \(-0.306009\pi\) | ||||
0.572408 | + | 0.819969i | \(0.306009\pi\) | |||||||
\(740\) | 11.1806 | 0.411007 | ||||||||
\(741\) | −16.6591 | −0.611989 | ||||||||
\(742\) | 3.07067 | 0.112728 | ||||||||
\(743\) | −22.3465 | −0.819815 | −0.409907 | − | 0.912127i | \(-0.634439\pi\) | ||||
−0.409907 | + | 0.912127i | \(0.634439\pi\) | |||||||
\(744\) | −1.05973 | −0.0388516 | ||||||||
\(745\) | −74.2283 | −2.71952 | ||||||||
\(746\) | 15.5728 | 0.570159 | ||||||||
\(747\) | 6.29883 | 0.230462 | ||||||||
\(748\) | 43.9282 | 1.60617 | ||||||||
\(749\) | 66.9599 | 2.44666 | ||||||||
\(750\) | 29.7682 | 1.08698 | ||||||||
\(751\) | −41.3430 | −1.50863 | −0.754313 | − | 0.656515i | \(-0.772030\pi\) | ||||
−0.754313 | + | 0.656515i | \(0.772030\pi\) | |||||||
\(752\) | −19.0204 | −0.693604 | ||||||||
\(753\) | −33.7713 | −1.23069 | ||||||||
\(754\) | −2.46537 | −0.0897834 | ||||||||
\(755\) | 18.5778 | 0.676116 | ||||||||
\(756\) | −7.35908 | −0.267647 | ||||||||
\(757\) | −5.70532 | −0.207364 | −0.103682 | − | 0.994611i | \(-0.533062\pi\) | ||||
−0.103682 | + | 0.994611i | \(0.533062\pi\) | |||||||
\(758\) | −11.7674 | −0.427411 | ||||||||
\(759\) | 32.2084 | 1.16909 | ||||||||
\(760\) | −37.3083 | −1.35332 | ||||||||
\(761\) | 15.1656 | 0.549754 | 0.274877 | − | 0.961479i | \(-0.411363\pi\) | ||||
0.274877 | + | 0.961479i | \(0.411363\pi\) | |||||||
\(762\) | −0.537505 | −0.0194718 | ||||||||
\(763\) | −53.9739 | −1.95399 | ||||||||
\(764\) | 38.0935 | 1.37817 | ||||||||
\(765\) | −53.0748 | −1.91892 | ||||||||
\(766\) | −7.55388 | −0.272933 | ||||||||
\(767\) | −9.78075 | −0.353162 | ||||||||
\(768\) | −16.7924 | −0.605943 | ||||||||
\(769\) | 5.23538 | 0.188793 | 0.0943964 | − | 0.995535i | \(-0.469908\pi\) | ||||
0.0943964 | + | 0.995535i | \(0.469908\pi\) | |||||||
\(770\) | 44.9181 | 1.61874 | ||||||||
\(771\) | 67.5710 | 2.43351 | ||||||||
\(772\) | −12.0071 | −0.432145 | ||||||||
\(773\) | −27.0422 | −0.972641 | −0.486321 | − | 0.873780i | \(-0.661661\pi\) | ||||
−0.486321 | + | 0.873780i | \(0.661661\pi\) | |||||||
\(774\) | 8.31453 | 0.298860 | ||||||||
\(775\) | −2.03136 | −0.0729687 | ||||||||
\(776\) | 20.5070 | 0.736160 | ||||||||
\(777\) | −15.4186 | −0.553139 | ||||||||
\(778\) | 4.80973 | 0.172437 | ||||||||
\(779\) | −51.4050 | −1.84177 | ||||||||
\(780\) | −24.6754 | −0.883521 | ||||||||
\(781\) | 25.8338 | 0.924407 | ||||||||
\(782\) | 9.66459 | 0.345605 | ||||||||
\(783\) | 2.88435 | 0.103078 | ||||||||
