Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.09110 | −1.47863 | −0.739316 | − | 0.673358i | \(-0.764851\pi\) | ||||
−0.739316 | + | 0.673358i | \(0.764851\pi\) | |||||||
\(3\) | −1.81594 | −1.04843 | −0.524217 | − | 0.851584i | \(-0.675642\pi\) | ||||
−0.524217 | + | 0.851584i | \(0.675642\pi\) | |||||||
\(4\) | 2.37271 | 1.18635 | ||||||||
\(5\) | 1.01486 | 0.453859 | 0.226930 | − | 0.973911i | \(-0.427131\pi\) | ||||
0.226930 | + | 0.973911i | \(0.427131\pi\) | |||||||
\(6\) | 3.79732 | 1.55025 | ||||||||
\(7\) | 2.98461 | 1.12808 | 0.564038 | − | 0.825749i | \(-0.309247\pi\) | ||||
0.564038 | + | 0.825749i | \(0.309247\pi\) | |||||||
\(8\) | −0.779370 | −0.275549 | ||||||||
\(9\) | 0.297648 | 0.0992159 | ||||||||
\(10\) | −2.12218 | −0.671091 | ||||||||
\(11\) | −2.86797 | −0.864725 | −0.432363 | − | 0.901700i | \(-0.642320\pi\) | ||||
−0.432363 | + | 0.901700i | \(0.642320\pi\) | |||||||
\(12\) | −4.30870 | −1.24381 | ||||||||
\(13\) | 0.868290 | 0.240820 | 0.120410 | − | 0.992724i | \(-0.461579\pi\) | ||||
0.120410 | + | 0.992724i | \(0.461579\pi\) | |||||||
\(14\) | −6.24112 | −1.66801 | ||||||||
\(15\) | −1.84293 | −0.475842 | ||||||||
\(16\) | −3.11567 | −0.778918 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −0.622412 | −0.146704 | ||||||||
\(19\) | 1.72172 | 0.394991 | 0.197495 | − | 0.980304i | \(-0.436719\pi\) | ||||
0.197495 | + | 0.980304i | \(0.436719\pi\) | |||||||
\(20\) | 2.40797 | 0.538437 | ||||||||
\(21\) | −5.41988 | −1.18271 | ||||||||
\(22\) | 5.99722 | 1.27861 | ||||||||
\(23\) | −6.20821 | −1.29450 | −0.647251 | − | 0.762277i | \(-0.724081\pi\) | ||||
−0.647251 | + | 0.762277i | \(0.724081\pi\) | |||||||
\(24\) | 1.41529 | 0.288895 | ||||||||
\(25\) | −3.97006 | −0.794012 | ||||||||
\(26\) | −1.81568 | −0.356085 | ||||||||
\(27\) | 4.90732 | 0.944414 | ||||||||
\(28\) | 7.08160 | 1.33830 | ||||||||
\(29\) | −0.219151 | −0.0406953 | −0.0203476 | − | 0.999793i | \(-0.506477\pi\) | ||||
−0.0203476 | + | 0.999793i | \(0.506477\pi\) | |||||||
\(30\) | 3.85375 | 0.703595 | ||||||||
\(31\) | 5.98951 | 1.07575 | 0.537874 | − | 0.843025i | \(-0.319228\pi\) | ||||
0.537874 | + | 0.843025i | \(0.319228\pi\) | |||||||
\(32\) | 8.07393 | 1.42728 | ||||||||
\(33\) | 5.20807 | 0.906608 | ||||||||
\(34\) | −2.09110 | −0.358621 | ||||||||
\(35\) | 3.02896 | 0.511987 | ||||||||
\(36\) | 0.706231 | 0.117705 | ||||||||
\(37\) | 4.78509 | 0.786664 | 0.393332 | − | 0.919396i | \(-0.371322\pi\) | ||||
0.393332 | + | 0.919396i | \(0.371322\pi\) | |||||||
\(38\) | −3.60030 | −0.584046 | ||||||||
\(39\) | −1.57677 | −0.252485 | ||||||||
\(40\) | −0.790951 | −0.125060 | ||||||||
\(41\) | 9.96704 | 1.55659 | 0.778295 | − | 0.627899i | \(-0.216085\pi\) | ||||
0.778295 | + | 0.627899i | \(0.216085\pi\) | |||||||
\(42\) | 11.3335 | 1.74880 | ||||||||
\(43\) | 3.15469 | 0.481085 | 0.240543 | − | 0.970639i | \(-0.422675\pi\) | ||||
0.240543 | + | 0.970639i | \(0.422675\pi\) | |||||||
\(44\) | −6.80485 | −1.02587 | ||||||||
\(45\) | 0.302071 | 0.0450300 | ||||||||
\(46\) | 12.9820 | 1.91409 | ||||||||
\(47\) | −11.3131 | −1.65018 | −0.825090 | − | 0.565002i | \(-0.808876\pi\) | ||||
−0.825090 | + | 0.565002i | \(0.808876\pi\) | |||||||
\(48\) | 5.65788 | 0.816645 | ||||||||
\(49\) | 1.90788 | 0.272555 | ||||||||
\(50\) | 8.30180 | 1.17405 | ||||||||
\(51\) | −1.81594 | −0.254283 | ||||||||
\(52\) | 2.06020 | 0.285698 | ||||||||
\(53\) | 4.10300 | 0.563590 | 0.281795 | − | 0.959475i | \(-0.409070\pi\) | ||||
0.281795 | + | 0.959475i | \(0.409070\pi\) | |||||||
\(54\) | −10.2617 | −1.39644 | ||||||||
\(55\) | −2.91059 | −0.392463 | ||||||||
\(56\) | −2.32611 | −0.310840 | ||||||||
\(57\) | −3.12655 | −0.414122 | ||||||||
\(58\) | 0.458267 | 0.0601734 | ||||||||
\(59\) | −12.2362 | −1.59302 | −0.796509 | − | 0.604627i | \(-0.793322\pi\) | ||||
−0.796509 | + | 0.604627i | \(0.793322\pi\) | |||||||
\(60\) | −4.37273 | −0.564517 | ||||||||
\(61\) | 3.65797 | 0.468355 | 0.234178 | − | 0.972194i | \(-0.424760\pi\) | ||||
0.234178 | + | 0.972194i | \(0.424760\pi\) | |||||||
\(62\) | −12.5247 | −1.59064 | ||||||||
\(63\) | 0.888362 | 0.111923 | ||||||||
\(64\) | −10.6521 | −1.33151 | ||||||||
\(65\) | 0.881193 | 0.109299 | ||||||||
\(66\) | −10.8906 | −1.34054 | ||||||||
\(67\) | −11.9679 | −1.46212 | −0.731059 | − | 0.682315i | \(-0.760973\pi\) | ||||
−0.731059 | + | 0.682315i | \(0.760973\pi\) | |||||||
\(68\) | 2.37271 | 0.287733 | ||||||||
\(69\) | 11.2738 | 1.35720 | ||||||||
\(70\) | −6.33386 | −0.757041 | ||||||||
\(71\) | −5.83543 | −0.692538 | −0.346269 | − | 0.938135i | \(-0.612552\pi\) | ||||
−0.346269 | + | 0.938135i | \(0.612552\pi\) | |||||||
\(72\) | −0.231978 | −0.0273388 | ||||||||
\(73\) | −13.4525 | −1.57450 | −0.787248 | − | 0.616636i | \(-0.788495\pi\) | ||||
−0.787248 | + | 0.616636i | \(0.788495\pi\) | |||||||
\(74\) | −10.0061 | −1.16319 | ||||||||
\(75\) | 7.20940 | 0.832470 | ||||||||
\(76\) | 4.08515 | 0.468599 | ||||||||
\(77\) | −8.55976 | −0.975476 | ||||||||
\(78\) | 3.29718 | 0.373332 | ||||||||
\(79\) | 9.40040 | 1.05763 | 0.528814 | − | 0.848738i | \(-0.322637\pi\) | ||||
0.528814 | + | 0.848738i | \(0.322637\pi\) | |||||||
\(80\) | −3.16197 | −0.353519 | ||||||||
\(81\) | −9.80435 | −1.08937 | ||||||||
\(82\) | −20.8421 | −2.30162 | ||||||||
\(83\) | −12.4585 | −1.36750 | −0.683749 | − | 0.729717i | \(-0.739652\pi\) | ||||
−0.683749 | + | 0.729717i | \(0.739652\pi\) | |||||||
\(84\) | −12.8598 | −1.40312 | ||||||||
\(85\) | 1.01486 | 0.110077 | ||||||||
\(86\) | −6.59678 | −0.711349 | ||||||||
\(87\) | 0.397965 | 0.0426664 | ||||||||
\(88\) | 2.23521 | 0.238274 | ||||||||
\(89\) | 3.38629 | 0.358946 | 0.179473 | − | 0.983763i | \(-0.442561\pi\) | ||||
0.179473 | + | 0.983763i | \(0.442561\pi\) | |||||||
\(90\) | −0.631661 | −0.0665829 | ||||||||
\(91\) | 2.59151 | 0.271664 | ||||||||
\(92\) | −14.7303 | −1.53574 | ||||||||
\(93\) | −10.8766 | −1.12785 | ||||||||
\(94\) | 23.6568 | 2.44001 | ||||||||
\(95\) | 1.74731 | 0.179270 | ||||||||
\(96\) | −14.6618 | −1.49641 | ||||||||
\(97\) | 5.45836 | 0.554213 | 0.277106 | − | 0.960839i | \(-0.410625\pi\) | ||||
0.277106 | + | 0.960839i | \(0.410625\pi\) | |||||||
\(98\) | −3.98958 | −0.403008 | ||||||||
\(99\) | −0.853645 | −0.0857945 | ||||||||
\(100\) | −9.41979 | −0.941979 | ||||||||
\(101\) | 0.434914 | 0.0432756 | 0.0216378 | − | 0.999766i | \(-0.493112\pi\) | ||||
0.0216378 | + | 0.999766i | \(0.493112\pi\) | |||||||
\(102\) | 3.79732 | 0.375991 | ||||||||
\(103\) | −1.14666 | −0.112984 | −0.0564921 | − | 0.998403i | \(-0.517992\pi\) | ||||
−0.0564921 | + | 0.998403i | \(0.517992\pi\) | |||||||
\(104\) | −0.676720 | −0.0663578 | ||||||||
\(105\) | −5.50041 | −0.536785 | ||||||||
\(106\) | −8.57979 | −0.833343 | ||||||||
\(107\) | 8.98893 | 0.868992 | 0.434496 | − | 0.900674i | \(-0.356926\pi\) | ||||
0.434496 | + | 0.900674i | \(0.356926\pi\) | |||||||
\(108\) | 11.6436 | 1.12041 | ||||||||
\(109\) | 7.50538 | 0.718885 | 0.359442 | − | 0.933167i | \(-0.382967\pi\) | ||||
0.359442 | + | 0.933167i | \(0.382967\pi\) | |||||||
\(110\) | 6.08633 | 0.580309 | ||||||||
\(111\) | −8.68945 | −0.824766 | ||||||||
