Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, 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("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.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: | \(64.2556185065\) |
Analytic rank: | \(0\) |
Dimension: | \(156\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66092 | −1.88155 | −0.940776 | − | 0.339029i | \(-0.889901\pi\) | ||||
−0.940776 | + | 0.339029i | \(0.889901\pi\) | |||||||
\(3\) | −2.09208 | −1.20786 | −0.603932 | − | 0.797036i | \(-0.706400\pi\) | ||||
−0.603932 | + | 0.797036i | \(0.706400\pi\) | |||||||
\(4\) | 5.08047 | 2.54024 | ||||||||
\(5\) | 4.25784 | 1.90416 | 0.952081 | − | 0.305845i | \(-0.0989389\pi\) | ||||
0.952081 | + | 0.305845i | \(0.0989389\pi\) | |||||||
\(6\) | 5.56685 | 2.27266 | ||||||||
\(7\) | −2.19372 | −0.829150 | −0.414575 | − | 0.910015i | \(-0.636070\pi\) | ||||
−0.414575 | + | 0.910015i | \(0.636070\pi\) | |||||||
\(8\) | −8.19688 | −2.89803 | ||||||||
\(9\) | 1.37680 | 0.458934 | ||||||||
\(10\) | −11.3297 | −3.58278 | ||||||||
\(11\) | −2.56177 | −0.772403 | −0.386201 | − | 0.922414i | \(-0.626213\pi\) | ||||
−0.386201 | + | 0.922414i | \(0.626213\pi\) | |||||||
\(12\) | −10.6288 | −3.06826 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 5.83732 | 1.56009 | ||||||||
\(15\) | −8.90774 | −2.29997 | ||||||||
\(16\) | 11.6503 | 2.91256 | ||||||||
\(17\) | −0.0487115 | −0.0118143 | −0.00590713 | − | 0.999983i | \(-0.501880\pi\) | ||||
−0.00590713 | + | 0.999983i | \(0.501880\pi\) | |||||||
\(18\) | −3.66356 | −0.863508 | ||||||||
\(19\) | −7.89347 | −1.81089 | −0.905443 | − | 0.424469i | \(-0.860461\pi\) | ||||
−0.905443 | + | 0.424469i | \(0.860461\pi\) | |||||||
\(20\) | 21.6318 | 4.83702 | ||||||||
\(21\) | 4.58945 | 1.00150 | ||||||||
\(22\) | 6.81666 | 1.45332 | ||||||||
\(23\) | −5.85789 | −1.22145 | −0.610727 | − | 0.791841i | \(-0.709123\pi\) | ||||
−0.610727 | + | 0.791841i | \(0.709123\pi\) | |||||||
\(24\) | 17.1485 | 3.50043 | ||||||||
\(25\) | 13.1292 | 2.62584 | ||||||||
\(26\) | 2.66092 | 0.521848 | ||||||||
\(27\) | 3.39586 | 0.653534 | ||||||||
\(28\) | −11.1452 | −2.10624 | ||||||||
\(29\) | −3.33295 | −0.618914 | −0.309457 | − | 0.950913i | \(-0.600147\pi\) | ||||
−0.309457 | + | 0.950913i | \(0.600147\pi\) | |||||||
\(30\) | 23.7027 | 4.32751 | ||||||||
\(31\) | −3.07217 | −0.551778 | −0.275889 | − | 0.961189i | \(-0.588972\pi\) | ||||
−0.275889 | + | 0.961189i | \(0.588972\pi\) | |||||||
\(32\) | −14.6066 | −2.58210 | ||||||||
\(33\) | 5.35943 | 0.932957 | ||||||||
\(34\) | 0.129617 | 0.0222292 | ||||||||
\(35\) | −9.34052 | −1.57884 | ||||||||
\(36\) | 6.99481 | 1.16580 | ||||||||
\(37\) | 0.0566053 | 0.00930585 | 0.00465292 | − | 0.999989i | \(-0.498519\pi\) | ||||
0.00465292 | + | 0.999989i | \(0.498519\pi\) | |||||||
\(38\) | 21.0038 | 3.40727 | ||||||||
\(39\) | 2.09208 | 0.335001 | ||||||||
\(40\) | −34.9010 | −5.51833 | ||||||||
\(41\) | 9.57989 | 1.49613 | 0.748064 | − | 0.663627i | \(-0.230984\pi\) | ||||
0.748064 | + | 0.663627i | \(0.230984\pi\) | |||||||
\(42\) | −12.2121 | −1.88437 | ||||||||
\(43\) | 9.84631 | 1.50155 | 0.750774 | − | 0.660559i | \(-0.229681\pi\) | ||||
0.750774 | + | 0.660559i | \(0.229681\pi\) | |||||||
\(44\) | −13.0150 | −1.96209 | ||||||||
\(45\) | 5.86220 | 0.873885 | ||||||||
\(46\) | 15.5874 | 2.29823 | ||||||||
\(47\) | 5.51302 | 0.804157 | 0.402079 | − | 0.915605i | \(-0.368288\pi\) | ||||
0.402079 | + | 0.915605i | \(0.368288\pi\) | |||||||
\(48\) | −24.3733 | −3.51798 | ||||||||
\(49\) | −2.18757 | −0.312510 | ||||||||
\(50\) | −34.9356 | −4.94064 | ||||||||
\(51\) | 0.101908 | 0.0142700 | ||||||||
\(52\) | −5.08047 | −0.704535 | ||||||||
\(53\) | −4.99157 | −0.685644 | −0.342822 | − | 0.939400i | \(-0.611383\pi\) | ||||
−0.342822 | + | 0.939400i | \(0.611383\pi\) | |||||||
\(54\) | −9.03610 | −1.22966 | ||||||||
\(55\) | −10.9076 | −1.47078 | ||||||||
\(56\) | 17.9817 | 2.40290 | ||||||||
\(57\) | 16.5138 | 2.18730 | ||||||||
\(58\) | 8.86871 | 1.16452 | ||||||||
\(59\) | −10.6851 | −1.39108 | −0.695538 | − | 0.718489i | \(-0.744834\pi\) | ||||
−0.695538 | + | 0.718489i | \(0.744834\pi\) | |||||||
\(60\) | −45.2555 | −5.84246 | ||||||||
\(61\) | −8.10502 | −1.03774 | −0.518871 | − | 0.854853i | \(-0.673647\pi\) | ||||
−0.518871 | + | 0.854853i | \(0.673647\pi\) | |||||||
\(62\) | 8.17479 | 1.03820 | ||||||||
\(63\) | −3.02033 | −0.380525 | ||||||||
\(64\) | 15.5664 | 1.94580 | ||||||||
\(65\) | −4.25784 | −0.528120 | ||||||||
\(66\) | −14.2610 | −1.75541 | ||||||||
\(67\) | −0.382322 | −0.0467080 | −0.0233540 | − | 0.999727i | \(-0.507434\pi\) | ||||
−0.0233540 | + | 0.999727i | \(0.507434\pi\) | |||||||
\(68\) | −0.247477 | −0.0300110 | ||||||||
\(69\) | 12.2552 | 1.47535 | ||||||||
\(70\) | 24.8543 | 2.97066 | ||||||||
\(71\) | −7.73562 | −0.918049 | −0.459025 | − | 0.888423i | \(-0.651801\pi\) | ||||
−0.459025 | + | 0.888423i | \(0.651801\pi\) | |||||||
\(72\) | −11.2855 | −1.33001 | ||||||||
\(73\) | −2.84179 | −0.332606 | −0.166303 | − | 0.986075i | \(-0.553183\pi\) | ||||
−0.166303 | + | 0.986075i | \(0.553183\pi\) | |||||||
\(74\) | −0.150622 | −0.0175094 | ||||||||
\(75\) | −27.4673 | −3.17165 | ||||||||
\(76\) | −40.1025 | −4.60008 | ||||||||
\(77\) | 5.61982 | 0.640438 | ||||||||
\(78\) | −5.56685 | −0.630322 | ||||||||
\(79\) | −14.0172 | −1.57705 | −0.788527 | − | 0.615000i | \(-0.789156\pi\) | ||||
−0.788527 | + | 0.615000i | \(0.789156\pi\) | |||||||
\(80\) | 49.6049 | 5.54599 | ||||||||
\(81\) | −11.2348 | −1.24831 | ||||||||
\(82\) | −25.4913 | −2.81504 | ||||||||
\(83\) | 0.637871 | 0.0700154 | 0.0350077 | − | 0.999387i | \(-0.488854\pi\) | ||||
0.0350077 | + | 0.999387i | \(0.488854\pi\) | |||||||
\(84\) | 23.3166 | 2.54405 | ||||||||
\(85\) | −0.207406 | −0.0224963 | ||||||||
\(86\) | −26.2002 | −2.82524 | ||||||||
\(87\) | 6.97281 | 0.747564 | ||||||||
\(88\) | 20.9985 | 2.23845 | ||||||||
\(89\) | −6.45214 | −0.683926 | −0.341963 | − | 0.939713i | \(-0.611092\pi\) | ||||
−0.341963 | + | 0.939713i | \(0.611092\pi\) | |||||||
\(90\) | −15.5988 | −1.64426 | ||||||||
\(91\) | 2.19372 | 0.229965 | ||||||||
\(92\) | −29.7608 | −3.10278 | ||||||||
\(93\) | 6.42723 | 0.666473 | ||||||||
\(94\) | −14.6697 | −1.51306 | ||||||||
\(95\) | −33.6091 | −3.44822 | ||||||||
\(96\) | 30.5582 | 3.11883 | ||||||||
\(97\) | 17.8441 | 1.81180 | 0.905899 | − | 0.423495i | \(-0.139197\pi\) | ||||
0.905899 | + | 0.423495i | \(0.139197\pi\) | |||||||
\(98\) | 5.82094 | 0.588004 | ||||||||
\(99\) | −3.52705 | −0.354482 | ||||||||
\(100\) | 66.7024 | 6.67024 | ||||||||
\(101\) | −1.51832 | −0.151079 | −0.0755394 | − | 0.997143i | \(-0.524068\pi\) | ||||
−0.0755394 | + | 0.997143i | \(0.524068\pi\) | |||||||
\(102\) | −0.271170 | −0.0268498 | ||||||||
\(103\) | 11.8412 | 1.16674 | 0.583372 | − | 0.812205i | \(-0.301733\pi\) | ||||
0.583372 | + | 0.812205i | \(0.301733\pi\) | |||||||
\(104\) | 8.19688 | 0.803770 | ||||||||
\(105\) | 19.5411 | 1.90702 | ||||||||
\(106\) | 13.2821 | 1.29008 | ||||||||
\(107\) | −7.61406 | −0.736079 | −0.368039 | − | 0.929810i | \(-0.619971\pi\) | ||||
−0.368039 | + | 0.929810i | \(0.619971\pi\) | |||||||