\(784\) | 11.6227 | 0.415096 | ||||||||
\(785\) | −23.8738 | −0.852093 | ||||||||
\(786\) | −8.09294 | −0.288666 | ||||||||
\(787\) | −25.6221 | −0.913329 | −0.456665 | − | 0.889639i | \(-0.650956\pi\) | ||||
−0.456665 | + | 0.889639i | \(0.650956\pi\) | |||||||
\(788\) | −2.97459 | −0.105966 | ||||||||
\(789\) | 61.5092 | 2.18979 | ||||||||
\(790\) | 19.2361 | 0.684390 | ||||||||
\(791\) | −4.00769 | −0.142497 | ||||||||
\(792\) | −27.8169 | −0.988431 | ||||||||
\(793\) | 0.129565 | 0.00460097 | ||||||||
\(794\) | 21.0643 | 0.747545 | ||||||||
\(795\) | −12.0459 | −0.427226 | ||||||||
\(796\) | −5.55460 | −0.196878 | ||||||||
\(797\) | 28.8151 | 1.02068 | 0.510341 | − | 0.859972i | \(-0.329519\pi\) | ||||
0.510341 | + | 0.859972i | \(0.329519\pi\) | |||||||
\(798\) | 22.8848 | 0.810114 | ||||||||
\(799\) | −59.2823 | −2.09726 | ||||||||
\(800\) | −57.6371 | −2.03778 | ||||||||
\(801\) | −10.7375 | −0.379391 | ||||||||
\(802\) | 1.09436 | 0.0386430 | ||||||||
\(803\) | 69.8642 | 2.46545 | ||||||||
\(804\) | −47.2649 | −1.66690 | ||||||||
\(805\) | −39.8137 | −1.40325 | ||||||||
\(806\) | −0.212702 | −0.00749210 | ||||||||
\(807\) | −22.0351 | −0.775671 | ||||||||
\(808\) | 15.7734 | 0.554905 | ||||||||
\(809\) | 20.6265 | 0.725188 | 0.362594 | − | 0.931947i | \(-0.381891\pi\) | ||||
0.362594 | + | 0.931947i | \(0.381891\pi\) | |||||||
\(810\) | −25.3481 | −0.890641 | ||||||||
\(811\) | 45.2088 | 1.58749 | 0.793747 | − | 0.608248i | \(-0.208127\pi\) | ||||
0.793747 | + | 0.608248i | \(0.208127\pi\) | |||||||
\(812\) | −13.6442 | −0.478817 | ||||||||
\(813\) | −13.7132 | −0.480942 | ||||||||
\(814\) | 5.60675 | 0.196516 | ||||||||
\(815\) | 4.69176 | 0.164345 | ||||||||
\(816\) | 22.8791 | 0.800930 | ||||||||
\(817\) | −22.5295 | −0.788208 | ||||||||
\(818\) | 2.40848 | 0.0842106 | ||||||||
\(819\) | 15.3539 | 0.536509 | ||||||||
\(820\) | −76.1407 | −2.65895 | ||||||||
\(821\) | 23.2674 | 0.812039 | 0.406019 | − | 0.913864i | \(-0.366917\pi\) | ||||
0.406019 | + | 0.913864i | \(0.366917\pi\) | |||||||
\(822\) | 25.2924 | 0.882172 | ||||||||
\(823\) | 2.12031 | 0.0739095 | 0.0369547 | − | 0.999317i | \(-0.488234\pi\) | ||||
0.0369547 | + | 0.999317i | \(0.488234\pi\) | |||||||
\(824\) | −0.238556 | −0.00831049 | ||||||||
\(825\) | −118.175 | −4.11433 | ||||||||
\(826\) | 13.4359 | 0.467495 | ||||||||
\(827\) | −16.5417 | −0.575213 | −0.287606 | − | 0.957749i | \(-0.592859\pi\) | ||||