\(112\) | −9.29906 | −0.878679 | ||||||||
\(113\) | 11.6881 | 1.09952 | 0.549761 | − | 0.835322i | \(-0.314719\pi\) | ||||
0.549761 | + | 0.835322i | \(0.314719\pi\) | |||||||
\(114\) | 6.53794 | 0.612334 | ||||||||
\(115\) | −6.30046 | −0.587521 | ||||||||
\(116\) | −0.519981 | −0.0482790 | ||||||||
\(117\) | 0.258445 | 0.0238932 | ||||||||
\(118\) | 25.5871 | 2.35549 | ||||||||
\(119\) | 2.98461 | 0.273599 | ||||||||
\(120\) | 1.43632 | 0.131118 | ||||||||
\(121\) | −2.77475 | −0.252250 | ||||||||
\(122\) | −7.64919 | −0.692526 | ||||||||
\(123\) | −18.0996 | −1.63198 | ||||||||
\(124\) | 14.2114 | 1.27622 | ||||||||
\(125\) | −9.10335 | −0.814229 | ||||||||
\(126\) | −1.85766 | −0.165493 | ||||||||
\(127\) | 11.7746 | 1.04483 | 0.522413 | − | 0.852692i | \(-0.325032\pi\) | ||||
0.522413 | + | 0.852692i | \(0.325032\pi\) | |||||||
\(128\) | 6.12670 | 0.541529 | ||||||||
\(129\) | −5.72873 | −0.504387 | ||||||||
\(130\) | −1.84266 | −0.161612 | ||||||||
\(131\) | −7.72977 | −0.675353 | −0.337676 | − | 0.941262i | \(-0.609641\pi\) | ||||
−0.337676 | + | 0.941262i | \(0.609641\pi\) | |||||||
\(132\) | 12.3572 | 1.07556 | ||||||||
\(133\) | 5.13867 | 0.445579 | ||||||||
\(134\) | 25.0262 | 2.16193 | ||||||||
\(135\) | 4.98024 | 0.428631 | ||||||||
\(136\) | −0.779370 | −0.0668304 | ||||||||
\(137\) | −7.44727 | −0.636264 | −0.318132 | − | 0.948046i | \(-0.603055\pi\) | ||||
−0.318132 | + | 0.948046i | \(0.603055\pi\) | |||||||
\(138\) | −23.5746 | −2.00680 | ||||||||
\(139\) | 10.8714 | 0.922103 | 0.461051 | − | 0.887373i | \(-0.347472\pi\) | ||||
0.461051 | + | 0.887373i | \(0.347472\pi\) | |||||||
\(140\) | 7.18683 | 0.607398 | ||||||||
\(141\) | 20.5439 | 1.73011 | ||||||||
\(142\) | 12.2025 | 1.02401 | ||||||||
\(143\) | −2.49023 | −0.208243 | ||||||||
\(144\) | −0.927373 | −0.0772811 | ||||||||
\(145\) | −0.222407 | −0.0184699 | ||||||||
\(146\) | 28.1306 | 2.32810 | ||||||||
\(147\) | −3.46461 | −0.285756 | ||||||||
\(148\) | 11.3536 | 0.933262 | ||||||||
\(149\) | −14.2643 | −1.16858 | −0.584289 | − | 0.811546i | \(-0.698627\pi\) | ||||
−0.584289 | + | 0.811546i | \(0.698627\pi\) | |||||||
\(150\) | −15.0756 | −1.23092 | ||||||||
\(151\) | −5.01201 | −0.407872 | −0.203936 | − | 0.978984i | \(-0.565373\pi\) | ||||
−0.203936 | + | 0.978984i | \(0.565373\pi\) | |||||||
\(152\) | −1.34186 | −0.108839 | ||||||||
\(153\) | 0.297648 | 0.0240634 | ||||||||
\(154\) | 17.8993 | 1.44237 | ||||||||
\(155\) | 6.07852 | 0.488238 | ||||||||
\(156\) | −3.74120 | −0.299536 | ||||||||
\(157\) | −1.86289 | −0.148675 | −0.0743374 | − | 0.997233i | \(-0.523684\pi\) | ||||
−0.0743374 | + | 0.997233i | \(0.523684\pi\) | |||||||
\(158\) | −19.6572 | −1.56384 | ||||||||
\(159\) | −7.45081 | −0.590888 | ||||||||
\(160\) | 8.19391 | 0.647785 | ||||||||
\(161\) | −18.5291 | −1.46030 | ||||||||
\(162\) | 20.5019 | 1.61078 | ||||||||
\(163\) | −13.3781 | −1.04785 | −0.523925 | − | 0.851764i | \(-0.675533\pi\) | ||||
−0.523925 | + | 0.851764i | \(0.675533\pi\) | |||||||
\(164\) | 23.6489 | 1.84667 | ||||||||
\(165\) | 5.28546 | 0.411472 | ||||||||
\(166\) | 26.0520 | 2.02203 | ||||||||
\(167\) | 4.81218 | 0.372378 | 0.186189 | − | 0.982514i | \(-0.440386\pi\) | ||||
0.186189 | + | 0.982514i | \(0.440386\pi\) | |||||||
\(168\) | 4.22409 | 0.325896 | ||||||||
\(169\) | −12.2461 | −0.942006 | ||||||||
\(170\) | −2.12218 | −0.162763 | ||||||||
\(171\) | 0.512467 | 0.0391894 | ||||||||
\(172\) | 7.48515 | 0.570738 | ||||||||
\(173\) | 19.2610 | 1.46439 | 0.732193 | − | 0.681097i | \(-0.238497\pi\) | ||||
0.732193 | + | 0.681097i | \(0.238497\pi\) | |||||||
\(174\) | −0.832186 | −0.0630879 | ||||||||
\(175\) | −11.8491 | −0.895706 | ||||||||
\(176\) | 8.93565 | 0.673550 | ||||||||
\(177\) | 22.2202 | 1.67018 | ||||||||
\(178\) | −7.08107 | −0.530749 | ||||||||
\(179\) | −11.3991 | −0.852010 | −0.426005 | − | 0.904721i | \(-0.640079\pi\) | ||||
−0.426005 | + | 0.904721i | \(0.640079\pi\) | |||||||
\(180\) | 0.716726 | 0.0534216 | ||||||||
\(181\) | 0.0779341 | 0.00579279 | 0.00289640 | − | 0.999996i | \(-0.499078\pi\) | ||||
0.00289640 | + | 0.999996i | \(0.499078\pi\) | |||||||
\(182\) | −5.41910 | −0.401691 | ||||||||
\(183\) | −6.64267 | −0.491040 | ||||||||
\(184\) | 4.83850 | 0.356699 | ||||||||
\(185\) | 4.85620 | 0.357035 | ||||||||
\(186\) | 22.7441 | 1.66768 | ||||||||
\(187\) | −2.86797 | −0.209727 | ||||||||
\(188\) | −26.8426 | −1.95770 | ||||||||
\(189\) | 14.6464 | 1.06537 | ||||||||
\(190\) | −3.65380 | −0.265075 | ||||||||
\(191\) | 25.8975 | 1.87388 | 0.936939 | − | 0.349493i | \(-0.113646\pi\) | ||||
0.936939 | + | 0.349493i | \(0.113646\pi\) | |||||||
\(192\) | 19.3435 | 1.39600 | ||||||||
\(193\) | −18.7292 | −1.34816 | −0.674080 | − | 0.738658i | \(-0.735460\pi\) | ||||
−0.674080 | + | 0.738658i | \(0.735460\pi\) | |||||||
\(194\) | −11.4140 | −0.819477 | ||||||||
\(195\) | −1.60020 | −0.114592 | ||||||||
\(196\) | 4.52685 | 0.323346 | ||||||||
\(197\) | −12.6599 | −0.901979 | −0.450989 | − | 0.892529i | \(-0.648929\pi\) | ||||
−0.450989 | + | 0.892529i | \(0.648929\pi\) | |||||||
\(198\) | 1.78506 | 0.126859 | ||||||||
\(199\) | 25.7766 | 1.82726 | 0.913629 | − | 0.406549i | \(-0.133268\pi\) | ||||
0.913629 | + | 0.406549i | \(0.133268\pi\) | |||||||
\(200\) | 3.09415 | 0.218789 | ||||||||
\(201\) | 21.7331 | 1.53293 | ||||||||
\(202\) | −0.909451 | −0.0639887 | ||||||||
\(203\) | −0.654079 | −0.0459074 | ||||||||
\(204\) | −4.30870 | −0.301669 | ||||||||
\(205\) | 10.1151 | 0.706472 | ||||||||
\(206\) | 2.39779 | 0.167062 | ||||||||
\(207\) | −1.84786 | −0.128435 | ||||||||
\(208\) | −2.70531 | −0.187579 | ||||||||
\(209\) | −4.93785 | −0.341558 | ||||||||
\(210\) | 11.5019 | 0.793708 | ||||||||
\(211\) | −12.1503 | −0.836460 | −0.418230 | − | 0.908341i | \(-0.637349\pi\) | ||||
−0.418230 | + | 0.908341i | \(0.637349\pi\) | |||||||
\(212\) | 9.73522 | 0.668617 | ||||||||
\(213\) | 10.5968 | 0.726081 | ||||||||
\(214\) | −18.7968 | −1.28492 | ||||||||
\(215\) | 3.20157 | 0.218345 | ||||||||
\(216\) | −3.82462 | −0.260232 | ||||||||
\(217\) | 17.8763 | 1.21353 | ||||||||
\(218\) | −15.6945 | −1.06297 | ||||||||
\(219\) | 24.4290 | 1.65076 | ||||||||
\(220\) | −6.90597 | −0.465600 | ||||||||
\(221\) | 0.868290 | 0.0584075 | ||||||||
\(222\) | 18.1705 | 1.21953 | ||||||||
\(223\) | 7.32543 | 0.490547 | 0.245273 | − | 0.969454i | \(-0.421122\pi\) | ||||
0.245273 | + | 0.969454i | \(0.421122\pi\) | |||||||
\(224\) | 24.0975 | 1.61008 | ||||||||
\(225\) | −1.18168 | −0.0787786 | ||||||||
\(226\) | −24.4409 | −1.62579 | ||||||||
\(227\) | 7.10532 | 0.471596 | 0.235798 | − | 0.971802i | \(-0.424230\pi\) | ||||
0.235798 | + | 0.971802i | \(0.424230\pi\) | |||||||
\(228\) | −7.41840 | −0.491295 | ||||||||
\(229\) | −11.1217 | −0.734944 | −0.367472 | − | 0.930035i | \(-0.619777\pi\) | ||||
−0.367472 | + | 0.930035i | \(0.619777\pi\) | |||||||
\(230\) | 13.1749 | 0.868728 | ||||||||
\(231\) | 15.5440 | 1.02272 | ||||||||
\(232\) | 0.170800 | 0.0112135 | ||||||||
\(233\) | −29.1623 | −1.91049 | −0.955243 | − | 0.295823i | \(-0.904406\pi\) | ||||
−0.955243 | + | 0.295823i | \(0.904406\pi\) | |||||||