\(108\) | 17.2526 | 1.66013 | ||||||||
\(109\) | −0.262369 | −0.0251304 | −0.0125652 | − | 0.999921i | \(-0.504000\pi\) | ||||
−0.0125652 | + | 0.999921i | \(0.504000\pi\) | |||||||
\(110\) | 29.0242 | 2.76735 | ||||||||
\(111\) | −0.118423 | −0.0112402 | ||||||||
\(112\) | −25.5575 | −2.41495 | ||||||||
\(113\) | −5.40954 | −0.508886 | −0.254443 | − | 0.967088i | \(-0.581892\pi\) | ||||
−0.254443 | + | 0.967088i | \(0.581892\pi\) | |||||||
\(114\) | −43.9417 | −4.11552 | ||||||||
\(115\) | −24.9419 | −2.32585 | ||||||||
\(116\) | −16.9330 | −1.57219 | ||||||||
\(117\) | −1.37680 | −0.127285 | ||||||||
\(118\) | 28.4321 | 2.61738 | ||||||||
\(119\) | 0.106860 | 0.00979580 | ||||||||
\(120\) | 73.0156 | 6.66539 | ||||||||
\(121\) | −4.43733 | −0.403394 | ||||||||
\(122\) | 21.5668 | 1.95256 | ||||||||
\(123\) | −20.0419 | −1.80712 | ||||||||
\(124\) | −15.6081 | −1.40165 | ||||||||
\(125\) | 34.6127 | 3.09586 | ||||||||
\(126\) | 8.03683 | 0.715978 | ||||||||
\(127\) | 4.70929 | 0.417882 | 0.208941 | − | 0.977928i | \(-0.432998\pi\) | ||||
0.208941 | + | 0.977928i | \(0.432998\pi\) | |||||||
\(128\) | −12.2077 | −1.07902 | ||||||||
\(129\) | −20.5993 | −1.81366 | ||||||||
\(130\) | 11.3297 | 0.993684 | ||||||||
\(131\) | −0.0874575 | −0.00764120 | −0.00382060 | − | 0.999993i | \(-0.501216\pi\) | ||||
−0.00382060 | + | 0.999993i | \(0.501216\pi\) | |||||||
\(132\) | 27.2284 | 2.36993 | ||||||||
\(133\) | 17.3161 | 1.50150 | ||||||||
\(134\) | 1.01733 | 0.0878836 | ||||||||
\(135\) | 14.4590 | 1.24443 | ||||||||
\(136\) | 0.399282 | 0.0342382 | ||||||||
\(137\) | 19.9043 | 1.70054 | 0.850270 | − | 0.526346i | \(-0.176438\pi\) | ||||
0.850270 | + | 0.526346i | \(0.176438\pi\) | |||||||
\(138\) | −32.6100 | −2.77595 | ||||||||
\(139\) | −6.83881 | −0.580061 | −0.290030 | − | 0.957017i | \(-0.593665\pi\) | ||||
−0.290030 | + | 0.957017i | \(0.593665\pi\) | |||||||
\(140\) | −47.4543 | −4.01062 | ||||||||
\(141\) | −11.5337 | −0.971312 | ||||||||
\(142\) | 20.5838 | 1.72736 | ||||||||
\(143\) | 2.56177 | 0.214226 | ||||||||
\(144\) | 16.0401 | 1.33667 | ||||||||
\(145\) | −14.1912 | −1.17851 | ||||||||
\(146\) | 7.56176 | 0.625816 | ||||||||
\(147\) | 4.57658 | 0.377470 | ||||||||
\(148\) | 0.287581 | 0.0236390 | ||||||||
\(149\) | 11.2806 | 0.924144 | 0.462072 | − | 0.886842i | \(-0.347106\pi\) | ||||
0.462072 | + | 0.886842i | \(0.347106\pi\) | |||||||
\(150\) | 73.0882 | 5.96762 | ||||||||
\(151\) | 9.06645 | 0.737817 | 0.368909 | − | 0.929466i | \(-0.379732\pi\) | ||||
0.368909 | + | 0.929466i | \(0.379732\pi\) | |||||||
\(152\) | 64.7018 | 5.24801 | ||||||||
\(153\) | −0.0670661 | −0.00542197 | ||||||||
\(154\) | −14.9539 | −1.20502 | ||||||||
\(155\) | −13.0808 | −1.05068 | ||||||||
\(156\) | 10.6288 | 0.850982 | ||||||||
\(157\) | −11.9636 | −0.954796 | −0.477398 | − | 0.878687i | \(-0.658420\pi\) | ||||
−0.477398 | + | 0.878687i | \(0.658420\pi\) | |||||||
\(158\) | 37.2985 | 2.96731 | ||||||||
\(159\) | 10.4428 | 0.828165 | ||||||||
\(160\) | −62.1925 | −4.91675 | ||||||||
\(161\) | 12.8506 | 1.01277 | ||||||||
\(162\) | 29.8949 | 2.34877 | ||||||||
\(163\) | −12.6085 | −0.987575 | −0.493787 | − | 0.869583i | \(-0.664388\pi\) | ||||
−0.493787 | + | 0.869583i | \(0.664388\pi\) | |||||||
\(164\) | 48.6704 | 3.80052 | ||||||||
\(165\) | 22.8196 | 1.77650 | ||||||||
\(166\) | −1.69732 | −0.131738 | ||||||||
\(167\) | −5.06926 | −0.392271 | −0.196136 | − | 0.980577i | \(-0.562839\pi\) | ||||
−0.196136 | + | 0.980577i | \(0.562839\pi\) | |||||||
\(168\) | −37.6192 | −2.90238 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.551889 | 0.0423279 | ||||||||
\(171\) | −10.8677 | −0.831077 | ||||||||
\(172\) | 50.0239 | 3.81429 | ||||||||
\(173\) | −17.7761 | −1.35149 | −0.675745 | − | 0.737136i | \(-0.736178\pi\) | ||||
−0.675745 | + | 0.737136i | \(0.736178\pi\) | |||||||
\(174\) | −18.5541 | −1.40658 | ||||||||
\(175\) | −28.8018 | −2.17721 | ||||||||
\(176\) | −29.8453 | −2.24967 | ||||||||
\(177\) | 22.3540 | 1.68023 | ||||||||
\(178\) | 17.1686 | 1.28684 | ||||||||
\(179\) | −14.7093 | −1.09942 | −0.549712 | − | 0.835354i | \(-0.685262\pi\) | ||||
−0.549712 | + | 0.835354i | \(0.685262\pi\) | |||||||
\(180\) | 29.7827 | 2.21988 | ||||||||
\(181\) | 26.1329 | 1.94244 | 0.971220 | − | 0.238184i | \(-0.0765522\pi\) | ||||
0.971220 | + | 0.238184i | \(0.0765522\pi\) | |||||||
\(182\) | −5.83732 | −0.432691 | ||||||||
\(183\) | 16.9564 | 1.25345 | ||||||||
\(184\) | 48.0164 | 3.53982 | ||||||||
\(185\) | 0.241016 | 0.0177198 | ||||||||
\(186\) | −17.1023 | −1.25400 | ||||||||
\(187\) | 0.124788 | 0.00912538 | ||||||||
\(188\) | 28.0088 | 2.04275 | ||||||||
\(189\) | −7.44958 | −0.541877 | ||||||||
\(190\) | 89.4310 | 6.48800 | ||||||||
\(191\) | 22.3449 | 1.61682 | 0.808411 | − | 0.588619i | \(-0.200328\pi\) | ||||
0.808411 | + | 0.588619i | \(0.200328\pi\) | |||||||
\(192\) | −32.5662 | −2.35026 | ||||||||
\(193\) | −2.14227 | −0.154204 | −0.0771019 | − | 0.997023i | \(-0.524567\pi\) | ||||
−0.0771019 | + | 0.997023i | \(0.524567\pi\) | |||||||
\(194\) | −47.4817 | −3.40899 | ||||||||
\(195\) | 8.90774 | 0.637897 | ||||||||
\(196\) | −11.1139 | −0.793850 | ||||||||
\(197\) | 7.79717 | 0.555525 | 0.277763 | − | 0.960650i | \(-0.410407\pi\) | ||||
0.277763 | + | 0.960650i | \(0.410407\pi\) | |||||||
\(198\) | 9.38519 | 0.666976 | ||||||||
\(199\) | 1.24150 | 0.0880075 | 0.0440038 | − | 0.999031i | \(-0.485989\pi\) | ||||
0.0440038 | + | 0.999031i | \(0.485989\pi\) | |||||||
\(200\) | −107.618 | −7.60976 | ||||||||
\(201\) | 0.799848 | 0.0564169 | ||||||||
\(202\) | 4.04013 | 0.284263 | ||||||||
\(203\) | 7.31158 | 0.513173 | ||||||||
\(204\) | 0.517743 | 0.0362492 | ||||||||
\(205\) | 40.7896 | 2.84887 | ||||||||
\(206\) | −31.5083 | −2.19529 | ||||||||
\(207\) | −8.06516 | −0.560567 | ||||||||
\(208\) | −11.6503 | −0.807800 | ||||||||
\(209\) | 20.2213 | 1.39873 | ||||||||
\(210\) | −51.9973 | −3.58815 | ||||||||
\(211\) | −8.34576 | −0.574546 | −0.287273 | − | 0.957849i | \(-0.592749\pi\) | ||||
−0.287273 | + | 0.957849i | \(0.592749\pi\) | |||||||
\(212\) | −25.3595 | −1.74170 | ||||||||
\(213\) | 16.1835 | 1.10888 | ||||||||
\(214\) | 20.2604 | 1.38497 | ||||||||
\(215\) | 41.9240 | 2.85919 | ||||||||
\(216\) | −27.8355 | −1.89396 | ||||||||
\(217\) | 6.73950 | 0.457507 | ||||||||
\(218\) | 0.698143 | 0.0472842 | ||||||||
\(219\) | 5.94526 | 0.401743 | ||||||||
\(220\) | −55.4158 | −3.73613 | ||||||||
\(221\) | 0.0487115 | 0.00327669 | ||||||||
\(222\) | 0.315113 | 0.0211490 | ||||||||
\(223\) | −10.3199 | −0.691070 | −0.345535 | − | 0.938406i | \(-0.612303\pi\) | ||||
−0.345535 | + | 0.938406i | \(0.612303\pi\) | |||||||
\(224\) | 32.0428 | 2.14095 | ||||||||
\(225\) | 18.0763 | 1.20509 | ||||||||
\(226\) | 14.3943 | 0.957496 | ||||||||
\(227\) | 7.72913 | 0.513000 | 0.256500 | − | 0.966544i | \(-0.417431\pi\) | ||||
0.256500 | + | 0.966544i | \(0.417431\pi\) | |||||||
\(228\) | 83.8977 | 5.55626 | ||||||||
\(229\) | −18.9669 | −1.25336 | −0.626682 | − | 0.779275i | \(-0.715588\pi\) | ||||
−0.626682 | + | 0.779275i | \(0.715588\pi\) | |||||||
\(230\) | 66.3684 | 4.37620 | ||||||||
