Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00485 | −1.41765 | −0.708823 | − | 0.705387i | \(-0.750773\pi\) | ||||
−0.708823 | + | 0.705387i | \(0.750773\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.01944 | 1.00972 | ||||||||
\(5\) | 2.86654 | 1.28195 | 0.640977 | − | 0.767560i | \(-0.278529\pi\) | ||||
0.640977 | + | 0.767560i | \(0.278529\pi\) | |||||||
\(6\) | −2.00485 | −0.818478 | ||||||||
\(7\) | −1.37721 | −0.520536 | −0.260268 | − | 0.965536i | \(-0.583811\pi\) | ||||
−0.260268 | + | 0.965536i | \(0.583811\pi\) | |||||||
\(8\) | −0.0389655 | −0.0137764 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.74699 | −1.81736 | ||||||||
\(11\) | 4.45661 | 1.34372 | 0.671859 | − | 0.740679i | \(-0.265496\pi\) | ||||
0.671859 | + | 0.740679i | \(0.265496\pi\) | |||||||
\(12\) | 2.01944 | 0.582961 | ||||||||
\(13\) | −0.546342 | −0.151528 | −0.0757640 | − | 0.997126i | \(-0.524140\pi\) | ||||
−0.0757640 | + | 0.997126i | \(0.524140\pi\) | |||||||
\(14\) | 2.76110 | 0.737935 | ||||||||
\(15\) | 2.86654 | 0.740137 | ||||||||
\(16\) | −3.96075 | −0.990188 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.00485 | −0.472548 | ||||||||
\(19\) | −5.48056 | −1.25733 | −0.628663 | − | 0.777678i | \(-0.716398\pi\) | ||||
−0.628663 | + | 0.777678i | \(0.716398\pi\) | |||||||
\(20\) | 5.78879 | 1.29441 | ||||||||
\(21\) | −1.37721 | −0.300531 | ||||||||
\(22\) | −8.93485 | −1.90492 | ||||||||
\(23\) | −5.85867 | −1.22162 | −0.610809 | − | 0.791778i | \(-0.709156\pi\) | ||||
−0.610809 | + | 0.791778i | \(0.709156\pi\) | |||||||
\(24\) | −0.0389655 | −0.00795381 | ||||||||
\(25\) | 3.21704 | 0.643407 | ||||||||
\(26\) | 1.09533 | 0.214813 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.78118 | −0.525594 | ||||||||
\(29\) | 1.43181 | 0.265880 | 0.132940 | − | 0.991124i | \(-0.457558\pi\) | ||||
0.132940 | + | 0.991124i | \(0.457558\pi\) | |||||||
\(30\) | −5.74699 | −1.04925 | ||||||||
\(31\) | −6.52595 | −1.17209 | −0.586047 | − | 0.810277i | \(-0.699317\pi\) | ||||
−0.586047 | + | 0.810277i | \(0.699317\pi\) | |||||||
\(32\) | 8.01865 | 1.41751 | ||||||||
\(33\) | 4.45661 | 0.775796 | ||||||||
\(34\) | 2.00485 | 0.343829 | ||||||||
\(35\) | −3.94782 | −0.667303 | ||||||||
\(36\) | 2.01944 | 0.336573 | ||||||||
\(37\) | 2.12031 | 0.348577 | 0.174288 | − | 0.984695i | \(-0.444238\pi\) | ||||
0.174288 | + | 0.984695i | \(0.444238\pi\) | |||||||
\(38\) | 10.9877 | 1.78244 | ||||||||
\(39\) | −0.546342 | −0.0874847 | ||||||||
\(40\) | −0.111696 | −0.0176607 | ||||||||
\(41\) | 4.65531 | 0.727037 | 0.363518 | − | 0.931587i | \(-0.381575\pi\) | ||||
0.363518 | + | 0.931587i | \(0.381575\pi\) | |||||||
\(42\) | 2.76110 | 0.426047 | ||||||||