\(234\) | −0.540434 | −0.0353293 | ||||||||
\(235\) | −11.4812 | −0.748949 | ||||||||
\(236\) | −29.0329 | −1.88988 | ||||||||
\(237\) | −17.0706 | −1.10885 | ||||||||
\(238\) | −6.24112 | −0.404552 | ||||||||
\(239\) | −22.8964 | −1.48104 | −0.740522 | − | 0.672033i | \(-0.765421\pi\) | ||||
−0.740522 | + | 0.672033i | \(0.765421\pi\) | |||||||
\(240\) | 5.74196 | 0.370642 | ||||||||
\(241\) | 3.15808 | 0.203430 | 0.101715 | − | 0.994814i | \(-0.467567\pi\) | ||||
0.101715 | + | 0.994814i | \(0.467567\pi\) | |||||||
\(242\) | 5.80229 | 0.372985 | ||||||||
\(243\) | 3.08219 | 0.197722 | ||||||||
\(244\) | 8.67930 | 0.555635 | ||||||||
\(245\) | 1.93623 | 0.123701 | ||||||||
\(246\) | 37.8481 | 2.41310 | ||||||||
\(247\) | 1.49496 | 0.0951218 | ||||||||
\(248\) | −4.66805 | −0.296421 | ||||||||
\(249\) | 22.6239 | 1.43373 | ||||||||
\(250\) | 19.0360 | 1.20394 | ||||||||
\(251\) | 16.6537 | 1.05117 | 0.525586 | − | 0.850740i | \(-0.323846\pi\) | ||||
0.525586 | + | 0.850740i | \(0.323846\pi\) | |||||||
\(252\) | 2.10782 | 0.132780 | ||||||||
\(253\) | 17.8050 | 1.11939 | ||||||||
\(254\) | −24.6219 | −1.54491 | ||||||||
\(255\) | −1.84293 | −0.115409 | ||||||||
\(256\) | 8.49258 | 0.530786 | ||||||||
\(257\) | 17.5087 | 1.09216 | 0.546080 | − | 0.837733i | \(-0.316119\pi\) | ||||
0.546080 | + | 0.837733i | \(0.316119\pi\) | |||||||
\(258\) | 11.9794 | 0.745803 | ||||||||
\(259\) | 14.2816 | 0.887417 | ||||||||
\(260\) | 2.09081 | 0.129667 | ||||||||
\(261\) | −0.0652298 | −0.00403762 | ||||||||
\(262\) | 16.1637 | 0.998599 | ||||||||
\(263\) | −17.0874 | −1.05366 | −0.526829 | − | 0.849972i | \(-0.676619\pi\) | ||||
−0.526829 | + | 0.849972i | \(0.676619\pi\) | |||||||
\(264\) | −4.05901 | −0.249815 | ||||||||
\(265\) | 4.16397 | 0.255791 | ||||||||
\(266\) | −10.7455 | −0.658848 | ||||||||
\(267\) | −6.14930 | −0.376331 | ||||||||
\(268\) | −28.3964 | −1.73459 | ||||||||
\(269\) | −22.4341 | −1.36783 | −0.683916 | − | 0.729561i | \(-0.739724\pi\) | ||||
−0.683916 | + | 0.729561i | \(0.739724\pi\) | |||||||
\(270\) | −10.4142 | −0.633787 | ||||||||
\(271\) | −4.21022 | −0.255753 | −0.127876 | − | 0.991790i | \(-0.540816\pi\) | ||||
−0.127876 | + | 0.991790i | \(0.540816\pi\) | |||||||
\(272\) | −3.11567 | −0.188915 | ||||||||
\(273\) | −4.70603 | −0.284822 | ||||||||
\(274\) | 15.5730 | 0.940800 | ||||||||
\(275\) | 11.3860 | 0.686602 | ||||||||
\(276\) | 26.7493 | 1.61012 | ||||||||
\(277\) | 27.1206 | 1.62952 | 0.814759 | − | 0.579800i | \(-0.196869\pi\) | ||||
0.814759 | + | 0.579800i | \(0.196869\pi\) | |||||||
\(278\) | −22.7333 | −1.36345 | ||||||||
\(279\) | 1.78277 | 0.106731 | ||||||||
\(280\) | −2.36068 | −0.141078 | ||||||||
\(281\) | 9.15554 | 0.546174 | 0.273087 | − | 0.961989i | \(-0.411955\pi\) | ||||
0.273087 | + | 0.961989i | \(0.411955\pi\) | |||||||
\(282\) | −42.9593 | −2.55819 | ||||||||
\(283\) | 27.0950 | 1.61063 | 0.805314 | − | 0.592849i | \(-0.201997\pi\) | ||||
0.805314 | + | 0.592849i | \(0.201997\pi\) | |||||||
\(284\) | −13.8458 | −0.821595 | ||||||||
\(285\) | −3.17301 | −0.187953 | ||||||||
\(286\) | 5.20732 | 0.307916 | ||||||||
\(287\) | 29.7477 | 1.75595 | ||||||||
\(288\) | 2.40319 | 0.141609 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0.465077 | 0.0273102 | ||||||||
\(291\) | −9.91207 | −0.581056 | ||||||||
\(292\) | −31.9189 | −1.86791 | ||||||||
\(293\) | −0.0277554 | −0.00162149 | −0.000810745 | − | 1.00000i | \(-0.500258\pi\) | ||||
−0.000810745 | 1.00000i | \(0.500258\pi\) | ||||||||
\(294\) | 7.24484 | 0.422528 | ||||||||
\(295\) | −12.4180 | −0.723005 | ||||||||
\(296\) | −3.72936 | −0.216765 | ||||||||
\(297\) | −14.0740 | −0.816658 | ||||||||
\(298\) | 29.8281 | 1.72790 | ||||||||
\(299\) | −5.39053 | −0.311742 | ||||||||
\(300\) | 17.1058 | 0.987604 | ||||||||
\(301\) | 9.41551 | 0.542701 | ||||||||
\(302\) | 10.4806 | 0.603093 | ||||||||
\(303\) | −0.789780 | −0.0453717 | ||||||||
\(304\) | −5.36433 | −0.307665 | ||||||||
\(305\) | 3.71233 | 0.212567 | ||||||||
\(306\) | −0.622412 | −0.0355809 | ||||||||
\(307\) | −27.8195 | −1.58774 | −0.793871 | − | 0.608086i | \(-0.791938\pi\) | ||||
−0.793871 | + | 0.608086i | \(0.791938\pi\) | |||||||
\(308\) | −20.3098 | −1.15726 | ||||||||
\(309\) | 2.08227 | 0.118456 | ||||||||
\(310\) | −12.7108 | −0.721925 | ||||||||
\(311\) | −1.57795 | −0.0894775 | −0.0447387 | − | 0.998999i | \(-0.514246\pi\) | ||||
−0.0447387 | + | 0.998999i | \(0.514246\pi\) | |||||||
\(312\) | 1.22888 | 0.0695719 | ||||||||
\(313\) | 24.4018 | 1.37927 | 0.689636 | − | 0.724156i | \(-0.257771\pi\) | ||||
0.689636 | + | 0.724156i | \(0.257771\pi\) | |||||||
\(314\) | 3.89549 | 0.219835 | ||||||||
\(315\) | 0.901563 | 0.0507973 | ||||||||
\(316\) | 22.3044 | 1.25472 | ||||||||
\(317\) | 23.1314 | 1.29919 | 0.649594 | − | 0.760281i | \(-0.274939\pi\) | ||||
0.649594 | + | 0.760281i | \(0.274939\pi\) | |||||||
\(318\) | 15.5804 | 0.873706 | ||||||||
\(319\) | 0.628518 | 0.0351903 | ||||||||
\(320\) | −10.8104 | −0.604317 | ||||||||
\(321\) | −16.3234 | −0.911082 | ||||||||
\(322\) | 38.7462 | 2.15924 | ||||||||
\(323\) | 1.72172 | 0.0957993 | ||||||||
\(324\) | −23.2629 | −1.29238 | ||||||||
\(325\) | −3.44716 | −0.191214 | ||||||||
\(326\) | 27.9749 | 1.54939 | ||||||||
\(327\) | −13.6293 | −0.753704 | ||||||||
\(328\) | −7.76801 | −0.428917 | ||||||||
\(329\) | −33.7650 | −1.86153 | ||||||||
\(330\) | −11.0524 | −0.608416 | ||||||||
\(331\) | 23.1059 | 1.27001 | 0.635007 | − | 0.772507i | \(-0.280997\pi\) | ||||
0.635007 | + | 0.772507i | \(0.280997\pi\) | |||||||
\(332\) | −29.5604 | −1.62234 | ||||||||
\(333\) | 1.42427 | 0.0780496 | ||||||||
\(334\) | −10.0628 | −0.550610 | ||||||||
\(335\) | −12.1458 | −0.663595 | ||||||||
\(336\) | 16.8866 | 0.921238 | ||||||||
\(337\) | 22.1749 | 1.20794 | 0.603971 | − | 0.797006i | \(-0.293584\pi\) | ||||
0.603971 | + | 0.797006i | \(0.293584\pi\) | |||||||
\(338\) | 25.6078 | 1.39288 | ||||||||
\(339\) | −21.2249 | −1.15278 | ||||||||
\(340\) | 2.40797 | 0.130590 | ||||||||
\(341\) | −17.1777 | −0.930227 | ||||||||
\(342\) | −1.07162 | −0.0579467 | ||||||||
\(343\) | −15.1980 | −0.820613 | ||||||||
\(344\) | −2.45867 | −0.132563 | ||||||||
\(345\) | 11.4413 | 0.615978 | ||||||||
\(346\) | −40.2767 | −2.16529 | ||||||||
\(347\) | −33.2416 | −1.78450 | −0.892251 | − | 0.451541i | \(-0.850875\pi\) | ||||
−0.892251 | + | 0.451541i | \(0.850875\pi\) | |||||||
\(348\) | 0.944256 | 0.0506174 | ||||||||
\(349\) | −24.9642 | −1.33630 | −0.668152 | − | 0.744025i | \(-0.732914\pi\) | ||||
−0.668152 | + | 0.744025i | \(0.732914\pi\) | |||||||
\(350\) | 24.7776 | 1.32442 | ||||||||
\(351\) | 4.26098 | 0.227434 | ||||||||
\(352\) | −23.1558 | −1.23421 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | −46.4648 | −2.46958 | ||||||||
\(355\) | −5.92214 | −0.314315 | ||||||||
\(356\) | 8.03467 | 0.425837 | ||||||||
\(357\) | −5.41988 | −0.286850 | ||||||||
\(358\) | 23.8367 | 1.25981 | ||||||||
\(359\) | −5.77716 | −0.304907 | −0.152453 | − | 0.988311i | \(-0.548717\pi\) | ||||
−0.152453 | + | 0.988311i | \(0.548717\pi\) | |||||||
\(360\) | −0.235425 | −0.0124080 | ||||||||