−0.287606 | + | 0.957749i | \(0.592859\pi\) | |||||||
\(828\) | 10.9669 | 0.381125 | ||||||||
\(829\) | 2.61675 | 0.0908835 | 0.0454418 | − | 0.998967i | \(-0.485530\pi\) | ||||
0.0454418 | + | 0.998967i | \(0.485530\pi\) | |||||||
\(830\) | 6.27501 | 0.217809 | ||||||||
\(831\) | 13.1024 | 0.454516 | ||||||||
\(832\) | −0.0443806 | −0.00153862 | ||||||||
\(833\) | 36.2252 | 1.25513 | ||||||||
\(834\) | 28.9108 | 1.00110 | ||||||||
\(835\) | 3.50823 | 0.121407 | ||||||||
\(836\) | 33.5263 | 1.15953 | ||||||||
\(837\) | 0.248850 | 0.00860152 | ||||||||
\(838\) | −0.403668 | −0.0139445 | ||||||||
\(839\) | 40.9480 | 1.41368 | 0.706841 | − | 0.707373i | \(-0.250120\pi\) | ||||
0.706841 | + | 0.707373i | \(0.250120\pi\) | |||||||
\(840\) | 76.2074 | 2.62940 | ||||||||
\(841\) | −23.6522 | −0.815594 | ||||||||
\(842\) | −8.37275 | −0.288544 | ||||||||
\(843\) | −11.0279 | −0.379821 | ||||||||
\(844\) | 3.73655 | 0.128617 | ||||||||
\(845\) | 39.5178 | 1.35945 | ||||||||
\(846\) | 16.6976 | 0.574074 | ||||||||
\(847\) | −50.2428 | −1.72636 | ||||||||
\(848\) | 2.34297 | 0.0804580 | ||||||||
\(849\) | 44.9068 | 1.54120 | ||||||||
\(850\) | −35.4601 | −1.21627 | ||||||||
\(851\) | −4.96961 | −0.170356 | ||||||||
\(852\) | 19.4952 | 0.667893 | ||||||||
\(853\) | 17.3933 | 0.595537 | 0.297768 | − | 0.954638i | \(-0.403758\pi\) | ||||
0.297768 | + | 0.954638i | \(0.403758\pi\) | |||||||
\(854\) | −0.177984 | −0.00609049 | ||||||||
\(855\) | −40.5070 | −1.38531 | ||||||||
\(856\) | −41.3101 | −1.41195 | ||||||||
\(857\) | 16.7101 | 0.570805 | 0.285402 | − | 0.958408i | \(-0.407873\pi\) | ||||
0.285402 | + | 0.958408i | \(0.407873\pi\) | |||||||
\(858\) | −12.3740 | −0.422441 | ||||||||
\(859\) | 13.9877 | 0.477255 | 0.238628 | − | 0.971111i | \(-0.423302\pi\) | ||||
0.238628 | + | 0.971111i | \(0.423302\pi\) | |||||||
\(860\) | −33.3706 | −1.13793 | ||||||||
\(861\) | 105.002 | 3.57845 | ||||||||
\(862\) | 16.9126 | 0.576045 | ||||||||
\(863\) | −23.1575 | −0.788290 | −0.394145 | − | 0.919048i | \(-0.628959\pi\) | ||||
−0.394145 | + | 0.919048i | \(0.628959\pi\) | |||||||
\(864\) | 7.06078 | 0.240212 | ||||||||
\(865\) | −48.1446 | −1.63696 | ||||||||
\(866\) | 13.0791 | 0.444445 | ||||||||
\(867\) | 31.5619 | 1.07190 | ||||||||
\(868\) | −1.17716 | −0.0399556 | ||||||||
\(869\) | −38.8628 | −1.31833 | ||||||||
\(870\) | −13.2857 | −0.450427 | ||||||||
\(871\) | −21.3281 | −0.722676 | ||||||||
\(872\) | 33.2986 | 1.12763 | ||||||||