\(231\) | −11.7571 | −0.773562 | ||||||||
\(232\) | 27.3198 | 1.79363 | ||||||||
\(233\) | −1.01051 | −0.0662007 | −0.0331004 | − | 0.999452i | \(-0.510538\pi\) | ||||
−0.0331004 | + | 0.999452i | \(0.510538\pi\) | |||||||
\(234\) | 3.66356 | 0.239494 | ||||||||
\(235\) | 23.4736 | 1.53125 | ||||||||
\(236\) | −54.2852 | −3.53366 | ||||||||
\(237\) | 29.3250 | 1.90487 | ||||||||
\(238\) | −0.284344 | −0.0184313 | ||||||||
\(239\) | 20.4487 | 1.32272 | 0.661359 | − | 0.750069i | \(-0.269980\pi\) | ||||
0.661359 | + | 0.750069i | \(0.269980\pi\) | |||||||
\(240\) | −103.777 | −6.69880 | ||||||||
\(241\) | −3.76017 | −0.242214 | −0.121107 | − | 0.992639i | \(-0.538644\pi\) | ||||
−0.121107 | + | 0.992639i | \(0.538644\pi\) | |||||||
\(242\) | 11.8074 | 0.759006 | ||||||||
\(243\) | 13.3166 | 0.854259 | ||||||||
\(244\) | −41.1773 | −2.63611 | ||||||||
\(245\) | −9.31432 | −0.595070 | ||||||||
\(246\) | 53.3298 | 3.40018 | ||||||||
\(247\) | 7.89347 | 0.502249 | ||||||||
\(248\) | 25.1822 | 1.59907 | ||||||||
\(249\) | −1.33448 | −0.0845690 | ||||||||
\(250\) | −92.1015 | −5.82501 | ||||||||
\(251\) | 24.8042 | 1.56563 | 0.782814 | − | 0.622256i | \(-0.213784\pi\) | ||||
0.782814 | + | 0.622256i | \(0.213784\pi\) | |||||||
\(252\) | −15.3447 | −0.966624 | ||||||||
\(253\) | 15.0066 | 0.943455 | ||||||||
\(254\) | −12.5310 | −0.786266 | ||||||||
\(255\) | 0.433909 | 0.0271724 | ||||||||
\(256\) | 1.35083 | 0.0844268 | ||||||||
\(257\) | 1.04927 | 0.0654518 | 0.0327259 | − | 0.999464i | \(-0.489581\pi\) | ||||
0.0327259 | + | 0.999464i | \(0.489581\pi\) | |||||||
\(258\) | 54.8129 | 3.41250 | ||||||||
\(259\) | −0.124176 | −0.00771594 | ||||||||
\(260\) | −21.6318 | −1.34155 | ||||||||
\(261\) | −4.58882 | −0.284041 | ||||||||
\(262\) | 0.232717 | 0.0143773 | ||||||||
\(263\) | −27.0288 | −1.66667 | −0.833333 | − | 0.552771i | \(-0.813570\pi\) | ||||
−0.833333 | + | 0.552771i | \(0.813570\pi\) | |||||||
\(264\) | −43.9306 | −2.70374 | ||||||||
\(265\) | −21.2533 | −1.30558 | ||||||||
\(266\) | −46.0767 | −2.82514 | ||||||||
\(267\) | 13.4984 | 0.826089 | ||||||||
\(268\) | −1.94237 | −0.118649 | ||||||||
\(269\) | −28.5487 | −1.74065 | −0.870323 | − | 0.492482i | \(-0.836090\pi\) | ||||
−0.870323 | + | 0.492482i | \(0.836090\pi\) | |||||||
\(270\) | −38.4742 | −2.34147 | ||||||||
\(271\) | 10.6010 | 0.643964 | 0.321982 | − | 0.946746i | \(-0.395651\pi\) | ||||
0.321982 | + | 0.946746i | \(0.395651\pi\) | |||||||
\(272\) | −0.567501 | −0.0344098 | ||||||||
\(273\) | −4.58945 | −0.277766 | ||||||||
\(274\) | −52.9637 | −3.19966 | ||||||||
\(275\) | −33.6339 | −2.02820 | ||||||||
\(276\) | 62.2621 | 3.74774 | ||||||||
\(277\) | −17.5562 | −1.05485 | −0.527425 | − | 0.849601i | \(-0.676843\pi\) | ||||
−0.527425 | + | 0.849601i | \(0.676843\pi\) | |||||||
\(278\) | 18.1975 | 1.09141 | ||||||||
\(279\) | −4.22977 | −0.253230 | ||||||||
\(280\) | 76.5631 | 4.57552 | ||||||||
\(281\) | −12.6242 | −0.753098 | −0.376549 | − | 0.926397i | \(-0.622889\pi\) | ||||
−0.376549 | + | 0.926397i | \(0.622889\pi\) | |||||||
\(282\) | 30.6902 | 1.82757 | ||||||||
\(283\) | 32.3108 | 1.92068 | 0.960340 | − | 0.278832i | \(-0.0899471\pi\) | ||||
0.960340 | + | 0.278832i | \(0.0899471\pi\) | |||||||
\(284\) | −39.3006 | −2.33206 | ||||||||
\(285\) | 70.3129 | 4.16498 | ||||||||
\(286\) | −6.81666 | −0.403077 | ||||||||
\(287\) | −21.0156 | −1.24051 | ||||||||
\(288\) | −20.1104 | −1.18502 | ||||||||
\(289\) | −16.9976 | −0.999860 | ||||||||
\(290\) | 37.7615 | 2.21743 | ||||||||
\(291\) | −37.3314 | −2.18840 | ||||||||
\(292\) | −14.4376 | −0.844899 | ||||||||
\(293\) | −1.13335 | −0.0662112 | −0.0331056 | − | 0.999452i | \(-0.510540\pi\) | ||||
−0.0331056 | + | 0.999452i | \(0.510540\pi\) | |||||||
\(294\) | −12.1779 | −0.710229 | ||||||||
\(295\) | −45.4953 | −2.64884 | ||||||||
\(296\) | −0.463986 | −0.0269687 | ||||||||
\(297\) | −8.69942 | −0.504791 | ||||||||
\(298\) | −30.0168 | −1.73883 | ||||||||
\(299\) | 5.85789 | 0.338771 | ||||||||
\(300\) | −139.547 | −8.05674 | ||||||||
\(301\) | −21.6001 | −1.24501 | ||||||||
\(302\) | −24.1251 | −1.38824 | ||||||||
\(303\) | 3.17646 | 0.182483 | ||||||||
\(304\) | −91.9609 | −5.27432 | ||||||||
\(305\) | −34.5099 | −1.97603 | ||||||||
\(306\) | 0.178457 | 0.0102017 | ||||||||
\(307\) | −15.5403 | −0.886931 | −0.443466 | − | 0.896291i | \(-0.646251\pi\) | ||||
−0.443466 | + | 0.896291i | \(0.646251\pi\) | |||||||
\(308\) | 28.5513 | 1.62686 | ||||||||
\(309\) | −24.7727 | −1.40927 | ||||||||
\(310\) | 34.8069 | 1.97690 | ||||||||
\(311\) | −9.79658 | −0.555513 | −0.277757 | − | 0.960652i | \(-0.589591\pi\) | ||||
−0.277757 | + | 0.960652i | \(0.589591\pi\) | |||||||
\(312\) | −17.1485 | −0.970844 | ||||||||
\(313\) | 9.93644 | 0.561641 | 0.280820 | − | 0.959760i | \(-0.409393\pi\) | ||||
0.280820 | + | 0.959760i | \(0.409393\pi\) | |||||||
\(314\) | 31.8340 | 1.79650 | ||||||||
\(315\) | −12.8601 | −0.724582 | ||||||||
\(316\) | −71.2138 | −4.00609 | ||||||||
\(317\) | 35.0213 | 1.96699 | 0.983496 | − | 0.180929i | \(-0.0579105\pi\) | ||||
0.983496 | + | 0.180929i | \(0.0579105\pi\) | |||||||
\(318\) | −27.7873 | −1.55823 | ||||||||
\(319\) | 8.53826 | 0.478051 | ||||||||
\(320\) | 66.2792 | 3.70512 | ||||||||
\(321\) | 15.9292 | 0.889083 | ||||||||
\(322\) | −34.1944 | −1.90558 | ||||||||
\(323\) | 0.384502 | 0.0213943 | ||||||||
\(324\) | −57.0782 | −3.17101 | ||||||||
\(325\) | −13.1292 | −0.728276 | ||||||||
\(326\) | 33.5502 | 1.85817 | ||||||||
\(327\) | 0.548898 | 0.0303541 | ||||||||
\(328\) | −78.5252 | −4.33583 | ||||||||
\(329\) | −12.0941 | −0.666767 | ||||||||
\(330\) | −60.7210 | −3.34258 | ||||||||
\(331\) | 19.8516 | 1.09114 | 0.545570 | − | 0.838065i | \(-0.316313\pi\) | ||||
0.545570 | + | 0.838065i | \(0.316313\pi\) | |||||||
\(332\) | 3.24068 | 0.177856 | ||||||||
\(333\) | 0.0779343 | 0.00427077 | ||||||||
\(334\) | 13.4889 | 0.738079 | ||||||||
\(335\) | −1.62786 | −0.0889397 | ||||||||
\(336\) | 53.4683 | 2.91693 | ||||||||
\(337\) | −3.65214 | −0.198944 | −0.0994722 | − | 0.995040i | \(-0.531715\pi\) | ||||
−0.0994722 | + | 0.995040i | \(0.531715\pi\) | |||||||
\(338\) | −2.66092 | −0.144735 | ||||||||
\(339\) | 11.3172 | 0.614665 | ||||||||
\(340\) | −1.05372 | −0.0571459 | ||||||||
\(341\) | 7.87020 | 0.426195 | ||||||||
\(342\) | 28.9181 | 1.56371 | ||||||||
\(343\) | 20.1550 | 1.08827 | ||||||||
\(344\) | −80.7090 | −4.35154 | ||||||||
\(345\) | 52.1806 | 2.80931 | ||||||||
\(346\) | 47.3006 | 2.54290 | ||||||||
\(347\) | 6.35221 | 0.341005 | 0.170502 | − | 0.985357i | \(-0.445461\pi\) | ||||
0.170502 | + | 0.985357i | \(0.445461\pi\) | |||||||
\(348\) | 35.4252 | 1.89899 | ||||||||
\(349\) | −20.6778 | −1.10686 | −0.553428 | − | 0.832897i | \(-0.686680\pi\) | ||||
−0.553428 | + | 0.832897i | \(0.686680\pi\) | |||||||
\(350\) | 76.6392 | 4.09654 | ||||||||
\(351\) | −3.39586 | −0.181258 | ||||||||
\(352\) | 37.4187 | 1.99443 | ||||||||
\(353\) | 9.99774 | 0.532126 | 0.266063 | − | 0.963956i | \(-0.414277\pi\) | ||||
0.266063 | + | 0.963956i | \(0.414277\pi\) | |||||||
\(354\) | −59.4822 | −3.16144 | ||||||||
\(355\) | −32.9370 | −1.74812 | ||||||||