\(361\) | −16.0357 | −0.843982 | ||||||||
\(362\) | −0.162968 | −0.00856541 | ||||||||
\(363\) | 5.03879 | 0.264468 | ||||||||
\(364\) | 6.14889 | 0.322289 | ||||||||
\(365\) | −13.6524 | −0.714600 | ||||||||
\(366\) | 13.8905 | 0.726068 | ||||||||
\(367\) | 32.5860 | 1.70098 | 0.850488 | − | 0.525994i | \(-0.176307\pi\) | ||||
0.850488 | + | 0.525994i | \(0.176307\pi\) | |||||||
\(368\) | 19.3428 | 1.00831 | ||||||||
\(369\) | 2.96667 | 0.154439 | ||||||||
\(370\) | −10.1548 | −0.527923 | ||||||||
\(371\) | 12.2458 | 0.635772 | ||||||||
\(372\) | −25.8070 | −1.33803 | ||||||||
\(373\) | −7.80508 | −0.404132 | −0.202066 | − | 0.979372i | \(-0.564766\pi\) | ||||
−0.202066 | + | 0.979372i | \(0.564766\pi\) | |||||||
\(374\) | 5.99722 | 0.310109 | ||||||||
\(375\) | 16.5312 | 0.853666 | ||||||||
\(376\) | 8.81706 | 0.454705 | ||||||||
\(377\) | −0.190287 | −0.00980026 | ||||||||
\(378\) | −30.6271 | −1.57529 | ||||||||
\(379\) | 16.5589 | 0.850574 | 0.425287 | − | 0.905058i | \(-0.360173\pi\) | ||||
0.425287 | + | 0.905058i | \(0.360173\pi\) | |||||||
\(380\) | 4.14585 | 0.212678 | ||||||||
\(381\) | −21.3820 | −1.09543 | ||||||||
\(382\) | −54.1543 | −2.77078 | ||||||||
\(383\) | 18.8729 | 0.964359 | 0.482180 | − | 0.876072i | \(-0.339845\pi\) | ||||
0.482180 | + | 0.876072i | \(0.339845\pi\) | |||||||
\(384\) | −11.1257 | −0.567758 | ||||||||
\(385\) | −8.68696 | −0.442728 | ||||||||
\(386\) | 39.1648 | 1.99343 | ||||||||
\(387\) | 0.938986 | 0.0477313 | ||||||||
\(388\) | 12.9511 | 0.657492 | ||||||||
\(389\) | 4.08555 | 0.207145 | 0.103573 | − | 0.994622i | \(-0.466973\pi\) | ||||
0.103573 | + | 0.994622i | \(0.466973\pi\) | |||||||
\(390\) | 3.34617 | 0.169440 | ||||||||
\(391\) | −6.20821 | −0.313963 | ||||||||
\(392\) | −1.48695 | −0.0751022 | ||||||||
\(393\) | 14.0368 | 0.708064 | ||||||||
\(394\) | 26.4731 | 1.33369 | ||||||||
\(395\) | 9.54008 | 0.480014 | ||||||||
\(396\) | −2.02545 | −0.101783 | ||||||||
\(397\) | −2.99310 | −0.150219 | −0.0751097 | − | 0.997175i | \(-0.523931\pi\) | ||||
−0.0751097 | + | 0.997175i | \(0.523931\pi\) | |||||||
\(398\) | −53.9016 | −2.70184 | ||||||||
\(399\) | −9.33153 | −0.467161 | ||||||||
\(400\) | 12.3694 | 0.618470 | ||||||||
\(401\) | −19.8881 | −0.993166 | −0.496583 | − | 0.867989i | \(-0.665412\pi\) | ||||
−0.496583 | + | 0.867989i | \(0.665412\pi\) | |||||||
\(402\) | −45.4461 | −2.26665 | ||||||||
\(403\) | 5.20064 | 0.259062 | ||||||||
\(404\) | 1.03193 | 0.0513402 | ||||||||
\(405\) | −9.95004 | −0.494421 | ||||||||
\(406\) | 1.36775 | 0.0678801 | ||||||||
\(407\) | −13.7235 | −0.680248 | ||||||||
\(408\) | 1.41529 | 0.0700674 | ||||||||
\(409\) | −19.8486 | −0.981451 | −0.490725 | − | 0.871314i | \(-0.663268\pi\) | ||||
−0.490725 | + | 0.871314i | \(0.663268\pi\) | |||||||
\(410\) | −21.1518 | −1.04461 | ||||||||
\(411\) | 13.5238 | 0.667081 | ||||||||
\(412\) | −2.72070 | −0.134039 | ||||||||
\(413\) | −36.5203 | −1.79704 | ||||||||
\(414\) | 3.86406 | 0.189908 | ||||||||
\(415\) | −12.6436 | −0.620651 | ||||||||
\(416\) | 7.01052 | 0.343719 | ||||||||
\(417\) | −19.7419 | −0.966765 | ||||||||
\(418\) | 10.3256 | 0.505039 | ||||||||
\(419\) | −16.2220 | −0.792498 | −0.396249 | − | 0.918143i | \(-0.629688\pi\) | ||||
−0.396249 | + | 0.918143i | \(0.629688\pi\) | |||||||
\(420\) | −13.0509 | −0.636817 | ||||||||
\(421\) | 8.91700 | 0.434588 | 0.217294 | − | 0.976106i | \(-0.430277\pi\) | ||||
0.217294 | + | 0.976106i | \(0.430277\pi\) | |||||||
\(422\) | 25.4075 | 1.23682 | ||||||||
\(423\) | −3.36731 | −0.163724 | ||||||||
\(424\) | −3.19776 | −0.155297 | ||||||||
\(425\) | −3.97006 | −0.192576 | ||||||||
\(426\) | −22.1590 | −1.07361 | ||||||||
\(427\) | 10.9176 | 0.528340 | ||||||||
\(428\) | 21.3281 | 1.03093 | ||||||||
\(429\) | 4.52211 | 0.218330 | ||||||||
\(430\) | −6.69480 | −0.322852 | ||||||||
\(431\) | −35.5417 | −1.71198 | −0.855992 | − | 0.516988i | \(-0.827053\pi\) | ||||
−0.855992 | + | 0.516988i | \(0.827053\pi\) | |||||||
\(432\) | −15.2896 | −0.735621 | ||||||||
\(433\) | 22.5134 | 1.08193 | 0.540963 | − | 0.841047i | \(-0.318060\pi\) | ||||
0.540963 | + | 0.841047i | \(0.318060\pi\) | |||||||
\(434\) | −37.3813 | −1.79436 | ||||||||
\(435\) | 0.403879 | 0.0193645 | ||||||||
\(436\) | 17.8081 | 0.852852 | ||||||||
\(437\) | −10.6888 | −0.511316 | ||||||||
\(438\) | −51.0835 | −2.44086 | ||||||||
\(439\) | −37.9037 | −1.80904 | −0.904522 | − | 0.426428i | \(-0.859772\pi\) | ||||
−0.904522 | + | 0.426428i | \(0.859772\pi\) | |||||||
\(440\) | 2.26842 | 0.108143 | ||||||||
\(441\) | 0.567877 | 0.0270418 | ||||||||
\(442\) | −1.81568 | −0.0863633 | ||||||||
\(443\) | 2.51325 | 0.119408 | 0.0597040 | − | 0.998216i | \(-0.480984\pi\) | ||||
0.0597040 | + | 0.998216i | \(0.480984\pi\) | |||||||
\(444\) | −20.6175 | −0.978465 | ||||||||
\(445\) | 3.43661 | 0.162911 | ||||||||
\(446\) | −15.3182 | −0.725339 | ||||||||
\(447\) | 25.9032 | 1.22518 | ||||||||
\(448\) | −31.7922 | −1.50204 | ||||||||
\(449\) | −41.4836 | −1.95773 | −0.978865 | − | 0.204507i | \(-0.934441\pi\) | ||||
−0.978865 | + | 0.204507i | \(0.934441\pi\) | |||||||
\(450\) | 2.47101 | 0.116485 | ||||||||
\(451\) | −28.5852 | −1.34602 | ||||||||
\(452\) | 27.7324 | 1.30442 | ||||||||
\(453\) | 9.10153 | 0.427627 | ||||||||
\(454\) | −14.8579 | −0.697318 | ||||||||
\(455\) | 2.63001 | 0.123297 | ||||||||
\(456\) | 2.43674 | 0.114111 | ||||||||
\(457\) | 30.2560 | 1.41532 | 0.707659 | − | 0.706555i | \(-0.249752\pi\) | ||||
0.707659 | + | 0.706555i | \(0.249752\pi\) | |||||||
\(458\) | 23.2567 | 1.08671 | ||||||||
\(459\) | 4.90732 | 0.229054 | ||||||||
\(460\) | −14.9492 | −0.697008 | ||||||||
\(461\) | 39.6776 | 1.84797 | 0.923986 | − | 0.382427i | \(-0.124911\pi\) | ||||
0.923986 | + | 0.382427i | \(0.124911\pi\) | |||||||
\(462\) | −32.5042 | −1.51223 | ||||||||
\(463\) | −10.7520 | −0.499686 | −0.249843 | − | 0.968286i | \(-0.580379\pi\) | ||||
−0.249843 | + | 0.968286i | \(0.580379\pi\) | |||||||
\(464\) | 0.682802 | 0.0316983 | ||||||||
\(465\) | −11.0382 | −0.511886 | ||||||||
\(466\) | 60.9813 | 2.82491 | ||||||||
\(467\) | 6.51316 | 0.301393 | 0.150696 | − | 0.988580i | \(-0.451848\pi\) | ||||
0.150696 | + | 0.988580i | \(0.451848\pi\) | |||||||
\(468\) | 0.613214 | 0.0283458 | ||||||||
\(469\) | −35.7196 | −1.64938 | ||||||||
\(470\) | 24.0083 | 1.10742 | ||||||||
\(471\) | 3.38290 | 0.155876 | ||||||||
\(472\) | 9.53653 | 0.438954 | ||||||||
\(473\) | −9.04755 | −0.416007 | ||||||||
\(474\) | 35.6963 | 1.63959 | ||||||||
\(475\) | −6.83535 | −0.313627 | ||||||||
\(476\) | 7.08160 | 0.324585 | ||||||||
\(477\) | 1.22125 | 0.0559171 | ||||||||
\(478\) | 47.8787 | 2.18992 | ||||||||
\(479\) | 7.54319 | 0.344657 | 0.172329 | − | 0.985040i | \(-0.444871\pi\) | ||||
0.172329 | + | 0.985040i | \(0.444871\pi\) | |||||||
\(480\) | −14.8797 | −0.679161 | ||||||||
\(481\) | 4.15485 | 0.189445 | ||||||||
\(482\) | −6.60387 | −0.300798 | ||||||||
\(483\) | 33.6477 | 1.53103 | ||||||||
\(484\) | −6.58368 | −0.299258 | ||||||||
\(485\) | 5.53947 | 0.251534 | ||||||||
\(486\) | −6.44516 | −0.292359 | ||||||||
\(487\) | −34.5474 | −1.56549 | −0.782747 | − | 0.622340i | \(-0.786182\pi\) | ||||