\(873\) | 22.2652 | 0.753564 | ||||||||
\(874\) | 7.37608 | 0.249499 | ||||||||
\(875\) | 74.3418 | 2.51321 | ||||||||
\(876\) | 52.7221 | 1.78131 | ||||||||
\(877\) | 40.3104 | 1.36119 | 0.680594 | − | 0.732661i | \(-0.261722\pi\) | ||||
0.680594 | + | 0.732661i | \(0.261722\pi\) | |||||||
\(878\) | 8.03326 | 0.271110 | ||||||||
\(879\) | 30.4276 | 1.02630 | ||||||||
\(880\) | 34.2733 | 1.15535 | ||||||||
\(881\) | −23.2156 | −0.782152 | −0.391076 | − | 0.920358i | \(-0.627897\pi\) | ||||
−0.391076 | + | 0.920358i | \(0.627897\pi\) | |||||||
\(882\) | −10.2033 | −0.343562 | ||||||||
\(883\) | −0.920055 | −0.0309623 | −0.0154812 | − | 0.999880i | \(-0.504928\pi\) | ||||
−0.0154812 | + | 0.999880i | \(0.504928\pi\) | |||||||
\(884\) | 14.9587 | 0.503117 | ||||||||
\(885\) | −52.7078 | −1.77175 | ||||||||
\(886\) | −14.7608 | −0.495897 | ||||||||
\(887\) | −28.9082 | −0.970643 | −0.485321 | − | 0.874336i | \(-0.661297\pi\) | ||||
−0.485321 | + | 0.874336i | \(0.661297\pi\) | |||||||
\(888\) | 9.51233 | 0.319213 | ||||||||
\(889\) | −1.34234 | −0.0450207 | ||||||||
\(890\) | −10.6969 | −0.358561 | ||||||||
\(891\) | 51.2109 | 1.71563 | ||||||||
\(892\) | 2.81257 | 0.0941720 | ||||||||
\(893\) | −45.2446 | −1.51405 | ||||||||
\(894\) | −28.0901 | −0.939473 | ||||||||
\(895\) | 39.0641 | 1.30577 | ||||||||
\(896\) | −41.6299 | −1.39076 | ||||||||
\(897\) | 10.9679 | 0.366206 | ||||||||
\(898\) | −22.6330 | −0.755273 | ||||||||
\(899\) | 0.461384 | 0.0153880 | ||||||||
\(900\) | −40.2383 | −1.34128 | ||||||||
\(901\) | 7.30250 | 0.243282 | ||||||||
\(902\) | −38.1823 | −1.27133 | ||||||||
\(903\) | 46.0196 | 1.53144 | ||||||||
\(904\) | 2.47250 | 0.0822341 | ||||||||
\(905\) | 66.4290 | 2.20817 | ||||||||
\(906\) | 7.03037 | 0.233568 | ||||||||
\(907\) | 36.3884 | 1.20826 | 0.604128 | − | 0.796887i | \(-0.293522\pi\) | ||||
0.604128 | + | 0.796887i | \(0.293522\pi\) | |||||||
\(908\) | −6.98007 | −0.231642 | ||||||||
\(909\) | 17.1257 | 0.568024 | ||||||||
\(910\) | 15.2958 | 0.507052 | ||||||||
\(911\) | −10.8289 | −0.358776 | −0.179388 | − | 0.983778i | \(-0.557412\pi\) | ||||
−0.179388 | + | 0.983778i | \(0.557412\pi\) | |||||||
\(912\) | 17.4615 | 0.578208 | ||||||||
\(913\) | −12.6774 | −0.419562 | ||||||||
\(914\) | 14.7580 | 0.488150 | ||||||||
\(915\) | 0.698214 | 0.0230823 | ||||||||
\(916\) | −10.0008 | −0.330437 | ||||||||
\(917\) | −20.2110 | −0.667424 | ||||||||
\(918\) | 4.34401 | 0.143374 | ||||||||