\(356\) | −32.7799 | −1.73733 | ||||||||
\(357\) | −0.223559 | −0.0118320 | ||||||||
\(358\) | 39.1402 | 2.06862 | ||||||||
\(359\) | 25.3745 | 1.33922 | 0.669608 | − | 0.742715i | \(-0.266462\pi\) | ||||
0.669608 | + | 0.742715i | \(0.266462\pi\) | |||||||
\(360\) | −48.0517 | −2.53255 | ||||||||
\(361\) | 43.3068 | 2.27931 | ||||||||
\(362\) | −69.5373 | −3.65480 | ||||||||
\(363\) | 9.28325 | 0.487244 | ||||||||
\(364\) | 11.1452 | 0.584165 | ||||||||
\(365\) | −12.0999 | −0.633337 | ||||||||
\(366\) | −45.1194 | −2.35843 | ||||||||
\(367\) | 14.1222 | 0.737174 | 0.368587 | − | 0.929593i | \(-0.379842\pi\) | ||||
0.368587 | + | 0.929593i | \(0.379842\pi\) | |||||||
\(368\) | −68.2459 | −3.55756 | ||||||||
\(369\) | 13.1896 | 0.686624 | ||||||||
\(370\) | −0.641323 | −0.0333408 | ||||||||
\(371\) | 10.9501 | 0.568502 | ||||||||
\(372\) | 32.6534 | 1.69300 | ||||||||
\(373\) | 7.88850 | 0.408451 | 0.204226 | − | 0.978924i | \(-0.434532\pi\) | ||||
0.204226 | + | 0.978924i | \(0.434532\pi\) | |||||||
\(374\) | −0.332049 | −0.0171699 | ||||||||
\(375\) | −72.4126 | −3.73937 | ||||||||
\(376\) | −45.1896 | −2.33047 | ||||||||
\(377\) | 3.33295 | 0.171656 | ||||||||
\(378\) | 19.8227 | 1.01957 | ||||||||
\(379\) | −5.33030 | −0.273799 | −0.136899 | − | 0.990585i | \(-0.543714\pi\) | ||||
−0.136899 | + | 0.990585i | \(0.543714\pi\) | |||||||
\(380\) | −170.750 | −8.75929 | ||||||||
\(381\) | −9.85222 | −0.504744 | ||||||||
\(382\) | −59.4579 | −3.04213 | ||||||||
\(383\) | −8.88155 | −0.453826 | −0.226913 | − | 0.973915i | \(-0.572863\pi\) | ||||
−0.226913 | + | 0.973915i | \(0.572863\pi\) | |||||||
\(384\) | 25.5395 | 1.30331 | ||||||||
\(385\) | 23.9283 | 1.21950 | ||||||||
\(386\) | 5.70039 | 0.290142 | ||||||||
\(387\) | 13.5564 | 0.689112 | ||||||||
\(388\) | 90.6566 | 4.60239 | ||||||||
\(389\) | 14.5176 | 0.736073 | 0.368036 | − | 0.929811i | \(-0.380030\pi\) | ||||
0.368036 | + | 0.929811i | \(0.380030\pi\) | |||||||
\(390\) | −23.7027 | −1.20024 | ||||||||
\(391\) | 0.285346 | 0.0144306 | ||||||||
\(392\) | 17.9313 | 0.905665 | ||||||||
\(393\) | 0.182968 | 0.00922952 | ||||||||
\(394\) | −20.7476 | −1.04525 | ||||||||
\(395\) | −59.6828 | −3.00297 | ||||||||
\(396\) | −17.9191 | −0.900468 | ||||||||
\(397\) | −24.4665 | −1.22794 | −0.613970 | − | 0.789329i | \(-0.710428\pi\) | ||||
−0.613970 | + | 0.789329i | \(0.710428\pi\) | |||||||
\(398\) | −3.30352 | −0.165591 | ||||||||
\(399\) | −36.2267 | −1.81360 | ||||||||
\(400\) | 152.958 | 7.64791 | ||||||||
\(401\) | 28.4922 | 1.42283 | 0.711416 | − | 0.702771i | \(-0.248054\pi\) | ||||
0.711416 | + | 0.702771i | \(0.248054\pi\) | |||||||
\(402\) | −2.12833 | −0.106151 | ||||||||
\(403\) | 3.07217 | 0.153036 | ||||||||
\(404\) | −7.71380 | −0.383776 | ||||||||
\(405\) | −47.8360 | −2.37699 | ||||||||
\(406\) | −19.4555 | −0.965561 | ||||||||
\(407\) | −0.145010 | −0.00718786 | ||||||||
\(408\) | −0.835330 | −0.0413550 | ||||||||
\(409\) | −2.31126 | −0.114285 | −0.0571423 | − | 0.998366i | \(-0.518199\pi\) | ||||
−0.0571423 | + | 0.998366i | \(0.518199\pi\) | |||||||
\(410\) | −108.538 | −5.36029 | ||||||||
\(411\) | −41.6414 | −2.05402 | ||||||||
\(412\) | 60.1587 | 2.96381 | ||||||||
\(413\) | 23.4401 | 1.15341 | ||||||||
\(414\) | 21.4607 | 1.05474 | ||||||||
\(415\) | 2.71595 | 0.133321 | ||||||||
\(416\) | 14.6066 | 0.716147 | ||||||||
\(417\) | 14.3073 | 0.700634 | ||||||||
\(418\) | −53.8070 | −2.63179 | ||||||||
\(419\) | 20.1880 | 0.986246 | 0.493123 | − | 0.869960i | \(-0.335855\pi\) | ||||
0.493123 | + | 0.869960i | \(0.335855\pi\) | |||||||
\(420\) | 99.2782 | 4.84428 | ||||||||
\(421\) | 31.8332 | 1.55145 | 0.775727 | − | 0.631069i | \(-0.217383\pi\) | ||||
0.775727 | + | 0.631069i | \(0.217383\pi\) | |||||||
\(422\) | 22.2074 | 1.08104 | ||||||||
\(423\) | 7.59035 | 0.369055 | ||||||||
\(424\) | 40.9153 | 1.98702 | ||||||||
\(425\) | −0.639542 | −0.0310223 | ||||||||
\(426\) | −43.0631 | −2.08641 | ||||||||
\(427\) | 17.7802 | 0.860443 | ||||||||
\(428\) | −38.6830 | −1.86981 | ||||||||
\(429\) | −5.35943 | −0.258756 | ||||||||
\(430\) | −111.556 | −5.37972 | ||||||||
\(431\) | 15.9389 | 0.767752 | 0.383876 | − | 0.923385i | \(-0.374589\pi\) | ||||
0.383876 | + | 0.923385i | \(0.374589\pi\) | |||||||
\(432\) | 39.5626 | 1.90346 | ||||||||
\(433\) | 21.6680 | 1.04130 | 0.520650 | − | 0.853770i | \(-0.325690\pi\) | ||||
0.520650 | + | 0.853770i | \(0.325690\pi\) | |||||||
\(434\) | −17.9332 | −0.860823 | ||||||||
\(435\) | 29.6891 | 1.42348 | ||||||||
\(436\) | −1.33296 | −0.0638372 | ||||||||
\(437\) | 46.2391 | 2.21191 | ||||||||
\(438\) | −15.8198 | −0.755900 | ||||||||
\(439\) | −38.4248 | −1.83392 | −0.916958 | − | 0.398983i | \(-0.869363\pi\) | ||||
−0.916958 | + | 0.398983i | \(0.869363\pi\) | |||||||
\(440\) | 89.4083 | 4.26237 | ||||||||
\(441\) | −3.01185 | −0.143422 | ||||||||
\(442\) | −0.129617 | −0.00616526 | ||||||||
\(443\) | 6.22370 | 0.295697 | 0.147848 | − | 0.989010i | \(-0.452765\pi\) | ||||
0.147848 | + | 0.989010i | \(0.452765\pi\) | |||||||
\(444\) | −0.601644 | −0.0285527 | ||||||||
\(445\) | −27.4722 | −1.30231 | ||||||||
\(446\) | 27.4603 | 1.30028 | ||||||||
\(447\) | −23.6000 | −1.11624 | ||||||||
\(448\) | −34.1484 | −1.61336 | ||||||||
\(449\) | 18.7352 | 0.884168 | 0.442084 | − | 0.896974i | \(-0.354239\pi\) | ||||
0.442084 | + | 0.896974i | \(0.354239\pi\) | |||||||
\(450\) | −48.0995 | −2.26743 | ||||||||
\(451\) | −24.5415 | −1.15561 | ||||||||
\(452\) | −27.4830 | −1.29269 | ||||||||
\(453\) | −18.9677 | −0.891182 | ||||||||
\(454\) | −20.5666 | −0.965236 | ||||||||
\(455\) | 9.34052 | 0.437890 | ||||||||
\(456\) | −135.361 | −6.33888 | ||||||||
\(457\) | −7.88256 | −0.368731 | −0.184365 | − | 0.982858i | \(-0.559023\pi\) | ||||
−0.184365 | + | 0.982858i | \(0.559023\pi\) | |||||||
\(458\) | 50.4692 | 2.35827 | ||||||||
\(459\) | −0.165417 | −0.00772102 | ||||||||
\(460\) | −126.717 | −5.90820 | ||||||||
\(461\) | −18.6407 | −0.868183 | −0.434092 | − | 0.900869i | \(-0.642931\pi\) | ||||
−0.434092 | + | 0.900869i | \(0.642931\pi\) | |||||||
\(462\) | 31.2847 | 1.45550 | ||||||||
\(463\) | 6.60668 | 0.307039 | 0.153519 | − | 0.988146i | \(-0.450939\pi\) | ||||
0.153519 | + | 0.988146i | \(0.450939\pi\) | |||||||
\(464\) | −38.8298 | −1.80263 | ||||||||
\(465\) | 27.3661 | 1.26907 | ||||||||
\(466\) | 2.68888 | 0.124560 | ||||||||
\(467\) | 39.0178 | 1.80553 | 0.902765 | − | 0.430133i | \(-0.141534\pi\) | ||||
0.902765 | + | 0.430133i | \(0.141534\pi\) | |||||||
\(468\) | −6.99481 | −0.323335 | ||||||||
\(469\) | 0.838709 | 0.0387280 | ||||||||
\(470\) | −62.4612 | −2.88112 | ||||||||
\(471\) | 25.0287 | 1.15326 | ||||||||
\(472\) | 87.5842 | 4.03139 | ||||||||
\(473\) | −25.2240 | −1.15980 | ||||||||
\(474\) | −78.0314 | −3.58410 | ||||||||
\(475\) | −103.635 | −4.75509 | ||||||||
\(476\) | 0.542897 | 0.0248837 | ||||||||
\(477\) | −6.87240 | −0.314666 | ||||||||
\(478\) | −54.4123 | −2.48876 | ||||||||
\(479\) | 13.0169 | 0.594759 | 0.297380 | − | 0.954759i | \(-0.403887\pi\) | ||||
0.297380 | + | 0.954759i | \(0.403887\pi\) | |||||||
\(480\) | 130.112 | 5.93876 | ||||||||