−0.782747 | + | 0.622340i | \(0.786182\pi\) | |||||||
\(488\) | −2.85092 | −0.129055 | ||||||||
\(489\) | 24.2938 | 1.09860 | ||||||||
\(490\) | −4.04886 | −0.182909 | ||||||||
\(491\) | 5.75212 | 0.259589 | 0.129795 | − | 0.991541i | \(-0.458568\pi\) | ||||
0.129795 | + | 0.991541i | \(0.458568\pi\) | |||||||
\(492\) | −42.9450 | −1.93611 | ||||||||
\(493\) | −0.219151 | −0.00987006 | ||||||||
\(494\) | −3.12611 | −0.140650 | ||||||||
\(495\) | −0.866329 | −0.0389386 | ||||||||
\(496\) | −18.6614 | −0.837920 | ||||||||
\(497\) | −17.4165 | −0.781235 | ||||||||
\(498\) | −47.3089 | −2.11996 | ||||||||
\(499\) | −27.6169 | −1.23630 | −0.618151 | − | 0.786059i | \(-0.712118\pi\) | ||||
−0.618151 | + | 0.786059i | \(0.712118\pi\) | |||||||
\(500\) | −21.5996 | −0.965963 | ||||||||
\(501\) | −8.73864 | −0.390414 | ||||||||
\(502\) | −34.8246 | −1.55430 | ||||||||
\(503\) | 4.01701 | 0.179110 | 0.0895548 | − | 0.995982i | \(-0.471456\pi\) | ||||
0.0895548 | + | 0.995982i | \(0.471456\pi\) | |||||||
\(504\) | −0.692363 | −0.0308403 | ||||||||
\(505\) | 0.441377 | 0.0196410 | ||||||||
\(506\) | −37.2320 | −1.65516 | ||||||||
\(507\) | 22.2382 | 0.987632 | ||||||||
\(508\) | 27.9377 | 1.23953 | ||||||||
\(509\) | −17.0152 | −0.754184 | −0.377092 | − | 0.926176i | \(-0.623076\pi\) | ||||
−0.377092 | + | 0.926176i | \(0.623076\pi\) | |||||||
\(510\) | 3.85375 | 0.170647 | ||||||||
\(511\) | −40.1505 | −1.77615 | ||||||||
\(512\) | −30.0123 | −1.32637 | ||||||||
\(513\) | 8.44905 | 0.373035 | ||||||||
\(514\) | −36.6124 | −1.61490 | ||||||||
\(515\) | −1.16370 | −0.0512789 | ||||||||
\(516\) | −13.5926 | −0.598381 | ||||||||
\(517\) | 32.4455 | 1.42695 | ||||||||
\(518\) | −29.8643 | −1.31216 | ||||||||
\(519\) | −34.9769 | −1.53531 | ||||||||
\(520\) | −0.686775 | −0.0301171 | ||||||||
\(521\) | −4.25927 | −0.186602 | −0.0933009 | − | 0.995638i | \(-0.529742\pi\) | ||||
−0.0933009 | + | 0.995638i | \(0.529742\pi\) | |||||||
\(522\) | 0.136402 | 0.00597016 | ||||||||
\(523\) | −36.2561 | −1.58537 | −0.792684 | − | 0.609633i | \(-0.791317\pi\) | ||||
−0.792684 | + | 0.609633i | \(0.791317\pi\) | |||||||
\(524\) | −18.3405 | −0.801208 | ||||||||
\(525\) | 21.5172 | 0.939089 | ||||||||
\(526\) | 35.7316 | 1.55797 | ||||||||
\(527\) | 5.98951 | 0.260907 | ||||||||
\(528\) | −16.2266 | −0.706174 | ||||||||
\(529\) | 15.5419 | 0.675734 | ||||||||
\(530\) | −8.70728 | −0.378220 | ||||||||
\(531\) | −3.64208 | −0.158053 | ||||||||
\(532\) | 12.1926 | 0.528615 | ||||||||
\(533\) | 8.65428 | 0.374859 | ||||||||
\(534\) | 12.8588 | 0.556456 | ||||||||
\(535\) | 9.12250 | 0.394400 | ||||||||
\(536\) | 9.32746 | 0.402885 | ||||||||
\(537\) | 20.7001 | 0.893277 | ||||||||
\(538\) | 46.9120 | 2.02252 | ||||||||
\(539\) | −5.47175 | −0.235685 | ||||||||
\(540\) | 11.8166 | 0.508508 | ||||||||
\(541\) | −29.7495 | −1.27903 | −0.639516 | − | 0.768778i | \(-0.720865\pi\) | ||||
−0.639516 | + | 0.768778i | \(0.720865\pi\) | |||||||
\(542\) | 8.80400 | 0.378164 | ||||||||
\(543\) | −0.141524 | −0.00607337 | ||||||||
\(544\) | 8.07393 | 0.346167 | ||||||||
\(545\) | 7.61691 | 0.326272 | ||||||||
\(546\) | 9.84078 | 0.421147 | ||||||||
\(547\) | 34.0493 | 1.45584 | 0.727922 | − | 0.685660i | \(-0.240486\pi\) | ||||
0.727922 | + | 0.685660i | \(0.240486\pi\) | |||||||
\(548\) | −17.6702 | −0.754834 | ||||||||
\(549\) | 1.08879 | 0.0464683 | ||||||||
\(550\) | −23.8093 | −1.01523 | ||||||||
\(551\) | −0.377317 | −0.0160743 | ||||||||
\(552\) | −8.78643 | −0.373975 | ||||||||
\(553\) | 28.0565 | 1.19308 | ||||||||
\(554\) | −56.7119 | −2.40946 | ||||||||
\(555\) | −8.81857 | −0.374328 | ||||||||
\(556\) | 25.7947 | 1.09394 | ||||||||
\(557\) | −33.7253 | −1.42899 | −0.714493 | − | 0.699643i | \(-0.753342\pi\) | ||||
−0.714493 | + | 0.699643i | \(0.753342\pi\) | |||||||
\(558\) | −3.72794 | −0.157816 | ||||||||
\(559\) | 2.73918 | 0.115855 | ||||||||
\(560\) | −9.43724 | −0.398796 | ||||||||
\(561\) | 5.20807 | 0.219885 | ||||||||
\(562\) | −19.1452 | −0.807591 | ||||||||
\(563\) | −12.2703 | −0.517131 | −0.258566 | − | 0.965994i | \(-0.583250\pi\) | ||||
−0.258566 | + | 0.965994i | \(0.583250\pi\) | |||||||
\(564\) | 48.7446 | 2.05252 | ||||||||
\(565\) | 11.8617 | 0.499028 | ||||||||
\(566\) | −56.6583 | −2.38153 | ||||||||
\(567\) | −29.2621 | −1.22889 | ||||||||
\(568\) | 4.54796 | 0.190828 | ||||||||
\(569\) | −10.4652 | −0.438723 | −0.219362 | − | 0.975644i | \(-0.570397\pi\) | ||||
−0.219362 | + | 0.975644i | \(0.570397\pi\) | |||||||
\(570\) | 6.63509 | 0.277913 | ||||||||
\(571\) | −24.5470 | −1.02726 | −0.513631 | − | 0.858011i | \(-0.671700\pi\) | ||||
−0.513631 | + | 0.858011i | \(0.671700\pi\) | |||||||
\(572\) | −5.90859 | −0.247050 | ||||||||
\(573\) | −47.0284 | −1.96464 | ||||||||
\(574\) | −62.2055 | −2.59641 | ||||||||
\(575\) | 24.6470 | 1.02785 | ||||||||
\(576\) | −3.17056 | −0.132107 | ||||||||
\(577\) | −33.0579 | −1.37622 | −0.688109 | − | 0.725608i | \(-0.741559\pi\) | ||||
−0.688109 | + | 0.725608i | \(0.741559\pi\) | |||||||
\(578\) | −2.09110 | −0.0869784 | ||||||||
\(579\) | 34.0112 | 1.41346 | ||||||||
\(580\) | −0.527708 | −0.0219119 | ||||||||
\(581\) | −37.1837 | −1.54264 | ||||||||
\(582\) | 20.7272 | 0.859168 | ||||||||
\(583\) | −11.7673 | −0.487351 | ||||||||
\(584\) | 10.4845 | 0.433851 | ||||||||
\(585\) | 0.262285 | 0.0108442 | ||||||||
\(586\) | 0.0580394 | 0.00239759 | ||||||||
\(587\) | −4.57179 | −0.188698 | −0.0943489 | − | 0.995539i | \(-0.530077\pi\) | ||||
−0.0943489 | + | 0.995539i | \(0.530077\pi\) | |||||||
\(588\) | −8.22050 | −0.339008 | ||||||||
\(589\) | 10.3123 | 0.424911 | ||||||||
\(590\) | 25.9674 | 1.06906 | ||||||||
\(591\) | 22.9896 | 0.945666 | ||||||||
\(592\) | −14.9088 | −0.612747 | ||||||||
\(593\) | 5.36899 | 0.220478 | 0.110239 | − | 0.993905i | \(-0.464838\pi\) | ||||
0.110239 | + | 0.993905i | \(0.464838\pi\) | |||||||
\(594\) | 29.4302 | 1.20754 | ||||||||
\(595\) | 3.02896 | 0.124175 | ||||||||
\(596\) | −33.8450 | −1.38635 | ||||||||
\(597\) | −46.8089 | −1.91576 | ||||||||
\(598\) | 11.2721 | 0.460952 | ||||||||
\(599\) | −0.612818 | −0.0250391 | −0.0125195 | − | 0.999922i | \(-0.503985\pi\) | ||||
−0.0125195 | + | 0.999922i | \(0.503985\pi\) | |||||||
\(600\) | −5.61879 | −0.229386 | ||||||||
\(601\) | −9.75933 | −0.398091 | −0.199046 | − | 0.979990i | \(-0.563784\pi\) | ||||
−0.199046 | + | 0.979990i | \(0.563784\pi\) | |||||||
\(602\) | −19.6888 | −0.802455 | ||||||||
\(603\) | −3.56223 | −0.145065 | ||||||||
\(604\) | −11.8920 | −0.483880 | ||||||||
\(605\) | −2.81598 | −0.114486 | ||||||||
\(606\) | 1.65151 | 0.0670880 | ||||||||
\(607\) | 6.89616 | 0.279906 | 0.139953 | − | 0.990158i | \(-0.455305\pi\) | ||||
0.139953 | + | 0.990158i | \(0.455305\pi\) | |||||||
\(608\) | 13.9011 | 0.563763 | ||||||||
\(609\) | 1.18777 | 0.0481309 | ||||||||
\(610\) | −7.76286 | −0.314309 | ||||||||
\(611\) | −9.82302 | −0.397397 | ||||||||
\(612\) | 0.706231 | 0.0285477 | ||||||||
\(613\) | −15.3003 | −0.617973 | −0.308987 | − | 0.951066i | \(-0.599990\pi\) | ||||
−0.308987 | + | 0.951066i | \(0.599990\pi\) | |||||||