\(919\) | 28.3998 | 0.936823 | 0.468412 | − | 0.883510i | \(-0.344826\pi\) | ||||
0.468412 | + | 0.883510i | \(0.344826\pi\) | |||||||
\(920\) | 24.5626 | 0.809806 | ||||||||
\(921\) | −26.9747 | −0.888847 | ||||||||
\(922\) | −11.2977 | −0.372071 | ||||||||
\(923\) | 8.79712 | 0.289561 | ||||||||
\(924\) | −68.4820 | −2.25289 | ||||||||
\(925\) | 18.2339 | 0.599526 | ||||||||
\(926\) | 20.1906 | 0.663505 | ||||||||
\(927\) | −0.259009 | −0.00850696 | ||||||||
\(928\) | 13.0911 | 0.429737 | ||||||||
\(929\) | −32.8431 | −1.07755 | −0.538774 | − | 0.842451i | \(-0.681112\pi\) | ||||
−0.538774 | + | 0.842451i | \(0.681112\pi\) | |||||||
\(930\) | −1.14623 | −0.0375865 | ||||||||
\(931\) | 27.6473 | 0.906104 | ||||||||
\(932\) | −22.1621 | −0.725944 | ||||||||
\(933\) | −54.1361 | −1.77233 | ||||||||
\(934\) | 7.75371 | 0.253709 | ||||||||
\(935\) | 106.822 | 3.49345 | ||||||||
\(936\) | −9.47242 | −0.309616 | ||||||||
\(937\) | 4.11911 | 0.134566 | 0.0672828 | − | 0.997734i | \(-0.478567\pi\) | ||||
0.0672828 | + | 0.997734i | \(0.478567\pi\) | |||||||
\(938\) | 29.2986 | 0.956635 | ||||||||
\(939\) | −18.4450 | −0.601930 | ||||||||
\(940\) | −67.0161 | −2.18582 | ||||||||
\(941\) | −8.26409 | −0.269402 | −0.134701 | − | 0.990886i | \(-0.543007\pi\) | ||||
−0.134701 | + | 0.990886i | \(0.543007\pi\) | |||||||
\(942\) | −9.03452 | −0.294361 | ||||||||
\(943\) | 33.8434 | 1.10209 | ||||||||
\(944\) | 10.2518 | 0.333668 | ||||||||
\(945\) | −17.8953 | −0.582136 | ||||||||
\(946\) | −16.7344 | −0.544081 | ||||||||
\(947\) | 43.3860 | 1.40986 | 0.704928 | − | 0.709279i | \(-0.250979\pi\) | ||||
0.704928 | + | 0.709279i | \(0.250979\pi\) | |||||||
\(948\) | −29.3273 | −0.952506 | ||||||||
\(949\) | 23.7907 | 0.772277 | ||||||||
\(950\) | −27.0634 | −0.878051 | ||||||||
\(951\) | −5.57218 | −0.180690 | ||||||||
\(952\) | −46.1985 | −1.49730 | ||||||||
\(953\) | −26.7790 | −0.867457 | −0.433728 | − | 0.901044i | \(-0.642802\pi\) | ||||
−0.433728 | + | 0.901044i | \(0.642802\pi\) | |||||||
\(954\) | −2.05684 | −0.0665925 | ||||||||
\(955\) | 92.6333 | 2.99754 | ||||||||
\(956\) | 31.0722 | 1.00495 | ||||||||
\(957\) | 26.8412 | 0.867651 | ||||||||
\(958\) | −9.55772 | −0.308796 | ||||||||
\(959\) | 63.1640 | 2.03967 | ||||||||
\(960\) | −0.239164 | −0.00771898 | ||||||||
\(961\) | −30.9602 | −0.998716 | ||||||||
\(962\) | 1.90925 | 0.0615567 | ||||||||
\(963\) | −44.8519 | −1.44533 | ||||||||