\(43\) | −3.60649 | −0.549984 | −0.274992 | − | 0.961446i | \(-0.588675\pi\) | ||||
−0.274992 | + | 0.961446i | \(0.588675\pi\) | |||||||
\(44\) | 8.99984 | 1.35678 | ||||||||
\(45\) | 2.86654 | 0.427318 | ||||||||
\(46\) | 11.7458 | 1.73182 | ||||||||
\(47\) | −3.40324 | −0.496413 | −0.248207 | − | 0.968707i | \(-0.579841\pi\) | ||||
−0.248207 | + | 0.968707i | \(0.579841\pi\) | |||||||
\(48\) | −3.96075 | −0.571685 | ||||||||
\(49\) | −5.10330 | −0.729043 | ||||||||
\(50\) | −6.44969 | −0.912123 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −1.10330 | −0.153000 | ||||||||
\(53\) | −3.06822 | −0.421452 | −0.210726 | − | 0.977545i | \(-0.567583\pi\) | ||||
−0.210726 | + | 0.977545i | \(0.567583\pi\) | |||||||
\(54\) | −2.00485 | −0.272826 | ||||||||
\(55\) | 12.7750 | 1.72259 | ||||||||
\(56\) | 0.0536636 | 0.00717110 | ||||||||
\(57\) | −5.48056 | −0.725918 | ||||||||
\(58\) | −2.87056 | −0.376923 | ||||||||
\(59\) | 14.2269 | 1.85218 | 0.926092 | − | 0.377299i | \(-0.123147\pi\) | ||||
0.926092 | + | 0.377299i | \(0.123147\pi\) | |||||||
\(60\) | 5.78879 | 0.747329 | ||||||||
\(61\) | −4.18725 | −0.536122 | −0.268061 | − | 0.963402i | \(-0.586383\pi\) | ||||
−0.268061 | + | 0.963402i | \(0.586383\pi\) | |||||||
\(62\) | 13.0836 | 1.66161 | ||||||||
\(63\) | −1.37721 | −0.173512 | ||||||||
\(64\) | −8.15472 | −1.01934 | ||||||||
\(65\) | −1.56611 | −0.194252 | ||||||||
\(66\) | −8.93485 | −1.09980 | ||||||||
\(67\) | −10.6886 | −1.30582 | −0.652910 | − | 0.757435i | \(-0.726452\pi\) | ||||
−0.652910 | + | 0.757435i | \(0.726452\pi\) | |||||||
\(68\) | −2.01944 | −0.244893 | ||||||||
\(69\) | −5.85867 | −0.705301 | ||||||||
\(70\) | 7.91479 | 0.945999 | ||||||||
\(71\) | 1.13125 | 0.134255 | 0.0671273 | − | 0.997744i | \(-0.478617\pi\) | ||||
0.0671273 | + | 0.997744i | \(0.478617\pi\) | |||||||
\(72\) | −0.0389655 | −0.00459213 | ||||||||
\(73\) | −13.2237 | −1.54772 | −0.773860 | − | 0.633356i | \(-0.781677\pi\) | ||||
−0.773860 | + | 0.633356i | \(0.781677\pi\) | |||||||
\(74\) | −4.25091 | −0.494158 | ||||||||
\(75\) | 3.21704 | 0.371471 | ||||||||
\(76\) | −11.0676 | −1.26954 | ||||||||
\(77\) | −6.13768 | −0.699453 | ||||||||
\(78\) | 1.09533 | 0.124022 | ||||||||
\(79\) | −4.80443 | −0.540541 | −0.270271 | − | 0.962784i | \(-0.587113\pi\) | ||||
−0.270271 | + | 0.962784i | \(0.587113\pi\) | |||||||
\(80\) | −11.3536 | −1.26938 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.33321 | −1.03068 | ||||||||
\(83\) | 2.37540 | 0.260734 | 0.130367 | − | 0.991466i | \(-0.458384\pi\) | ||||
0.130367 | + | 0.991466i | \(0.458384\pi\) | |||||||
\(84\) | −2.78118 | −0.303452 | ||||||||
\(85\) | −2.86654 | −0.310920 | ||||||||
\(86\) | 7.23048 | 0.779682 | ||||||||