\(614\) | 58.1734 | 2.34769 | ||||||||
\(615\) | −18.3685 | −0.740690 | ||||||||
\(616\) | 6.67122 | 0.268791 | ||||||||
\(617\) | −21.0660 | −0.848085 | −0.424042 | − | 0.905642i | \(-0.639389\pi\) | ||||
−0.424042 | + | 0.905642i | \(0.639389\pi\) | |||||||
\(618\) | −4.35425 | −0.175154 | ||||||||
\(619\) | −40.4684 | −1.62656 | −0.813281 | − | 0.581871i | \(-0.802321\pi\) | ||||
−0.813281 | + | 0.581871i | \(0.802321\pi\) | |||||||
\(620\) | 14.4225 | 0.579223 | ||||||||
\(621\) | −30.4657 | −1.22254 | ||||||||
\(622\) | 3.29966 | 0.132304 | ||||||||
\(623\) | 10.1067 | 0.404918 | ||||||||
\(624\) | 4.91269 | 0.196665 | ||||||||
\(625\) | 10.6117 | 0.424467 | ||||||||
\(626\) | −51.0267 | −2.03944 | ||||||||
\(627\) | 8.96686 | 0.358102 | ||||||||
\(628\) | −4.42009 | −0.176381 | ||||||||
\(629\) | 4.78509 | 0.190794 | ||||||||
\(630\) | −1.88526 | −0.0751105 | ||||||||
\(631\) | −6.58365 | −0.262091 | −0.131045 | − | 0.991376i | \(-0.541833\pi\) | ||||
−0.131045 | + | 0.991376i | \(0.541833\pi\) | |||||||
\(632\) | −7.32639 | −0.291428 | ||||||||
\(633\) | 22.0642 | 0.876974 | ||||||||
\(634\) | −48.3701 | −1.92102 | ||||||||
\(635\) | 11.9496 | 0.474204 | ||||||||
\(636\) | −17.6786 | −0.701002 | ||||||||
\(637\) | 1.65660 | 0.0656367 | ||||||||
\(638\) | −1.31430 | −0.0520334 | ||||||||
\(639\) | −1.73690 | −0.0687108 | ||||||||
\(640\) | 6.21774 | 0.245778 | ||||||||
\(641\) | 0.415617 | 0.0164159 | 0.00820795 | − | 0.999966i | \(-0.497387\pi\) | ||||
0.00820795 | + | 0.999966i | \(0.497387\pi\) | |||||||
\(642\) | 34.1338 | 1.34716 | ||||||||
\(643\) | −11.8308 | −0.466560 | −0.233280 | − | 0.972410i | \(-0.574946\pi\) | ||||
−0.233280 | + | 0.972410i | \(0.574946\pi\) | |||||||
\(644\) | −43.9641 | −1.73243 | ||||||||
\(645\) | −5.81386 | −0.228921 | ||||||||
\(646\) | −3.60030 | −0.141652 | ||||||||
\(647\) | −19.6497 | −0.772510 | −0.386255 | − | 0.922392i | \(-0.626232\pi\) | ||||
−0.386255 | + | 0.922392i | \(0.626232\pi\) | |||||||
\(648\) | 7.64122 | 0.300175 | ||||||||
\(649\) | 35.0930 | 1.37752 | ||||||||
\(650\) | 7.20837 | 0.282736 | ||||||||
\(651\) | −32.4624 | −1.27230 | ||||||||
\(652\) | −31.7422 | −1.24312 | ||||||||
\(653\) | 4.94129 | 0.193368 | 0.0966838 | − | 0.995315i | \(-0.469176\pi\) | ||||
0.0966838 | + | 0.995315i | \(0.469176\pi\) | |||||||
\(654\) | 28.5003 | 1.11445 | ||||||||
\(655\) | −7.84463 | −0.306515 | ||||||||
\(656\) | −31.0540 | −1.21246 | ||||||||
\(657\) | −4.00411 | −0.156215 | ||||||||
\(658\) | 70.6062 | 2.75251 | ||||||||
\(659\) | −26.9771 | −1.05088 | −0.525439 | − | 0.850831i | \(-0.676099\pi\) | ||||
−0.525439 | + | 0.850831i | \(0.676099\pi\) | |||||||
\(660\) | 12.5408 | 0.488152 | ||||||||
\(661\) | 23.6325 | 0.919196 | 0.459598 | − | 0.888127i | \(-0.347993\pi\) | ||||
0.459598 | + | 0.888127i | \(0.347993\pi\) | |||||||
\(662\) | −48.3167 | −1.87788 | ||||||||
\(663\) | −1.57677 | −0.0612365 | ||||||||
\(664\) | 9.70978 | 0.376813 | ||||||||
\(665\) | 5.21503 | 0.202230 | ||||||||
\(666\) | −2.97830 | −0.115407 | ||||||||
\(667\) | 1.36053 | 0.0526801 | ||||||||
\(668\) | 11.4179 | 0.441772 | ||||||||
\(669\) | −13.3026 | −0.514307 | ||||||||
\(670\) | 25.3981 | 0.981213 | ||||||||
\(671\) | −10.4910 | −0.404999 | ||||||||
\(672\) | −43.7597 | −1.68807 | ||||||||
\(673\) | 16.3553 | 0.630452 | 0.315226 | − | 0.949017i | \(-0.397920\pi\) | ||||
0.315226 | + | 0.949017i | \(0.397920\pi\) | |||||||
\(674\) | −46.3699 | −1.78610 | ||||||||
\(675\) | −19.4823 | −0.749876 | ||||||||
\(676\) | −29.0564 | −1.11755 | ||||||||
\(677\) | 22.4546 | 0.863001 | 0.431500 | − | 0.902113i | \(-0.357984\pi\) | ||||
0.431500 | + | 0.902113i | \(0.357984\pi\) | |||||||
\(678\) | 44.3834 | 1.70453 | ||||||||
\(679\) | 16.2911 | 0.625194 | ||||||||
\(680\) | −0.790951 | −0.0303316 | ||||||||
\(681\) | −12.9028 | −0.494438 | ||||||||
\(682\) | 35.9204 | 1.37546 | ||||||||
\(683\) | −39.5745 | −1.51428 | −0.757138 | − | 0.653255i | \(-0.773403\pi\) | ||||
−0.757138 | + | 0.653255i | \(0.773403\pi\) | |||||||
\(684\) | 1.21594 | 0.0464925 | ||||||||
\(685\) | −7.55794 | −0.288774 | ||||||||
\(686\) | 31.7805 | 1.21339 | ||||||||
\(687\) | 20.1964 | 0.770541 | ||||||||
\(688\) | −9.82898 | −0.374726 | ||||||||
\(689\) | 3.56259 | 0.135724 | ||||||||
\(690\) | −23.9249 | −0.910805 | ||||||||
\(691\) | 31.7324 | 1.20716 | 0.603578 | − | 0.797304i | \(-0.293741\pi\) | ||||
0.603578 | + | 0.797304i | \(0.293741\pi\) | |||||||
\(692\) | 45.7007 | 1.73728 | ||||||||
\(693\) | −2.54779 | −0.0967827 | ||||||||
\(694\) | 69.5115 | 2.63862 | ||||||||
\(695\) | 11.0330 | 0.418505 | ||||||||
\(696\) | −0.310162 | −0.0117567 | ||||||||
\(697\) | 9.96704 | 0.377529 | ||||||||
\(698\) | 52.2027 | 1.97590 | ||||||||
\(699\) | 52.9571 | 2.00302 | ||||||||
\(700\) | −28.1144 | −1.06262 | ||||||||
\(701\) | −15.8612 | −0.599068 | −0.299534 | − | 0.954086i | \(-0.596831\pi\) | ||||
−0.299534 | + | 0.954086i | \(0.596831\pi\) | |||||||
\(702\) | −8.91013 | −0.336291 | ||||||||
\(703\) | 8.23861 | 0.310725 | ||||||||
\(704\) | 30.5498 | 1.15139 | ||||||||
\(705\) | 20.8491 | 0.785224 | ||||||||
\(706\) | −2.09110 | −0.0786997 | ||||||||
\(707\) | 1.29805 | 0.0488182 | ||||||||
\(708\) | 52.7221 | 1.98142 | ||||||||
\(709\) | 22.0290 | 0.827317 | 0.413658 | − | 0.910432i | \(-0.364251\pi\) | ||||
0.413658 | + | 0.910432i | \(0.364251\pi\) | |||||||
\(710\) | 12.3838 | 0.464756 | ||||||||
\(711\) | 2.79801 | 0.104933 | ||||||||
\(712\) | −2.63917 | −0.0989071 | ||||||||
\(713\) | −37.1842 | −1.39256 | ||||||||
\(714\) | 11.3335 | 0.424146 | ||||||||
\(715\) | −2.52723 | −0.0945132 | ||||||||
\(716\) | −27.0468 | −1.01079 | ||||||||
\(717\) | 41.5785 | 1.55278 | ||||||||
\(718\) | 12.0806 | 0.450845 | ||||||||
\(719\) | 3.09202 | 0.115313 | 0.0576564 | − | 0.998336i | \(-0.481637\pi\) | ||||
0.0576564 | + | 0.998336i | \(0.481637\pi\) | |||||||
\(720\) | −0.941154 | −0.0350747 | ||||||||
\(721\) | −3.42234 | −0.127455 | ||||||||
\(722\) | 33.5322 | 1.24794 | ||||||||
\(723\) | −5.73489 | −0.213283 | ||||||||
\(724\) | 0.184915 | 0.00687230 | ||||||||
\(725\) | 0.870042 | 0.0323126 | ||||||||
\(726\) | −10.5366 | −0.391051 | ||||||||
\(727\) | −49.1080 | −1.82131 | −0.910657 | − | 0.413164i | \(-0.864424\pi\) | ||||
−0.910657 | + | 0.413164i | \(0.864424\pi\) | |||||||
\(728\) | −2.01974 | −0.0748566 | ||||||||
\(729\) | 23.8160 | 0.882073 | ||||||||
\(730\) | 28.5486 | 1.05663 | ||||||||
\(731\) | 3.15469 | 0.116680 | ||||||||
\(732\) | −15.7611 | −0.582548 | ||||||||
\(733\) | 36.5012 | 1.34820 | 0.674101 | − | 0.738640i | \(-0.264531\pi\) | ||||
0.674101 | + | 0.738640i | \(0.264531\pi\) | |||||||
\(734\) | −68.1407 | −2.51512 | ||||||||
\(735\) | −3.51609 | −0.129693 | ||||||||
\(736\) | −50.1247 | −1.84762 | ||||||||
\(737\) | 34.3237 | 1.26433 | ||||||||
\(738\) | −6.20360 | −0.228358 | ||||||||
\(739\) | 42.5923 | 1.56678 | 0.783391 | − | 0.621529i | \(-0.213488\pi\) | ||||
0.783391 | + | 0.621529i | \(0.213488\pi\) | |||||||
\(740\) | 11.5223 | 0.423569 | ||||||||
\(741\) | −2.71476 | −0.0997290 | ||||||||
\(742\) | −25.6073 | −0.940074 | ||||||||