\(481\) | −0.0566053 | −0.00258098 | ||||||||
\(482\) | 10.0055 | 0.455738 | ||||||||
\(483\) | −26.8845 | −1.22329 | ||||||||
\(484\) | −22.5437 | −1.02472 | ||||||||
\(485\) | 75.9774 | 3.44996 | ||||||||
\(486\) | −35.4343 | −1.60733 | ||||||||
\(487\) | −2.03931 | −0.0924101 | −0.0462051 | − | 0.998932i | \(-0.514713\pi\) | ||||
−0.0462051 | + | 0.998932i | \(0.514713\pi\) | |||||||
\(488\) | 66.4359 | 3.00741 | ||||||||
\(489\) | 26.3780 | 1.19286 | ||||||||
\(490\) | 24.7846 | 1.11966 | ||||||||
\(491\) | 26.2021 | 1.18249 | 0.591243 | − | 0.806493i | \(-0.298637\pi\) | ||||
0.591243 | + | 0.806493i | \(0.298637\pi\) | |||||||
\(492\) | −101.822 | −4.59050 | ||||||||
\(493\) | 0.162353 | 0.00731202 | ||||||||
\(494\) | −21.0038 | −0.945008 | ||||||||
\(495\) | −15.0176 | −0.674992 | ||||||||
\(496\) | −35.7916 | −1.60709 | ||||||||
\(497\) | 16.9698 | 0.761201 | ||||||||
\(498\) | 3.55093 | 0.159121 | ||||||||
\(499\) | −23.2292 | −1.03988 | −0.519941 | − | 0.854202i | \(-0.674046\pi\) | ||||
−0.519941 | + | 0.854202i | \(0.674046\pi\) | |||||||
\(500\) | 175.849 | 7.86420 | ||||||||
\(501\) | 10.6053 | 0.473810 | ||||||||
\(502\) | −66.0019 | −2.94581 | ||||||||
\(503\) | 10.2239 | 0.455863 | 0.227931 | − | 0.973677i | \(-0.426804\pi\) | ||||
0.227931 | + | 0.973677i | \(0.426804\pi\) | |||||||
\(504\) | 24.7572 | 1.10278 | ||||||||
\(505\) | −6.46478 | −0.287679 | ||||||||
\(506\) | −39.9312 | −1.77516 | ||||||||
\(507\) | −2.09208 | −0.0929126 | ||||||||
\(508\) | 23.9254 | 1.06152 | ||||||||
\(509\) | 4.90604 | 0.217456 | 0.108728 | − | 0.994072i | \(-0.465322\pi\) | ||||
0.108728 | + | 0.994072i | \(0.465322\pi\) | |||||||
\(510\) | −1.15460 | −0.0511264 | ||||||||
\(511\) | 6.23411 | 0.275781 | ||||||||
\(512\) | 20.8209 | 0.920164 | ||||||||
\(513\) | −26.8051 | −1.18347 | ||||||||
\(514\) | −2.79203 | −0.123151 | ||||||||
\(515\) | 50.4178 | 2.22167 | ||||||||
\(516\) | −104.654 | −4.60714 | ||||||||
\(517\) | −14.1231 | −0.621133 | ||||||||
\(518\) | 0.330423 | 0.0145179 | ||||||||
\(519\) | 37.1890 | 1.63241 | ||||||||
\(520\) | 34.9010 | 1.53051 | ||||||||
\(521\) | −1.52132 | −0.0666500 | −0.0333250 | − | 0.999445i | \(-0.510610\pi\) | ||||
−0.0333250 | + | 0.999445i | \(0.510610\pi\) | |||||||
\(522\) | 12.2105 | 0.534437 | ||||||||
\(523\) | −25.8525 | −1.13045 | −0.565226 | − | 0.824936i | \(-0.691211\pi\) | ||||
−0.565226 | + | 0.824936i | \(0.691211\pi\) | |||||||
\(524\) | −0.444325 | −0.0194104 | ||||||||
\(525\) | 60.2557 | 2.62977 | ||||||||
\(526\) | 71.9213 | 3.13592 | ||||||||
\(527\) | 0.149650 | 0.00651886 | ||||||||
\(528\) | 62.4387 | 2.71730 | ||||||||
\(529\) | 11.3149 | 0.491951 | ||||||||
\(530\) | 56.5532 | 2.45651 | ||||||||
\(531\) | −14.7112 | −0.638413 | ||||||||
\(532\) | 87.9739 | 3.81415 | ||||||||
\(533\) | −9.57989 | −0.414951 | ||||||||
\(534\) | −35.9181 | −1.55433 | ||||||||
\(535\) | −32.4194 | −1.40161 | ||||||||
\(536\) | 3.13384 | 0.135361 | ||||||||
\(537\) | 30.7730 | 1.32795 | ||||||||
\(538\) | 75.9657 | 3.27511 | ||||||||
\(539\) | 5.60406 | 0.241384 | ||||||||
\(540\) | 73.4587 | 3.16116 | ||||||||
\(541\) | −23.8204 | −1.02412 | −0.512059 | − | 0.858950i | \(-0.671117\pi\) | ||||
−0.512059 | + | 0.858950i | \(0.671117\pi\) | |||||||
\(542\) | −28.2083 | −1.21165 | ||||||||
\(543\) | −54.6721 | −2.34620 | ||||||||
\(544\) | 0.711509 | 0.0305057 | ||||||||
\(545\) | −1.11713 | −0.0478524 | ||||||||
\(546\) | 12.2121 | 0.522631 | ||||||||
\(547\) | −39.6112 | −1.69365 | −0.846827 | − | 0.531868i | \(-0.821490\pi\) | ||||
−0.846827 | + | 0.531868i | \(0.821490\pi\) | |||||||
\(548\) | 101.123 | 4.31978 | ||||||||
\(549\) | −11.1590 | −0.476255 | ||||||||
\(550\) | 89.4971 | 3.81617 | ||||||||
\(551\) | 26.3086 | 1.12078 | ||||||||
\(552\) | −100.454 | −4.27561 | ||||||||
\(553\) | 30.7498 | 1.30761 | ||||||||
\(554\) | 46.7156 | 1.98476 | ||||||||
\(555\) | −0.504225 | −0.0214032 | ||||||||
\(556\) | −34.7444 | −1.47349 | ||||||||
\(557\) | −44.3056 | −1.87729 | −0.938645 | − | 0.344884i | \(-0.887918\pi\) | ||||
−0.938645 | + | 0.344884i | \(0.887918\pi\) | |||||||
\(558\) | 11.2551 | 0.476465 | ||||||||
\(559\) | −9.84631 | −0.416454 | ||||||||
\(560\) | −108.819 | −4.59846 | ||||||||
\(561\) | −0.261066 | −0.0110222 | ||||||||
\(562\) | 33.5920 | 1.41699 | ||||||||
\(563\) | −29.5074 | −1.24359 | −0.621795 | − | 0.783180i | \(-0.713596\pi\) | ||||
−0.621795 | + | 0.783180i | \(0.713596\pi\) | |||||||
\(564\) | −58.5966 | −2.46736 | ||||||||
\(565\) | −23.0329 | −0.969003 | ||||||||
\(566\) | −85.9764 | −3.61386 | ||||||||
\(567\) | 24.6461 | 1.03504 | ||||||||
\(568\) | 63.4079 | 2.66054 | ||||||||
\(569\) | −2.84976 | −0.119468 | −0.0597340 | − | 0.998214i | \(-0.519025\pi\) | ||||
−0.0597340 | + | 0.998214i | \(0.519025\pi\) | |||||||
\(570\) | −187.097 | −7.83662 | ||||||||
\(571\) | 7.21477 | 0.301929 | 0.150964 | − | 0.988539i | \(-0.451762\pi\) | ||||
0.150964 | + | 0.988539i | \(0.451762\pi\) | |||||||
\(572\) | 13.0150 | 0.544185 | ||||||||
\(573\) | −46.7474 | −1.95290 | ||||||||
\(574\) | 55.9208 | 2.33409 | ||||||||
\(575\) | −76.9093 | −3.20734 | ||||||||
\(576\) | 21.4318 | 0.892994 | ||||||||
\(577\) | 9.90077 | 0.412174 | 0.206087 | − | 0.978534i | \(-0.433927\pi\) | ||||
0.206087 | + | 0.978534i | \(0.433927\pi\) | |||||||
\(578\) | 45.2293 | 1.88129 | ||||||||
\(579\) | 4.48180 | 0.186257 | ||||||||
\(580\) | −72.0979 | −2.99370 | ||||||||
\(581\) | −1.39931 | −0.0580533 | ||||||||
\(582\) | 99.3356 | 4.11759 | ||||||||
\(583\) | 12.7873 | 0.529594 | ||||||||
\(584\) | 23.2938 | 0.963905 | ||||||||
\(585\) | −5.86220 | −0.242372 | ||||||||
\(586\) | 3.01576 | 0.124580 | ||||||||
\(587\) | 20.0961 | 0.829456 | 0.414728 | − | 0.909945i | \(-0.363877\pi\) | ||||
0.414728 | + | 0.909945i | \(0.363877\pi\) | |||||||
\(588\) | 23.2512 | 0.958862 | ||||||||
\(589\) | 24.2501 | 0.999207 | ||||||||
\(590\) | 121.059 | 4.98392 | ||||||||
\(591\) | −16.3123 | −0.670998 | ||||||||
\(592\) | 0.659466 | 0.0271039 | ||||||||
\(593\) | −8.40611 | −0.345198 | −0.172599 | − | 0.984992i | \(-0.555216\pi\) | ||||
−0.172599 | + | 0.984992i | \(0.555216\pi\) | |||||||
\(594\) | 23.1484 | 0.949791 | ||||||||
\(595\) | 0.454991 | 0.0186528 | ||||||||
\(596\) | 57.3109 | 2.34754 | ||||||||
\(597\) | −2.59732 | −0.106301 | ||||||||
\(598\) | −15.5874 | −0.637414 | ||||||||
\(599\) | −7.53129 | −0.307720 | −0.153860 | − | 0.988093i | \(-0.549170\pi\) | ||||
−0.153860 | + | 0.988093i | \(0.549170\pi\) | |||||||
\(600\) | 225.146 | 9.19155 | ||||||||
\(601\) | 21.6738 | 0.884093 | 0.442047 | − | 0.896992i | \(-0.354253\pi\) | ||||
0.442047 | + | 0.896992i | \(0.354253\pi\) | |||||||
\(602\) | 57.4760 | 2.34255 | ||||||||
\(603\) | −0.526382 | −0.0214359 | ||||||||
\(604\) | 46.0618 | 1.87423 | ||||||||
\(605\) | −18.8934 | −0.768127 | ||||||||
\(606\) | −8.45228 | −0.343351 | ||||||||
\(607\) | 33.6337 | 1.36515 | 0.682575 | − | 0.730815i | \(-0.260860\pi\) | ||||
0.682575 | + | 0.730815i | \(0.260860\pi\) | |||||||
\(608\) | 115.297 | 4.67590 | ||||||||
\(609\) | −15.2964 | −0.619842 | ||||||||
\(610\) | 91.8278 | 3.71800 | ||||||||