\(87\) | 1.43181 | 0.153506 | ||||||||
\(88\) | −0.173654 | −0.0185116 | ||||||||
\(89\) | −11.9624 | −1.26801 | −0.634006 | − | 0.773328i | \(-0.718590\pi\) | ||||
−0.634006 | + | 0.773328i | \(0.718590\pi\) | |||||||
\(90\) | −5.74699 | −0.605786 | ||||||||
\(91\) | 0.752426 | 0.0788757 | ||||||||
\(92\) | −11.8312 | −1.23349 | ||||||||
\(93\) | −6.52595 | −0.676709 | ||||||||
\(94\) | 6.82299 | 0.703738 | ||||||||
\(95\) | −15.7102 | −1.61183 | ||||||||
\(96\) | 8.01865 | 0.818401 | ||||||||
\(97\) | −10.3137 | −1.04720 | −0.523599 | − | 0.851965i | \(-0.675411\pi\) | ||||
−0.523599 | + | 0.851965i | \(0.675411\pi\) | |||||||
\(98\) | 10.2314 | 1.03352 | ||||||||
\(99\) | 4.45661 | 0.447906 | ||||||||
\(100\) | 6.49660 | 0.649660 | ||||||||
\(101\) | −8.96292 | −0.891843 | −0.445922 | − | 0.895072i | \(-0.647124\pi\) | ||||
−0.445922 | + | 0.895072i | \(0.647124\pi\) | |||||||
\(102\) | 2.00485 | 0.198510 | ||||||||
\(103\) | 0.659899 | 0.0650218 | 0.0325109 | − | 0.999471i | \(-0.489650\pi\) | ||||
0.0325109 | + | 0.999471i | \(0.489650\pi\) | |||||||
\(104\) | 0.0212885 | 0.00208751 | ||||||||
\(105\) | −3.94782 | −0.385267 | ||||||||
\(106\) | 6.15132 | 0.597469 | ||||||||
\(107\) | 6.63959 | 0.641873 | 0.320937 | − | 0.947101i | \(-0.396002\pi\) | ||||
0.320937 | + | 0.947101i | \(0.396002\pi\) | |||||||
\(108\) | 2.01944 | 0.194320 | ||||||||
\(109\) | 3.59660 | 0.344492 | 0.172246 | − | 0.985054i | \(-0.444898\pi\) | ||||
0.172246 | + | 0.985054i | \(0.444898\pi\) | |||||||
\(110\) | −25.6121 | −2.44202 | ||||||||
\(111\) | 2.12031 | 0.201251 | ||||||||
\(112\) | 5.45478 | 0.515428 | ||||||||
\(113\) | −2.47427 | −0.232760 | −0.116380 | − | 0.993205i | \(-0.537129\pi\) | ||||
−0.116380 | + | 0.993205i | \(0.537129\pi\) | |||||||
\(114\) | 10.9877 | 1.02909 | ||||||||
\(115\) | −16.7941 | −1.56606 | ||||||||
\(116\) | 2.89144 | 0.268463 | ||||||||
\(117\) | −0.546342 | −0.0505093 | ||||||||
\(118\) | −28.5228 | −2.62574 | ||||||||
\(119\) | 1.37721 | 0.126248 | ||||||||
\(120\) | −0.111696 | −0.0101964 | ||||||||
\(121\) | 8.86138 | 0.805580 | ||||||||
\(122\) | 8.39482 | 0.760031 | ||||||||
\(123\) | 4.65531 | 0.419755 | ||||||||
\(124\) | −13.1787 | −1.18348 | ||||||||
\(125\) | −5.11093 | −0.457136 | ||||||||
\(126\) | 2.76110 | 0.245978 | ||||||||
\(127\) | −8.77605 | −0.778749 | −0.389374 | − | 0.921080i | \(-0.627309\pi\) | ||||
−0.389374 | + | 0.921080i | \(0.627309\pi\) | |||||||
\(128\) | 0.311710 | 0.0275515 | ||||||||
\(129\) | −3.60649 | −0.317534 | ||||||||
\(130\) | 3.13982 | 0.275380 | ||||||||
\(131\) | −8.43184 | −0.736693 | −0.368346 | − | 0.929689i | \(-0.620076\pi\) | ||||
−0.368346 | + | 0.929689i | \(0.620076\pi\) | |||||||