\(964\) | 1.60229 | 0.0516062 | ||||||||
\(965\) | −29.1981 | −0.939922 | ||||||||
\(966\) | −15.0666 | −0.484761 | ||||||||
\(967\) | 7.46107 | 0.239932 | 0.119966 | − | 0.992778i | \(-0.461721\pi\) | ||||
0.119966 | + | 0.992778i | \(0.461721\pi\) | |||||||
\(968\) | 30.9967 | 0.996272 | ||||||||
\(969\) | 54.4234 | 1.74833 | ||||||||
\(970\) | 22.1810 | 0.712190 | ||||||||
\(971\) | −21.4365 | −0.687931 | −0.343966 | − | 0.938982i | \(-0.611770\pi\) | ||||
−0.343966 | + | 0.938982i | \(0.611770\pi\) | |||||||
\(972\) | 32.6501 | 1.04725 | ||||||||
\(973\) | 72.2006 | 2.31465 | ||||||||
\(974\) | 9.77548 | 0.313226 | ||||||||
\(975\) | −40.2419 | −1.28877 | ||||||||
\(976\) | −0.135805 | −0.00434700 | ||||||||
\(977\) | −30.9584 | −0.990446 | −0.495223 | − | 0.868766i | \(-0.664914\pi\) | ||||
−0.495223 | + | 0.868766i | \(0.664914\pi\) | |||||||
\(978\) | 1.77549 | 0.0567740 | ||||||||
\(979\) | 21.6110 | 0.690690 | ||||||||
\(980\) | 40.9510 | 1.30813 | ||||||||
\(981\) | 36.1535 | 1.15429 | ||||||||
\(982\) | −7.93592 | −0.253246 | ||||||||
\(983\) | 13.6397 | 0.435040 | 0.217520 | − | 0.976056i | \(-0.430203\pi\) | ||||
0.217520 | + | 0.976056i | \(0.430203\pi\) | |||||||
\(984\) | −64.7796 | −2.06510 | ||||||||
\(985\) | −7.23343 | −0.230476 | ||||||||
\(986\) | 8.05406 | 0.256494 | ||||||||
\(987\) | 92.4183 | 2.94171 | ||||||||
\(988\) | 11.4166 | 0.363211 | ||||||||
\(989\) | 14.8327 | 0.471653 | ||||||||
\(990\) | −30.0876 | −0.956247 | ||||||||
\(991\) | −46.0458 | −1.46269 | −0.731347 | − | 0.682006i | \(-0.761108\pi\) | ||||
−0.731347 | + | 0.682006i | \(0.761108\pi\) | |||||||
\(992\) | 1.12945 | 0.0358600 | ||||||||
\(993\) | −7.14508 | −0.226742 | ||||||||
\(994\) | −12.0847 | −0.383303 | ||||||||
\(995\) | −13.5073 | −0.428211 | ||||||||
\(996\) | −9.56685 | −0.303137 | ||||||||
\(997\) | 57.1775 | 1.81083 | 0.905415 | − | 0.424527i | \(-0.139560\pi\) | ||||
0.905415 | + | 0.424527i | \(0.139560\pi\) | |||||||
\(998\) | 26.4643 | 0.837711 | ||||||||
\(999\) | −2.23373 | −0.0706719 |
(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 | 241.2.a.a.1.4 | ✓ | 7 | |
3.2 | odd | 2 | 2169.2.a.e.1.4 | 7 | |||
4.3 | odd | 2 | 3856.2.a.j.1.1 | 7 | |||
5.4 | even | 2 | 6025.2.a.f.1.4 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
241.2.a.a.1.4 | ✓ | 7 | 1.1 | even | 1 | trivial | |
2169.2.a.e.1.4 | 7 | 3.2 | odd | 2 | |||
3856.2.a.j.1.1 | 7 | 4.3 | odd | 2 | |||
6025.2.a.f.1.4 | 7 | 5.4 | even | 2 |