\(611\) | −5.51302 | −0.223033 | ||||||||
\(612\) | −0.340727 | −0.0137731 | ||||||||
\(613\) | 7.20338 | 0.290942 | 0.145471 | − | 0.989363i | \(-0.453530\pi\) | ||||
0.145471 | + | 0.989363i | \(0.453530\pi\) | |||||||
\(614\) | 41.3514 | 1.66881 | ||||||||
\(615\) | −85.3351 | −3.44105 | ||||||||
\(616\) | −46.0650 | −1.85601 | ||||||||
\(617\) | 23.6395 | 0.951690 | 0.475845 | − | 0.879529i | \(-0.342142\pi\) | ||||
0.475845 | + | 0.879529i | \(0.342142\pi\) | |||||||
\(618\) | 65.9180 | 2.65161 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | −66.4567 | −2.66896 | ||||||||
\(621\) | −19.8926 | −0.798262 | ||||||||
\(622\) | 26.0679 | 1.04523 | ||||||||
\(623\) | 14.1542 | 0.567077 | ||||||||
\(624\) | 24.3733 | 0.975712 | ||||||||
\(625\) | 81.7294 | 3.26918 | ||||||||
\(626\) | −26.4400 | −1.05676 | ||||||||
\(627\) | −42.3045 | −1.68948 | ||||||||
\(628\) | −60.7805 | −2.42541 | ||||||||
\(629\) | −0.00275733 | −0.000109942 0 | ||||||||
\(630\) | 34.2195 | 1.36334 | ||||||||
\(631\) | 3.10127 | 0.123460 | 0.0617298 | − | 0.998093i | \(-0.480338\pi\) | ||||
0.0617298 | + | 0.998093i | \(0.480338\pi\) | |||||||
\(632\) | 114.897 | 4.57036 | ||||||||
\(633\) | 17.4600 | 0.693973 | ||||||||
\(634\) | −93.1887 | −3.70100 | ||||||||
\(635\) | 20.0514 | 0.795715 | ||||||||
\(636\) | 53.0542 | 2.10373 | ||||||||
\(637\) | 2.18757 | 0.0866747 | ||||||||
\(638\) | −22.7196 | −0.899478 | ||||||||
\(639\) | −10.6504 | −0.421324 | ||||||||
\(640\) | −51.9783 | −2.05462 | ||||||||
\(641\) | 44.3451 | 1.75153 | 0.875763 | − | 0.482740i | \(-0.160359\pi\) | ||||
0.875763 | + | 0.482740i | \(0.160359\pi\) | |||||||
\(642\) | −42.3863 | −1.67285 | ||||||||
\(643\) | −1.77387 | −0.0699544 | −0.0349772 | − | 0.999388i | \(-0.511136\pi\) | ||||
−0.0349772 | + | 0.999388i | \(0.511136\pi\) | |||||||
\(644\) | 65.2871 | 2.57267 | ||||||||
\(645\) | −87.7084 | −3.45351 | ||||||||
\(646\) | −1.02313 | −0.0402545 | ||||||||
\(647\) | 21.6865 | 0.852586 | 0.426293 | − | 0.904585i | \(-0.359819\pi\) | ||||
0.426293 | + | 0.904585i | \(0.359819\pi\) | |||||||
\(648\) | 92.0905 | 3.61765 | ||||||||
\(649\) | 27.3727 | 1.07447 | ||||||||
\(650\) | 34.9356 | 1.37029 | ||||||||
\(651\) | −14.0996 | −0.552606 | ||||||||
\(652\) | −64.0572 | −2.50867 | ||||||||
\(653\) | 19.6817 | 0.770205 | 0.385102 | − | 0.922874i | \(-0.374166\pi\) | ||||
0.385102 | + | 0.922874i | \(0.374166\pi\) | |||||||
\(654\) | −1.46057 | −0.0571129 | ||||||||
\(655\) | −0.372380 | −0.0145501 | ||||||||
\(656\) | 111.608 | 4.35757 | ||||||||
\(657\) | −3.91258 | −0.152644 | ||||||||
\(658\) | 32.1813 | 1.25456 | ||||||||
\(659\) | 20.0570 | 0.781310 | 0.390655 | − | 0.920537i | \(-0.372249\pi\) | ||||
0.390655 | + | 0.920537i | \(0.372249\pi\) | |||||||
\(660\) | 115.934 | 4.51274 | ||||||||
\(661\) | −28.6027 | −1.11252 | −0.556258 | − | 0.831010i | \(-0.687763\pi\) | ||||
−0.556258 | + | 0.831010i | \(0.687763\pi\) | |||||||
\(662\) | −52.8233 | −2.05304 | ||||||||
\(663\) | −0.101908 | −0.00395779 | ||||||||
\(664\) | −5.22855 | −0.202907 | ||||||||
\(665\) | 73.7291 | 2.85909 | ||||||||
\(666\) | −0.207376 | −0.00803568 | ||||||||
\(667\) | 19.5241 | 0.755975 | ||||||||
\(668\) | −25.7542 | −0.996462 | ||||||||
\(669\) | 21.5900 | 0.834719 | ||||||||
\(670\) | 4.33161 | 0.167345 | ||||||||
\(671\) | 20.7632 | 0.801555 | ||||||||
\(672\) | −67.0362 | −2.58598 | ||||||||
\(673\) | 4.16850 | 0.160684 | 0.0803419 | − | 0.996767i | \(-0.474399\pi\) | ||||
0.0803419 | + | 0.996767i | \(0.474399\pi\) | |||||||
\(674\) | 9.71802 | 0.374324 | ||||||||
\(675\) | 44.5849 | 1.71607 | ||||||||
\(676\) | 5.08047 | 0.195403 | ||||||||
\(677\) | −45.9935 | −1.76768 | −0.883838 | − | 0.467794i | \(-0.845049\pi\) | ||||
−0.883838 | + | 0.467794i | \(0.845049\pi\) | |||||||
\(678\) | −30.1141 | −1.15652 | ||||||||
\(679\) | −39.1451 | −1.50225 | ||||||||
\(680\) | 1.70008 | 0.0651950 | ||||||||
\(681\) | −16.1700 | −0.619634 | ||||||||
\(682\) | −20.9419 | −0.801908 | ||||||||
\(683\) | 28.2745 | 1.08189 | 0.540947 | − | 0.841056i | \(-0.318066\pi\) | ||||
0.540947 | + | 0.841056i | \(0.318066\pi\) | |||||||
\(684\) | −55.2133 | −2.11113 | ||||||||
\(685\) | 84.7494 | 3.23811 | ||||||||
\(686\) | −53.6308 | −2.04763 | ||||||||
\(687\) | 39.6802 | 1.51389 | ||||||||
\(688\) | 114.712 | 4.37335 | ||||||||
\(689\) | 4.99157 | 0.190164 | ||||||||
\(690\) | −138.848 | −5.28586 | ||||||||
\(691\) | −11.4830 | −0.436832 | −0.218416 | − | 0.975856i | \(-0.570089\pi\) | ||||
−0.218416 | + | 0.975856i | \(0.570089\pi\) | |||||||
\(692\) | −90.3108 | −3.43310 | ||||||||
\(693\) | 7.73738 | 0.293919 | ||||||||
\(694\) | −16.9027 | −0.641618 | ||||||||
\(695\) | −29.1186 | −1.10453 | ||||||||
\(696\) | −57.1553 | −2.16646 | ||||||||
\(697\) | −0.466651 | −0.0176756 | ||||||||
\(698\) | 55.0218 | 2.08261 | ||||||||
\(699\) | 2.11407 | 0.0799614 | ||||||||
\(700\) | −146.327 | −5.53063 | ||||||||
\(701\) | −23.0140 | −0.869228 | −0.434614 | − | 0.900617i | \(-0.643115\pi\) | ||||
−0.434614 | + | 0.900617i | \(0.643115\pi\) | |||||||
\(702\) | 9.03610 | 0.341046 | ||||||||
\(703\) | −0.446812 | −0.0168518 | ||||||||
\(704\) | −39.8775 | −1.50294 | ||||||||
\(705\) | −49.1086 | −1.84954 | ||||||||
\(706\) | −26.6031 | −1.00122 | ||||||||
\(707\) | 3.33078 | 0.125267 | ||||||||
\(708\) | 113.569 | 4.26818 | ||||||||
\(709\) | 7.52082 | 0.282450 | 0.141225 | − | 0.989978i | \(-0.454896\pi\) | ||||
0.141225 | + | 0.989978i | \(0.454896\pi\) | |||||||
\(710\) | 87.6426 | 3.28917 | ||||||||
\(711\) | −19.2989 | −0.723764 | ||||||||
\(712\) | 52.8874 | 1.98204 | ||||||||
\(713\) | 17.9964 | 0.673972 | ||||||||
\(714\) | 0.594871 | 0.0222625 | ||||||||
\(715\) | 10.9076 | 0.407921 | ||||||||
\(716\) | −74.7301 | −2.79280 | ||||||||
\(717\) | −42.7804 | −1.59766 | ||||||||
\(718\) | −67.5195 | −2.51980 | ||||||||
\(719\) | 21.8122 | 0.813456 | 0.406728 | − | 0.913549i | \(-0.366670\pi\) | ||||
0.406728 | + | 0.913549i | \(0.366670\pi\) | |||||||
\(720\) | 68.2961 | 2.54525 | ||||||||
\(721\) | −25.9763 | −0.967407 | ||||||||
\(722\) | −115.236 | −4.28863 | ||||||||
\(723\) | 7.86659 | 0.292562 | ||||||||
\(724\) | 132.767 | 4.93426 | ||||||||
\(725\) | −43.7589 | −1.62517 | ||||||||
\(726\) | −24.7020 | −0.916776 | ||||||||
\(727\) | −1.41184 | −0.0523624 | −0.0261812 | − | 0.999657i | \(-0.508335\pi\) | ||||
−0.0261812 | + | 0.999657i | \(0.508335\pi\) | |||||||
\(728\) | −17.9817 | −0.666446 | ||||||||
\(729\) | 5.84511 | 0.216486 | ||||||||
\(730\) | 32.1968 | 1.19166 | ||||||||
\(731\) | −0.479628 | −0.0177397 | ||||||||
\(732\) | 86.1463 | 3.18406 | ||||||||
\(733\) | 40.6012 | 1.49964 | 0.749821 | − | 0.661641i | \(-0.230140\pi\) | ||||
0.749821 | + | 0.661641i | \(0.230140\pi\) | |||||||
\(734\) | −37.5780 | −1.38703 | ||||||||
\(735\) | 19.4863 | 0.718764 | ||||||||
\(736\) | 85.5638 | 3.15392 | ||||||||
\(737\) | 0.979421 | 0.0360774 | ||||||||
\(738\) | −35.0964 | −1.29192 | ||||||||
\(739\) | −17.3318 | −0.637562 | −0.318781 | − | 0.947828i | \(-0.603273\pi\) | ||||
−0.318781 | + | 0.947828i | \(0.603273\pi\) | |||||||
\(740\) | 1.22447 | 0.0450126 | ||||||||