\(132\) | 8.99984 | 0.783335 | ||||||||
\(133\) | 7.54787 | 0.654483 | ||||||||
\(134\) | 21.4291 | 1.85119 | ||||||||
\(135\) | 2.86654 | 0.246712 | ||||||||
\(136\) | 0.0389655 | 0.00334127 | ||||||||
\(137\) | 3.68715 | 0.315015 | 0.157507 | − | 0.987518i | \(-0.449654\pi\) | ||||
0.157507 | + | 0.987518i | \(0.449654\pi\) | |||||||
\(138\) | 11.7458 | 0.999867 | ||||||||
\(139\) | 13.4100 | 1.13742 | 0.568709 | − | 0.822539i | \(-0.307443\pi\) | ||||
0.568709 | + | 0.822539i | \(0.307443\pi\) | |||||||
\(140\) | −7.97236 | −0.673788 | ||||||||
\(141\) | −3.40324 | −0.286604 | ||||||||
\(142\) | −2.26799 | −0.190325 | ||||||||
\(143\) | −2.43483 | −0.203611 | ||||||||
\(144\) | −3.96075 | −0.330063 | ||||||||
\(145\) | 4.10432 | 0.340846 | ||||||||
\(146\) | 26.5116 | 2.19412 | ||||||||
\(147\) | −5.10330 | −0.420913 | ||||||||
\(148\) | 4.28183 | 0.351964 | ||||||||
\(149\) | 3.58913 | 0.294033 | 0.147016 | − | 0.989134i | \(-0.453033\pi\) | ||||
0.147016 | + | 0.989134i | \(0.453033\pi\) | |||||||
\(150\) | −6.44969 | −0.526615 | ||||||||
\(151\) | −2.87926 | −0.234311 | −0.117156 | − | 0.993114i | \(-0.537378\pi\) | ||||
−0.117156 | + | 0.993114i | \(0.537378\pi\) | |||||||
\(152\) | 0.213553 | 0.0173214 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 12.3051 | 0.991577 | ||||||||
\(155\) | −18.7069 | −1.50257 | ||||||||
\(156\) | −1.10330 | −0.0883348 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 9.63218 | 0.766295 | ||||||||
\(159\) | −3.06822 | −0.243325 | ||||||||
\(160\) | 22.9858 | 1.81718 | ||||||||
\(161\) | 8.06861 | 0.635896 | ||||||||
\(162\) | −2.00485 | −0.157516 | ||||||||
\(163\) | 3.02948 | 0.237287 | 0.118644 | − | 0.992937i | \(-0.462145\pi\) | ||||
0.118644 | + | 0.992937i | \(0.462145\pi\) | |||||||
\(164\) | 9.40109 | 0.734102 | ||||||||
\(165\) | 12.7750 | 0.994536 | ||||||||
\(166\) | −4.76232 | −0.369628 | ||||||||
\(167\) | −8.82241 | −0.682698 | −0.341349 | − | 0.939937i | \(-0.610884\pi\) | ||||
−0.341349 | + | 0.939937i | \(0.610884\pi\) | |||||||
\(168\) | 0.0536636 | 0.00414024 | ||||||||
\(169\) | −12.7015 | −0.977039 | ||||||||
\(170\) | 5.74699 | 0.440774 | ||||||||
\(171\) | −5.48056 | −0.419109 | ||||||||
\(172\) | −7.28307 | −0.555329 | ||||||||
\(173\) | −3.88762 | −0.295571 | −0.147785 | − | 0.989019i | \(-0.547214\pi\) | ||||
−0.147785 | + | 0.989019i | \(0.547214\pi\) | |||||||
\(174\) | −2.87056 | −0.217617 | ||||||||
\(175\) | −4.43053 | −0.334916 | ||||||||
\(176\) | −17.6515 | −1.33053 | ||||||||
\(177\) | 14.2269 | 1.06936 | ||||||||
\(178\) | 23.9828 | 1.79759 | ||||||||
\(179\) | −20.5037 | −1.53252 | −0.766261 | − | 0.642530i | \(-0.777885\pi\) | ||||
−0.766261 | + | 0.642530i | \(0.777885\pi\) | |||||||