\(743\) | 25.5163 | 0.936104 | 0.468052 | − | 0.883701i | \(-0.344956\pi\) | ||||
0.468052 | + | 0.883701i | \(0.344956\pi\) | |||||||
\(744\) | 8.47691 | 0.310779 | ||||||||
\(745\) | −14.4763 | −0.530370 | ||||||||
\(746\) | 16.3212 | 0.597562 | ||||||||
\(747\) | −3.70824 | −0.135678 | ||||||||
\(748\) | −6.80485 | −0.248810 | ||||||||
\(749\) | 26.8284 | 0.980289 | ||||||||
\(750\) | −34.5684 | −1.26226 | ||||||||
\(751\) | 17.9162 | 0.653771 | 0.326886 | − | 0.945064i | \(-0.394001\pi\) | ||||
0.326886 | + | 0.945064i | \(0.394001\pi\) | |||||||
\(752\) | 35.2478 | 1.28536 | ||||||||
\(753\) | −30.2422 | −1.10209 | ||||||||
\(754\) | 0.397909 | 0.0144910 | ||||||||
\(755\) | −5.08649 | −0.185116 | ||||||||
\(756\) | 34.7517 | 1.26391 | ||||||||
\(757\) | −23.7269 | −0.862369 | −0.431185 | − | 0.902264i | \(-0.641904\pi\) | ||||
−0.431185 | + | 0.902264i | \(0.641904\pi\) | |||||||
\(758\) | −34.6264 | −1.25769 | ||||||||
\(759\) | −32.3328 | −1.17361 | ||||||||
\(760\) | −1.36180 | −0.0493977 | ||||||||
\(761\) | −15.7229 | −0.569953 | −0.284977 | − | 0.958534i | \(-0.591986\pi\) | ||||
−0.284977 | + | 0.958534i | \(0.591986\pi\) | |||||||
\(762\) | 44.7119 | 1.61974 | ||||||||
\(763\) | 22.4006 | 0.810957 | ||||||||
\(764\) | 61.4472 | 2.22308 | ||||||||
\(765\) | 0.302071 | 0.0109214 | ||||||||
\(766\) | −39.4651 | −1.42593 | ||||||||
\(767\) | −10.6246 | −0.383631 | ||||||||
\(768\) | −15.4220 | −0.556495 | ||||||||
\(769\) | 27.9600 | 1.00826 | 0.504131 | − | 0.863627i | \(-0.331813\pi\) | ||||
0.504131 | + | 0.863627i | \(0.331813\pi\) | |||||||
\(770\) | 18.1653 | 0.654633 | ||||||||
\(771\) | −31.7947 | −1.14506 | ||||||||
\(772\) | −44.4390 | −1.59940 | ||||||||
\(773\) | 45.1752 | 1.62484 | 0.812420 | − | 0.583073i | \(-0.198150\pi\) | ||||
0.812420 | + | 0.583073i | \(0.198150\pi\) | |||||||
\(774\) | −1.96352 | −0.0705771 | ||||||||
\(775\) | −23.7787 | −0.854157 | ||||||||
\(776\) | −4.25409 | −0.152713 | ||||||||
\(777\) | −25.9346 | −0.930399 | ||||||||
\(778\) | −8.54330 | −0.306292 | ||||||||
\(779\) | 17.1605 | 0.614839 | ||||||||
\(780\) | −3.79680 | −0.135947 | ||||||||
\(781\) | 16.7358 | 0.598855 | ||||||||
\(782\) | 12.9820 | 0.464235 | ||||||||
\(783\) | −1.07544 | −0.0384332 | ||||||||
\(784\) | −5.94434 | −0.212298 | ||||||||
\(785\) | −1.89057 | −0.0674774 | ||||||||
\(786\) | −29.3524 | −1.04697 | ||||||||
\(787\) | −27.7085 | −0.987702 | −0.493851 | − | 0.869547i | \(-0.664411\pi\) | ||||
−0.493851 | + | 0.869547i | \(0.664411\pi\) | |||||||
\(788\) | −30.0382 | −1.07007 | ||||||||
\(789\) | 31.0298 | 1.10469 | ||||||||
\(790\) | −19.9493 | −0.709764 | ||||||||
\(791\) | 34.8843 | 1.24034 | ||||||||
\(792\) | 0.665305 | 0.0236406 | ||||||||
\(793\) | 3.17618 | 0.112790 | ||||||||
\(794\) | 6.25888 | 0.222119 | ||||||||
\(795\) | −7.56153 | −0.268180 | ||||||||
\(796\) | 61.1605 | 2.16777 | ||||||||
\(797\) | 18.4155 | 0.652310 | 0.326155 | − | 0.945316i | \(-0.394247\pi\) | ||||
0.326155 | + | 0.945316i | \(0.394247\pi\) | |||||||
\(798\) | 19.5132 | 0.690759 | ||||||||
\(799\) | −11.3131 | −0.400227 | ||||||||
\(800\) | −32.0540 | −1.13328 | ||||||||
\(801\) | 1.00792 | 0.0356131 | ||||||||
\(802\) | 41.5881 | 1.46853 | ||||||||
\(803\) | 38.5814 | 1.36151 | ||||||||
\(804\) | 51.5663 | 1.81860 | ||||||||
\(805\) | −18.8044 | −0.662768 | ||||||||
\(806\) | −10.8751 | −0.383058 | ||||||||
\(807\) | 40.7390 | 1.43408 | ||||||||
\(808\) | −0.338959 | −0.0119246 | ||||||||
\(809\) | −11.8305 | −0.415939 | −0.207970 | − | 0.978135i | \(-0.566686\pi\) | ||||
−0.207970 | + | 0.978135i | \(0.566686\pi\) | |||||||
\(810\) | 20.8065 | 0.731067 | ||||||||
\(811\) | 39.1848 | 1.37597 | 0.687983 | − | 0.725727i | \(-0.258497\pi\) | ||||
0.687983 | + | 0.725727i | \(0.258497\pi\) | |||||||
\(812\) | −1.55194 | −0.0544624 | ||||||||
\(813\) | 7.64552 | 0.268140 | ||||||||
\(814\) | 28.6972 | 1.00584 | ||||||||
\(815\) | −13.5768 | −0.475576 | ||||||||
\(816\) | 5.65788 | 0.198066 | ||||||||
\(817\) | 5.43150 | 0.190024 | ||||||||
\(818\) | 41.5055 | 1.45121 | ||||||||
\(819\) | 0.771356 | 0.0269534 | ||||||||
\(820\) | 24.0003 | 0.838126 | ||||||||
\(821\) | −10.1772 | −0.355188 | −0.177594 | − | 0.984104i | \(-0.556831\pi\) | ||||
−0.177594 | + | 0.984104i | \(0.556831\pi\) | |||||||
\(822\) | −28.2797 | −0.986368 | ||||||||
\(823\) | −39.7117 | −1.38426 | −0.692131 | − | 0.721771i | \(-0.743328\pi\) | ||||
−0.692131 | + | 0.721771i | \(0.743328\pi\) | |||||||
\(824\) | 0.893675 | 0.0311327 | ||||||||
\(825\) | −20.6763 | −0.719858 | ||||||||
\(826\) | 76.3676 | 2.65717 | ||||||||
\(827\) | −0.717797 | −0.0249603 | −0.0124801 | − | 0.999922i | \(-0.503973\pi\) | ||||
−0.0124801 | + | 0.999922i | \(0.503973\pi\) | |||||||
\(828\) | −4.38443 | −0.152370 | ||||||||
\(829\) | −22.4349 | −0.779198 | −0.389599 | − | 0.920985i | \(-0.627386\pi\) | ||||
−0.389599 | + | 0.920985i | \(0.627386\pi\) | |||||||
\(830\) | 26.4391 | 0.917715 | ||||||||
\(831\) | −49.2494 | −1.70844 | ||||||||
\(832\) | −9.24909 | −0.320654 | ||||||||
\(833\) | 1.90788 | 0.0661042 | ||||||||
\(834\) | 41.2823 | 1.42949 | ||||||||
\(835\) | 4.88369 | 0.169007 | ||||||||
\(836\) | −11.7161 | −0.405209 | ||||||||
\(837\) | 29.3924 | 1.01595 | ||||||||
\(838\) | 33.9219 | 1.17181 | ||||||||
\(839\) | −9.96119 | −0.343898 | −0.171949 | − | 0.985106i | \(-0.555007\pi\) | ||||
−0.171949 | + | 0.985106i | \(0.555007\pi\) | |||||||
\(840\) | 4.28686 | 0.147911 | ||||||||
\(841\) | −28.9520 | −0.998344 | ||||||||
\(842\) | −18.6464 | −0.642596 | ||||||||
\(843\) | −16.6259 | −0.572628 | ||||||||
\(844\) | −28.8291 | −0.992338 | ||||||||
\(845\) | −12.4280 | −0.427538 | ||||||||
\(846\) | 7.04138 | 0.242088 | ||||||||
\(847\) | −8.28155 | −0.284557 | ||||||||
\(848\) | −12.7836 | −0.438991 | ||||||||
\(849\) | −49.2029 | −1.68864 | ||||||||
\(850\) | 8.30180 | 0.284749 | ||||||||
\(851\) | −29.7069 | −1.01834 | ||||||||
\(852\) | 25.1431 | 0.861389 | ||||||||
\(853\) | 3.62093 | 0.123978 | 0.0619891 | − | 0.998077i | \(-0.480256\pi\) | ||||
0.0619891 | + | 0.998077i | \(0.480256\pi\) | |||||||
\(854\) | −22.8298 | −0.781221 | ||||||||
\(855\) | 0.520082 | 0.0177864 | ||||||||
\(856\) | −7.00570 | −0.239450 | ||||||||
\(857\) | −7.33351 | −0.250508 | −0.125254 | − | 0.992125i | \(-0.539975\pi\) | ||||
−0.125254 | + | 0.992125i | \(0.539975\pi\) | |||||||
\(858\) | −9.45620 | −0.322829 | ||||||||
\(859\) | −48.8409 | −1.66643 | −0.833215 | − | 0.552950i | \(-0.813502\pi\) | ||||
−0.833215 | + | 0.552950i | \(0.813502\pi\) | |||||||
\(860\) | 7.59638 | 0.259034 | ||||||||
\(861\) | −54.0201 | −1.84100 | ||||||||
\(862\) | 74.3214 | 2.53140 | ||||||||
\(863\) | 20.6073 | 0.701479 | 0.350740 | − | 0.936473i | \(-0.385930\pi\) | ||||
0.350740 | + | 0.936473i | \(0.385930\pi\) | |||||||
\(864\) | 39.6213 | 1.34795 | ||||||||
\(865\) | 19.5472 | 0.664625 | ||||||||
\(866\) | −47.0778 | −1.59977 | ||||||||
\(867\) | −1.81594 | −0.0616726 | ||||||||
\(868\) | 42.4154 | 1.43967 | ||||||||
\(869\) | −26.9600 | −0.914557 | ||||||||
\(870\) | −0.844552 | −0.0286330 | ||||||||
\(871\) | −10.3916 | −0.352108 | ||||||||
\(872\) | −5.84947 | −0.198088 | ||||||||