\(741\) | −16.5138 | −0.606648 | ||||||||
\(742\) | −29.1374 | −1.06967 | ||||||||
\(743\) | −19.4534 | −0.713675 | −0.356837 | − | 0.934167i | \(-0.616145\pi\) | ||||
−0.356837 | + | 0.934167i | \(0.616145\pi\) | |||||||
\(744\) | −52.6832 | −1.93146 | ||||||||
\(745\) | 48.0310 | 1.75972 | ||||||||
\(746\) | −20.9906 | −0.768522 | ||||||||
\(747\) | 0.878222 | 0.0321325 | ||||||||
\(748\) | 0.633980 | 0.0231806 | ||||||||
\(749\) | 16.7031 | 0.610320 | ||||||||
\(750\) | 192.684 | 7.03582 | ||||||||
\(751\) | −31.6823 | −1.15610 | −0.578051 | − | 0.816001i | \(-0.696187\pi\) | ||||
−0.578051 | + | 0.816001i | \(0.696187\pi\) | |||||||
\(752\) | 64.2281 | 2.34216 | ||||||||
\(753\) | −51.8924 | −1.89106 | ||||||||
\(754\) | −8.86871 | −0.322979 | ||||||||
\(755\) | 38.6035 | 1.40492 | ||||||||
\(756\) | −37.8474 | −1.37650 | ||||||||
\(757\) | 10.3436 | 0.375945 | 0.187973 | − | 0.982174i | \(-0.439808\pi\) | ||||
0.187973 | + | 0.982174i | \(0.439808\pi\) | |||||||
\(758\) | 14.1835 | 0.515167 | ||||||||
\(759\) | −31.3950 | −1.13956 | ||||||||
\(760\) | 275.490 | 9.99306 | ||||||||
\(761\) | −13.7473 | −0.498338 | −0.249169 | − | 0.968460i | \(-0.580157\pi\) | ||||
−0.249169 | + | 0.968460i | \(0.580157\pi\) | |||||||
\(762\) | 26.2159 | 0.949702 | ||||||||
\(763\) | 0.575566 | 0.0208369 | ||||||||
\(764\) | 113.523 | 4.10711 | ||||||||
\(765\) | −0.285556 | −0.0103243 | ||||||||
\(766\) | 23.6331 | 0.853897 | ||||||||
\(767\) | 10.6851 | 0.385815 | ||||||||
\(768\) | −2.82604 | −0.101976 | ||||||||
\(769\) | 46.8264 | 1.68860 | 0.844301 | − | 0.535869i | \(-0.180016\pi\) | ||||
0.844301 | + | 0.535869i | \(0.180016\pi\) | |||||||
\(770\) | −63.6711 | −2.29455 | ||||||||
\(771\) | −2.19516 | −0.0790569 | ||||||||
\(772\) | −10.8837 | −0.391714 | ||||||||
\(773\) | 40.4557 | 1.45509 | 0.727544 | − | 0.686061i | \(-0.240662\pi\) | ||||
0.727544 | + | 0.686061i | \(0.240662\pi\) | |||||||
\(774\) | −36.0725 | −1.29660 | ||||||||
\(775\) | −40.3351 | −1.44888 | ||||||||
\(776\) | −146.266 | −5.25065 | ||||||||
\(777\) | 0.259787 | 0.00931981 | ||||||||
\(778\) | −38.6302 | −1.38496 | ||||||||
\(779\) | −75.6185 | −2.70931 | ||||||||
\(780\) | 45.2555 | 1.62041 | ||||||||
\(781\) | 19.8169 | 0.709104 | ||||||||
\(782\) | −0.759283 | −0.0271519 | ||||||||
\(783\) | −11.3182 | −0.404481 | ||||||||
\(784\) | −25.4858 | −0.910206 | ||||||||
\(785\) | −50.9389 | −1.81809 | ||||||||
\(786\) | −0.486863 | −0.0173658 | ||||||||
\(787\) | 47.1350 | 1.68018 | 0.840090 | − | 0.542447i | \(-0.182502\pi\) | ||||
0.840090 | + | 0.542447i | \(0.182502\pi\) | |||||||
\(788\) | 39.6133 | 1.41116 | ||||||||
\(789\) | 56.5464 | 2.01310 | ||||||||
\(790\) | 158.811 | 5.65024 | ||||||||
\(791\) | 11.8670 | 0.421943 | ||||||||
\(792\) | 28.9108 | 1.02730 | ||||||||
\(793\) | 8.10502 | 0.287818 | ||||||||
\(794\) | 65.1034 | 2.31043 | ||||||||
\(795\) | 44.4636 | 1.57696 | ||||||||
\(796\) | 6.30740 | 0.223560 | ||||||||
\(797\) | −50.4005 | −1.78528 | −0.892638 | − | 0.450774i | \(-0.851148\pi\) | ||||
−0.892638 | + | 0.450774i | \(0.851148\pi\) | |||||||
\(798\) | 96.3961 | 3.41239 | ||||||||
\(799\) | −0.268548 | −0.00950053 | ||||||||
\(800\) | −191.773 | −6.78018 | ||||||||
\(801\) | −8.88333 | −0.313877 | ||||||||
\(802\) | −75.8153 | −2.67713 | ||||||||
\(803\) | 7.28002 | 0.256906 | ||||||||
\(804\) | 4.06361 | 0.143312 | ||||||||
\(805\) | 54.7158 | 1.92848 | ||||||||
\(806\) | −8.17479 | −0.287945 | ||||||||
\(807\) | 59.7262 | 2.10246 | ||||||||
\(808\) | 12.4455 | 0.437832 | ||||||||
\(809\) | 49.3695 | 1.73574 | 0.867870 | − | 0.496792i | \(-0.165489\pi\) | ||||
0.867870 | + | 0.496792i | \(0.165489\pi\) | |||||||
\(810\) | 127.288 | 4.47243 | ||||||||
\(811\) | −10.9313 | −0.383849 | −0.191924 | − | 0.981410i | \(-0.561473\pi\) | ||||
−0.191924 | + | 0.981410i | \(0.561473\pi\) | |||||||
\(812\) | 37.1463 | 1.30358 | ||||||||
\(813\) | −22.1781 | −0.777821 | ||||||||
\(814\) | 0.385859 | 0.0135243 | ||||||||
\(815\) | −53.6850 | −1.88050 | ||||||||
\(816\) | 1.18726 | 0.0415624 | ||||||||
\(817\) | −77.7215 | −2.71913 | ||||||||
\(818\) | 6.15008 | 0.215033 | ||||||||
\(819\) | 3.02033 | 0.105539 | ||||||||
\(820\) | 207.230 | 7.23680 | ||||||||
\(821\) | 11.4406 | 0.399281 | 0.199640 | − | 0.979869i | \(-0.436023\pi\) | ||||
0.199640 | + | 0.979869i | \(0.436023\pi\) | |||||||
\(822\) | 110.804 | 3.86475 | ||||||||
\(823\) | 35.7812 | 1.24725 | 0.623626 | − | 0.781723i | \(-0.285659\pi\) | ||||
0.623626 | + | 0.781723i | \(0.285659\pi\) | |||||||
\(824\) | −97.0606 | −3.38127 | ||||||||
\(825\) | 70.3649 | 2.44979 | ||||||||
\(826\) | −62.3721 | −2.17020 | ||||||||
\(827\) | 23.5260 | 0.818079 | 0.409039 | − | 0.912517i | \(-0.365864\pi\) | ||||
0.409039 | + | 0.912517i | \(0.365864\pi\) | |||||||
\(828\) | −40.9748 | −1.42397 | ||||||||
\(829\) | 18.2384 | 0.633447 | 0.316723 | − | 0.948518i | \(-0.397417\pi\) | ||||
0.316723 | + | 0.948518i | \(0.397417\pi\) | |||||||
\(830\) | −7.22691 | −0.250850 | ||||||||
\(831\) | 36.7290 | 1.27412 | ||||||||
\(832\) | −15.5664 | −0.539668 | ||||||||
\(833\) | 0.106560 | 0.00369208 | ||||||||
\(834\) | −38.0706 | −1.31828 | ||||||||
\(835\) | −21.5841 | −0.746948 | ||||||||
\(836\) | 102.734 | 3.55311 | ||||||||
\(837\) | −10.4327 | −0.360606 | ||||||||
\(838\) | −53.7185 | −1.85567 | ||||||||
\(839\) | −25.7982 | −0.890654 | −0.445327 | − | 0.895368i | \(-0.646913\pi\) | ||||
−0.445327 | + | 0.895368i | \(0.646913\pi\) | |||||||
\(840\) | −160.176 | −5.52661 | ||||||||
\(841\) | −17.8914 | −0.616945 | ||||||||
\(842\) | −84.7054 | −2.91914 | ||||||||
\(843\) | 26.4109 | 0.909639 | ||||||||
\(844\) | −42.4004 | −1.45948 | ||||||||
\(845\) | 4.25784 | 0.146474 | ||||||||
\(846\) | −20.1973 | −0.694396 | ||||||||
\(847\) | 9.73428 | 0.334474 | ||||||||
\(848\) | −58.1530 | −1.99698 | ||||||||
\(849\) | −67.5969 | −2.31992 | ||||||||
\(850\) | 1.70177 | 0.0583701 | ||||||||
\(851\) | −0.331587 | −0.0113667 | ||||||||
\(852\) | 82.2201 | 2.81681 | ||||||||
\(853\) | −2.83012 | −0.0969016 | −0.0484508 | − | 0.998826i | \(-0.515428\pi\) | ||||
−0.0484508 | + | 0.998826i | \(0.515428\pi\) | |||||||
\(854\) | −47.3116 | −1.61897 | ||||||||
\(855\) | −46.2731 | −1.58251 | ||||||||
\(856\) | 62.4115 | 2.13318 | ||||||||
\(857\) | 13.8406 | 0.472787 | 0.236394 | − | 0.971657i | \(-0.424035\pi\) | ||||
0.236394 | + | 0.971657i | \(0.424035\pi\) | |||||||
\(858\) | 14.2610 | 0.486862 | ||||||||
\(859\) | −28.5254 | −0.973276 | −0.486638 | − | 0.873604i | \(-0.661777\pi\) | ||||
−0.486638 | + | 0.873604i | \(0.661777\pi\) | |||||||
\(860\) | 212.994 | 7.26302 | ||||||||
\(861\) | 43.9664 | 1.49837 | ||||||||
\(862\) | −42.4122 | −1.44456 | ||||||||
\(863\) | −53.5021 | −1.82123 | −0.910616 | − | 0.413254i | \(-0.864392\pi\) | ||||
−0.910616 | + | 0.413254i | \(0.864392\pi\) | |||||||
\(864\) | −49.6019 | −1.68749 | ||||||||
\(865\) | −75.6876 | −2.57346 | ||||||||
\(866\) | −57.6568 | −1.95926 | ||||||||
\(867\) | 35.5604 | 1.20769 | ||||||||
\(868\) | 34.2398 | 1.16218 | ||||||||
\(869\) | 35.9088 | 1.21812 | ||||||||
\(870\) | −79.0002 | −2.67836 | ||||||||
\(871\) | 0.382322 | 0.0129545 | ||||||||