\(180\) | 5.78879 | 0.431471 | ||||||||
\(181\) | 3.89160 | 0.289260 | 0.144630 | − | 0.989486i | \(-0.453801\pi\) | ||||
0.144630 | + | 0.989486i | \(0.453801\pi\) | |||||||
\(182\) | −1.50850 | −0.111818 | ||||||||
\(183\) | −4.18725 | −0.309530 | ||||||||
\(184\) | 0.228286 | 0.0168295 | ||||||||
\(185\) | 6.07795 | 0.446860 | ||||||||
\(186\) | 13.0836 | 0.959333 | ||||||||
\(187\) | −4.45661 | −0.325900 | ||||||||
\(188\) | −6.87262 | −0.501237 | ||||||||
\(189\) | −1.37721 | −0.100177 | ||||||||
\(190\) | 31.4967 | 2.28501 | ||||||||
\(191\) | 6.57405 | 0.475682 | 0.237841 | − | 0.971304i | \(-0.423560\pi\) | ||||
0.237841 | + | 0.971304i | \(0.423560\pi\) | |||||||
\(192\) | −8.15472 | −0.588516 | ||||||||
\(193\) | −17.4354 | −1.25503 | −0.627514 | − | 0.778605i | \(-0.715927\pi\) | ||||
−0.627514 | + | 0.778605i | \(0.715927\pi\) | |||||||
\(194\) | 20.6775 | 1.48456 | ||||||||
\(195\) | −1.56611 | −0.112151 | ||||||||
\(196\) | −10.3058 | −0.736127 | ||||||||
\(197\) | 0.733484 | 0.0522586 | 0.0261293 | − | 0.999659i | \(-0.491682\pi\) | ||||
0.0261293 | + | 0.999659i | \(0.491682\pi\) | |||||||
\(198\) | −8.93485 | −0.634972 | ||||||||
\(199\) | 18.3345 | 1.29970 | 0.649849 | − | 0.760063i | \(-0.274832\pi\) | ||||
0.649849 | + | 0.760063i | \(0.274832\pi\) | |||||||
\(200\) | −0.125354 | −0.00886383 | ||||||||
\(201\) | −10.6886 | −0.753916 | ||||||||
\(202\) | 17.9693 | 1.26432 | ||||||||
\(203\) | −1.97189 | −0.138400 | ||||||||
\(204\) | −2.01944 | −0.141389 | ||||||||
\(205\) | 13.3446 | 0.932028 | ||||||||
\(206\) | −1.32300 | −0.0921778 | ||||||||
\(207\) | −5.85867 | −0.407206 | ||||||||
\(208\) | 2.16392 | 0.150041 | ||||||||
\(209\) | −24.4247 | −1.68949 | ||||||||
\(210\) | 7.91479 | 0.546173 | ||||||||
\(211\) | 13.7689 | 0.947887 | 0.473944 | − | 0.880555i | \(-0.342830\pi\) | ||||
0.473944 | + | 0.880555i | \(0.342830\pi\) | |||||||
\(212\) | −6.19606 | −0.425547 | ||||||||
\(213\) | 1.13125 | 0.0775120 | ||||||||
\(214\) | −13.3114 | −0.909948 | ||||||||
\(215\) | −10.3381 | −0.705055 | ||||||||
\(216\) | −0.0389655 | −0.00265127 | ||||||||
\(217\) | 8.98758 | 0.610117 | ||||||||
\(218\) | −7.21066 | −0.488368 | ||||||||
\(219\) | −13.2237 | −0.893577 | ||||||||
\(220\) | 25.7984 | 1.73933 | ||||||||
\(221\) | 0.546342 | 0.0367509 | ||||||||
\(222\) | −4.25091 | −0.285302 | ||||||||
\(223\) | 28.8546 | 1.93225 | 0.966123 | − | 0.258081i | \(-0.0830901\pi\) | ||||
0.966123 | + | 0.258081i | \(0.0830901\pi\) | |||||||
\(224\) | −11.0434 | −0.737865 | ||||||||
\(225\) | 3.21704 | 0.214469 | ||||||||
\(226\) | 4.96054 | 0.329971 | ||||||||
\(227\) | 5.52235 | 0.366531 | 0.183266 | − | 0.983063i | \(-0.441333\pi\) | ||||