\(873\) | 1.62467 | 0.0549867 | ||||||||
\(874\) | 22.3514 | 0.756048 | ||||||||
\(875\) | −27.1699 | −0.918511 | ||||||||
\(876\) | 57.9628 | 1.95838 | ||||||||
\(877\) | 11.7031 | 0.395184 | 0.197592 | − | 0.980284i | \(-0.436688\pi\) | ||||
0.197592 | + | 0.980284i | \(0.436688\pi\) | |||||||
\(878\) | 79.2604 | 2.67491 | ||||||||
\(879\) | 0.0504023 | 0.00170003 | ||||||||
\(880\) | 9.06844 | 0.305697 | ||||||||
\(881\) | 14.8342 | 0.499776 | 0.249888 | − | 0.968275i | \(-0.419606\pi\) | ||||
0.249888 | + | 0.968275i | \(0.419606\pi\) | |||||||
\(882\) | −1.18749 | −0.0399848 | ||||||||
\(883\) | −46.7951 | −1.57478 | −0.787391 | − | 0.616454i | \(-0.788569\pi\) | ||||
−0.787391 | + | 0.616454i | \(0.788569\pi\) | |||||||
\(884\) | 2.06020 | 0.0692920 | ||||||||
\(885\) | 22.5504 | 0.758024 | ||||||||
\(886\) | −5.25545 | −0.176560 | ||||||||
\(887\) | −43.5365 | −1.46181 | −0.730906 | − | 0.682478i | \(-0.760902\pi\) | ||||
−0.730906 | + | 0.682478i | \(0.760902\pi\) | |||||||
\(888\) | 6.77230 | 0.227264 | ||||||||
\(889\) | 35.1426 | 1.17864 | ||||||||
\(890\) | −7.18630 | −0.240885 | ||||||||
\(891\) | 28.1186 | 0.942008 | ||||||||
\(892\) | 17.3811 | 0.581962 | ||||||||
\(893\) | −19.4780 | −0.651805 | ||||||||
\(894\) | −54.1662 | −1.81159 | ||||||||
\(895\) | −11.5685 | −0.386692 | ||||||||
\(896\) | 18.2858 | 0.610885 | ||||||||
\(897\) | 9.78889 | 0.326842 | ||||||||
\(898\) | 86.7464 | 2.89476 | ||||||||
\(899\) | −1.31261 | −0.0437779 | ||||||||
\(900\) | −2.80378 | −0.0934593 | ||||||||
\(901\) | 4.10300 | 0.136691 | ||||||||
\(902\) | 59.7745 | 1.99027 | ||||||||
\(903\) | −17.0980 | −0.568986 | ||||||||
\(904\) | −9.10933 | −0.302972 | ||||||||
\(905\) | 0.0790921 | 0.00262911 | ||||||||
\(906\) | −19.0322 | −0.632303 | ||||||||
\(907\) | 12.7894 | 0.424664 | 0.212332 | − | 0.977198i | \(-0.431894\pi\) | ||||
0.212332 | + | 0.977198i | \(0.431894\pi\) | |||||||
\(908\) | 16.8588 | 0.559480 | ||||||||
\(909\) | 0.129451 | 0.00429363 | ||||||||
\(910\) | −5.49963 | −0.182311 | ||||||||
\(911\) | −54.8850 | −1.81842 | −0.909210 | − | 0.416337i | \(-0.863314\pi\) | ||||
−0.909210 | + | 0.416337i | \(0.863314\pi\) | |||||||
\(912\) | 9.74132 | 0.322567 | ||||||||
\(913\) | 35.7306 | 1.18251 | ||||||||
\(914\) | −63.2684 | −2.09273 | ||||||||
\(915\) | −6.74138 | −0.222863 | ||||||||
\(916\) | −26.3886 | −0.871904 | ||||||||
\(917\) | −23.0703 | −0.761849 | ||||||||
\(918\) | −10.2617 | −0.338687 | ||||||||
\(919\) | 15.8466 | 0.522732 | 0.261366 | − | 0.965240i | \(-0.415827\pi\) | ||||
0.261366 | + | 0.965240i | \(0.415827\pi\) | |||||||
\(920\) | 4.91039 | 0.161891 | ||||||||
\(921\) | 50.5186 | 1.66464 | ||||||||
\(922\) | −82.9700 | −2.73247 | ||||||||
\(923\) | −5.06685 | −0.166777 | ||||||||
\(924\) | 36.8815 | 1.21331 | ||||||||
\(925\) | −18.9971 | −0.624621 | ||||||||
\(926\) | 22.4834 | 0.738852 | ||||||||
\(927\) | −0.341302 | −0.0112098 | ||||||||
\(928\) | −1.76941 | −0.0580837 | ||||||||
\(929\) | −25.7385 | −0.844451 | −0.422226 | − | 0.906491i | \(-0.638751\pi\) | ||||
−0.422226 | + | 0.906491i | \(0.638751\pi\) | |||||||
\(930\) | 23.0821 | 0.756891 | ||||||||
\(931\) | 3.28485 | 0.107657 | ||||||||
\(932\) | −69.1936 | −2.26651 | ||||||||
\(933\) | 2.86547 | 0.0938113 | ||||||||
\(934\) | −13.6197 | −0.445649 | ||||||||
\(935\) | −2.91059 | −0.0951863 | ||||||||
\(936\) | −0.201424 | −0.00658375 | ||||||||
\(937\) | 37.2581 | 1.21717 | 0.608585 | − | 0.793489i | \(-0.291737\pi\) | ||||
0.608585 | + | 0.793489i | \(0.291737\pi\) | |||||||
\(938\) | 74.6934 | 2.43883 | ||||||||
\(939\) | −44.3123 | −1.44608 | ||||||||
\(940\) | −27.2415 | −0.888518 | ||||||||
\(941\) | −1.59855 | −0.0521112 | −0.0260556 | − | 0.999660i | \(-0.508295\pi\) | ||||
−0.0260556 | + | 0.999660i | \(0.508295\pi\) | |||||||
\(942\) | −7.07399 | −0.230483 | ||||||||
\(943\) | −61.8775 | −2.01501 | ||||||||
\(944\) | 38.1240 | 1.24083 | ||||||||
\(945\) | 14.8641 | 0.483528 | ||||||||
\(946\) | 18.9193 | 0.615121 | ||||||||
\(947\) | −43.8586 | −1.42521 | −0.712606 | − | 0.701564i | \(-0.752485\pi\) | ||||
−0.712606 | + | 0.701564i | \(0.752485\pi\) | |||||||
\(948\) | −40.5035 | −1.31549 | ||||||||
\(949\) | −11.6807 | −0.379171 | ||||||||
\(950\) | 14.2934 | 0.463740 | ||||||||
\(951\) | −42.0053 | −1.36211 | ||||||||
\(952\) | −2.32611 | −0.0753898 | ||||||||
\(953\) | 15.6224 | 0.506060 | 0.253030 | − | 0.967458i | \(-0.418573\pi\) | ||||
0.253030 | + | 0.967458i | \(0.418573\pi\) | |||||||
\(954\) | −2.55376 | −0.0826809 | ||||||||
\(955\) | 26.2823 | 0.850476 | ||||||||
\(956\) | −54.3264 | −1.75704 | ||||||||
\(957\) | −1.14135 | −0.0368947 | ||||||||
\(958\) | −15.7736 | −0.509621 | ||||||||
\(959\) | −22.2272 | −0.717753 | ||||||||
\(960\) | 19.6310 | 0.633587 | ||||||||
\(961\) | 4.87427 | 0.157235 | ||||||||
\(962\) | −8.68821 | −0.280119 | ||||||||
\(963\) | 2.67553 | 0.0862179 | ||||||||
\(964\) | 7.49320 | 0.241340 | ||||||||
\(965\) | −19.0076 | −0.611875 | ||||||||
\(966\) | −70.3609 | −2.26382 | ||||||||
\(967\) | −7.61090 | −0.244750 | −0.122375 | − | 0.992484i | \(-0.539051\pi\) | ||||
−0.122375 | + | 0.992484i | \(0.539051\pi\) | |||||||
\(968\) | 2.16256 | 0.0695073 | ||||||||
\(969\) | −3.12655 | −0.100439 | ||||||||
\(970\) | −11.5836 | −0.371927 | ||||||||
\(971\) | −33.2528 | −1.06713 | −0.533567 | − | 0.845758i | \(-0.679149\pi\) | ||||
−0.533567 | + | 0.845758i | \(0.679149\pi\) | |||||||
\(972\) | 7.31313 | 0.234569 | ||||||||
\(973\) | 32.4470 | 1.04020 | ||||||||
\(974\) | 72.2422 | 2.31479 | ||||||||
\(975\) | 6.25985 | 0.200476 | ||||||||
\(976\) | −11.3970 | −0.364811 | ||||||||
\(977\) | 30.1237 | 0.963743 | 0.481872 | − | 0.876242i | \(-0.339957\pi\) | ||||
0.481872 | + | 0.876242i | \(0.339957\pi\) | |||||||
\(978\) | −50.8008 | −1.62443 | ||||||||
\(979\) | −9.71177 | −0.310389 | ||||||||
\(980\) | 4.59412 | 0.146754 | ||||||||
\(981\) | 2.23396 | 0.0713248 | ||||||||
\(982\) | −12.0283 | −0.383837 | ||||||||
\(983\) | −30.2007 | −0.963253 | −0.481627 | − | 0.876377i | \(-0.659954\pi\) | ||||
−0.481627 | + | 0.876377i | \(0.659954\pi\) | |||||||
\(984\) | 14.1063 | 0.449691 | ||||||||
\(985\) | −12.8480 | −0.409371 | ||||||||
\(986\) | 0.458267 | 0.0145942 | ||||||||
\(987\) | 61.3154 | 1.95169 | ||||||||
\(988\) | 3.54709 | 0.112848 | ||||||||
\(989\) | −19.5850 | −0.622766 | ||||||||
\(990\) | 1.81158 | 0.0575759 | ||||||||
\(991\) | −51.5450 | −1.63738 | −0.818691 | − | 0.574234i | \(-0.805300\pi\) | ||||
−0.818691 | + | 0.574234i | \(0.805300\pi\) | |||||||
\(992\) | 48.3589 | 1.53540 | ||||||||
\(993\) | −41.9589 | −1.33153 | ||||||||
\(994\) | 36.4196 | 1.15516 | ||||||||
\(995\) | 26.1597 | 0.829318 | ||||||||
\(996\) | 53.6800 | 1.70091 | ||||||||
\(997\) | 37.6421 | 1.19214 | 0.596069 | − | 0.802933i | \(-0.296728\pi\) | ||||
0.596069 | + | 0.802933i | \(0.296728\pi\) | |||||||
\(998\) | 57.7498 | 1.82804 | ||||||||
\(999\) | 23.4820 | 0.742936 |
(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 | 6001.2.a.b.1.20 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.b.1.20 | ✓ | 114 | 1.1 | even | 1 | trivial |