\(872\) | 2.15061 | 0.0728288 | ||||||||
\(873\) | 24.5678 | 0.831496 | ||||||||
\(874\) | −123.038 | −4.16183 | ||||||||
\(875\) | −75.9308 | −2.56693 | ||||||||
\(876\) | 30.2047 | 1.02052 | ||||||||
\(877\) | −20.1293 | −0.679717 | −0.339858 | − | 0.940477i | \(-0.610379\pi\) | ||||
−0.339858 | + | 0.940477i | \(0.610379\pi\) | |||||||
\(878\) | 102.245 | 3.45061 | ||||||||
\(879\) | 2.37107 | 0.0799741 | ||||||||
\(880\) | −127.076 | −4.28374 | ||||||||
\(881\) | 29.6932 | 1.00039 | 0.500194 | − | 0.865913i | \(-0.333262\pi\) | ||||
0.500194 | + | 0.865913i | \(0.333262\pi\) | |||||||
\(882\) | 8.01429 | 0.269855 | ||||||||
\(883\) | −3.97795 | −0.133869 | −0.0669343 | − | 0.997757i | \(-0.521322\pi\) | ||||
−0.0669343 | + | 0.997757i | \(0.521322\pi\) | |||||||
\(884\) | 0.247477 | 0.00832356 | ||||||||
\(885\) | 95.1798 | 3.19943 | ||||||||
\(886\) | −16.5607 | −0.556369 | ||||||||
\(887\) | 37.3483 | 1.25403 | 0.627017 | − | 0.779006i | \(-0.284276\pi\) | ||||
0.627017 | + | 0.779006i | \(0.284276\pi\) | |||||||
\(888\) | 0.970697 | 0.0325745 | ||||||||
\(889\) | −10.3309 | −0.346487 | ||||||||
\(890\) | 73.1012 | 2.45036 | ||||||||
\(891\) | 28.7810 | 0.964201 | ||||||||
\(892\) | −52.4299 | −1.75548 | ||||||||
\(893\) | −43.5169 | −1.45624 | ||||||||
\(894\) | 62.7975 | 2.10026 | ||||||||
\(895\) | −62.6297 | −2.09348 | ||||||||
\(896\) | 26.7803 | 0.894667 | ||||||||
\(897\) | −12.2552 | −0.409189 | ||||||||
\(898\) | −49.8528 | −1.66361 | ||||||||
\(899\) | 10.2394 | 0.341503 | ||||||||
\(900\) | 91.8361 | 3.06120 | ||||||||
\(901\) | 0.243147 | 0.00810039 | ||||||||
\(902\) | 65.3028 | 2.17435 | ||||||||
\(903\) | 45.1891 | 1.50380 | ||||||||
\(904\) | 44.3413 | 1.47477 | ||||||||
\(905\) | 111.269 | 3.69872 | ||||||||
\(906\) | 50.4716 | 1.67681 | ||||||||
\(907\) | 37.6220 | 1.24922 | 0.624609 | − | 0.780937i | \(-0.285258\pi\) | ||||
0.624609 | + | 0.780937i | \(0.285258\pi\) | |||||||
\(908\) | 39.2676 | 1.30314 | ||||||||
\(909\) | −2.09043 | −0.0693353 | ||||||||
\(910\) | −24.8543 | −0.823914 | ||||||||
\(911\) | −50.5532 | −1.67490 | −0.837451 | − | 0.546512i | \(-0.815955\pi\) | ||||
−0.837451 | + | 0.546512i | \(0.815955\pi\) | |||||||
\(912\) | 192.390 | 6.37066 | ||||||||
\(913\) | −1.63408 | −0.0540801 | ||||||||
\(914\) | 20.9748 | 0.693786 | ||||||||
\(915\) | 72.1974 | 2.38677 | ||||||||
\(916\) | −96.3606 | −3.18384 | ||||||||
\(917\) | 0.191858 | 0.00633570 | ||||||||
\(918\) | 0.440162 | 0.0145275 | ||||||||
\(919\) | −14.4343 | −0.476143 | −0.238072 | − | 0.971248i | \(-0.576515\pi\) | ||||
−0.238072 | + | 0.971248i | \(0.576515\pi\) | |||||||
\(920\) | 204.446 | 6.74039 | ||||||||
\(921\) | 32.5115 | 1.07129 | ||||||||
\(922\) | 49.6013 | 1.63353 | ||||||||
\(923\) | 7.73562 | 0.254621 | ||||||||
\(924\) | −59.7317 | −1.96503 | ||||||||
\(925\) | 0.743180 | 0.0244356 | ||||||||
\(926\) | −17.5798 | −0.577709 | ||||||||
\(927\) | 16.3029 | 0.535459 | ||||||||
\(928\) | 48.6831 | 1.59810 | ||||||||
\(929\) | 27.3775 | 0.898227 | 0.449113 | − | 0.893475i | \(-0.351740\pi\) | ||||
0.449113 | + | 0.893475i | \(0.351740\pi\) | |||||||
\(930\) | −72.8189 | −2.38783 | ||||||||
\(931\) | 17.2675 | 0.565920 | ||||||||
\(932\) | −5.13387 | −0.168165 | ||||||||
\(933\) | 20.4952 | 0.670984 | ||||||||
\(934\) | −103.823 | −3.39720 | ||||||||
\(935\) | 0.531326 | 0.0173762 | ||||||||
\(936\) | 11.2855 | 0.368877 | ||||||||
\(937\) | −41.6775 | −1.36155 | −0.680773 | − | 0.732495i | \(-0.738356\pi\) | ||||
−0.680773 | + | 0.732495i | \(0.738356\pi\) | |||||||
\(938\) | −2.23173 | −0.0728687 | ||||||||
\(939\) | −20.7878 | −0.678386 | ||||||||
\(940\) | 119.257 | 3.88973 | ||||||||
\(941\) | 21.4785 | 0.700180 | 0.350090 | − | 0.936716i | \(-0.386151\pi\) | ||||
0.350090 | + | 0.936716i | \(0.386151\pi\) | |||||||
\(942\) | −66.5994 | −2.16992 | ||||||||
\(943\) | −56.1179 | −1.82745 | ||||||||
\(944\) | −124.484 | −4.05160 | ||||||||
\(945\) | −31.7191 | −1.03182 | ||||||||
\(946\) | 67.1189 | 2.18222 | ||||||||
\(947\) | −29.5599 | −0.960569 | −0.480284 | − | 0.877113i | \(-0.659467\pi\) | ||||
−0.480284 | + | 0.877113i | \(0.659467\pi\) | |||||||
\(948\) | 148.985 | 4.83881 | ||||||||
\(949\) | 2.84179 | 0.0922484 | ||||||||
\(950\) | 275.763 | 8.94694 | ||||||||
\(951\) | −73.2674 | −2.37586 | ||||||||
\(952\) | −0.875915 | −0.0283886 | ||||||||
\(953\) | 15.8945 | 0.514873 | 0.257437 | − | 0.966295i | \(-0.417122\pi\) | ||||
0.257437 | + | 0.966295i | \(0.417122\pi\) | |||||||
\(954\) | 18.2869 | 0.592060 | ||||||||
\(955\) | 95.1410 | 3.07869 | ||||||||
\(956\) | 103.889 | 3.36002 | ||||||||
\(957\) | −17.8627 | −0.577420 | ||||||||
\(958\) | −34.6370 | −1.11907 | ||||||||
\(959\) | −43.6646 | −1.41000 | ||||||||
\(960\) | −138.661 | −4.47528 | ||||||||
\(961\) | −21.5618 | −0.695541 | ||||||||
\(962\) | 0.150622 | 0.00485624 | ||||||||
\(963\) | −10.4831 | −0.337812 | ||||||||
\(964\) | −19.1035 | −0.615281 | ||||||||
\(965\) | −9.12143 | −0.293629 | ||||||||
\(966\) | 71.5374 | 2.30168 | ||||||||
\(967\) | −26.5717 | −0.854489 | −0.427245 | − | 0.904136i | \(-0.640516\pi\) | ||||
−0.427245 | + | 0.904136i | \(0.640516\pi\) | |||||||
\(968\) | 36.3723 | 1.16905 | ||||||||
\(969\) | −0.804410 | −0.0258414 | ||||||||
\(970\) | −202.169 | −6.49127 | ||||||||
\(971\) | 44.5912 | 1.43100 | 0.715501 | − | 0.698612i | \(-0.246199\pi\) | ||||
0.715501 | + | 0.698612i | \(0.246199\pi\) | |||||||
\(972\) | 67.6545 | 2.17002 | ||||||||
\(973\) | 15.0025 | 0.480957 | ||||||||
\(974\) | 5.42644 | 0.173874 | ||||||||
\(975\) | 27.4673 | 0.879658 | ||||||||
\(976\) | −94.4255 | −3.02249 | ||||||||
\(977\) | −28.0861 | −0.898554 | −0.449277 | − | 0.893392i | \(-0.648318\pi\) | ||||
−0.449277 | + | 0.893392i | \(0.648318\pi\) | |||||||
\(978\) | −70.1897 | −2.24442 | ||||||||
\(979\) | 16.5289 | 0.528266 | ||||||||
\(980\) | −47.3212 | −1.51162 | ||||||||
\(981\) | −0.361231 | −0.0115332 | ||||||||
\(982\) | −69.7217 | −2.22491 | ||||||||
\(983\) | 48.4954 | 1.54676 | 0.773381 | − | 0.633941i | \(-0.218564\pi\) | ||||
0.773381 | + | 0.633941i | \(0.218564\pi\) | |||||||
\(984\) | 164.281 | 5.23709 | ||||||||
\(985\) | 33.1991 | 1.05781 | ||||||||
\(986\) | −0.432008 | −0.0137579 | ||||||||
\(987\) | 25.3017 | 0.805364 | ||||||||
\(988\) | 40.1025 | 1.27583 | ||||||||
\(989\) | −57.6786 | −1.83407 | ||||||||
\(990\) | 39.9606 | 1.27003 | ||||||||
\(991\) | −20.5805 | −0.653761 | −0.326880 | − | 0.945066i | \(-0.605997\pi\) | ||||
−0.326880 | + | 0.945066i | \(0.605997\pi\) | |||||||
\(992\) | 44.8739 | 1.42475 | ||||||||
\(993\) | −41.5311 | −1.31795 | ||||||||
\(994\) | −45.1553 | −1.43224 | ||||||||
\(995\) | 5.28610 | 0.167581 | ||||||||
\(996\) | −6.77977 | −0.214825 | ||||||||
\(997\) | 1.32641 | 0.0420078 | 0.0210039 | − | 0.999779i | \(-0.493314\pi\) | ||||
0.0210039 | + | 0.999779i | \(0.493314\pi\) | |||||||
\(998\) | 61.8110 | 1.95659 | ||||||||
\(999\) | 0.192224 | 0.00608168 |
(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 | 8047.2.a.d.1.4 | ✓ | 156 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.d.1.4 | ✓ | 156 | 1.1 | even | 1 | trivial |