0.183266 | + | 0.983063i | \(0.441333\pi\) | |||||||
\(228\) | −11.0676 | −0.732972 | ||||||||
\(229\) | −17.8130 | −1.17711 | −0.588557 | − | 0.808456i | \(-0.700304\pi\) | ||||
−0.588557 | + | 0.808456i | \(0.700304\pi\) | |||||||
\(230\) | 33.6697 | 2.22012 | ||||||||
\(231\) | −6.13768 | −0.403830 | ||||||||
\(232\) | −0.0557911 | −0.00366286 | ||||||||
\(233\) | −14.8035 | −0.969807 | −0.484903 | − | 0.874568i | \(-0.661145\pi\) | ||||
−0.484903 | + | 0.874568i | \(0.661145\pi\) | |||||||
\(234\) | 1.09533 | 0.0716043 | ||||||||
\(235\) | −9.75551 | −0.636379 | ||||||||
\(236\) | 28.7303 | 1.87018 | ||||||||
\(237\) | −4.80443 | −0.312081 | ||||||||
\(238\) | −2.76110 | −0.178975 | ||||||||
\(239\) | 29.1103 | 1.88299 | 0.941495 | − | 0.337028i | \(-0.109422\pi\) | ||||
0.941495 | + | 0.337028i | \(0.109422\pi\) | |||||||
\(240\) | −11.3536 | −0.732874 | ||||||||
\(241\) | −13.6700 | −0.880559 | −0.440280 | − | 0.897861i | \(-0.645121\pi\) | ||||
−0.440280 | + | 0.897861i | \(0.645121\pi\) | |||||||
\(242\) | −17.7658 | −1.14203 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −8.45588 | −0.541332 | ||||||||
\(245\) | −14.6288 | −0.934600 | ||||||||
\(246\) | −9.33321 | −0.595064 | ||||||||
\(247\) | 2.99426 | 0.190520 | ||||||||
\(248\) | 0.254287 | 0.0161472 | ||||||||
\(249\) | 2.37540 | 0.150535 | ||||||||
\(250\) | 10.2467 | 0.648056 | ||||||||
\(251\) | 5.63943 | 0.355958 | 0.177979 | − | 0.984034i | \(-0.443044\pi\) | ||||
0.177979 | + | 0.984034i | \(0.443044\pi\) | |||||||
\(252\) | −2.78118 | −0.175198 | ||||||||
\(253\) | −26.1098 | −1.64151 | ||||||||
\(254\) | 17.5947 | 1.10399 | ||||||||
\(255\) | −2.86654 | −0.179510 | ||||||||
\(256\) | 15.6845 | 0.980282 | ||||||||
\(257\) | 2.42232 | 0.151100 | 0.0755502 | − | 0.997142i | \(-0.475929\pi\) | ||||
0.0755502 | + | 0.997142i | \(0.475929\pi\) | |||||||
\(258\) | 7.23048 | 0.450150 | ||||||||
\(259\) | −2.92011 | −0.181447 | ||||||||
\(260\) | −3.16266 | −0.196140 | ||||||||
\(261\) | 1.43181 | 0.0886266 | ||||||||
\(262\) | 16.9046 | 1.04437 | ||||||||
\(263\) | −19.6566 | −1.21208 | −0.606039 | − | 0.795435i | \(-0.707242\pi\) | ||||
−0.606039 | + | 0.795435i | \(0.707242\pi\) | |||||||
\(264\) | −0.173654 | −0.0106877 | ||||||||
\(265\) | −8.79516 | −0.540282 | ||||||||
\(266\) | −15.1324 | −0.927825 | ||||||||
\(267\) | −11.9624 | −0.732087 | ||||||||
\(268\) | −21.5849 | −1.31851 | ||||||||
\(269\) | −21.6628 | −1.32081 | −0.660403 | − | 0.750912i | \(-0.729614\pi\) | ||||
−0.660403 | + | 0.750912i | \(0.729614\pi\) | |||||||
\(270\) | −5.74699 | −0.349750 | ||||||||
\(271\) | −4.11345 | −0.249874 | −0.124937 | − | 0.992165i | \(-0.539873\pi\) | ||||
−0.124937 | + | 0.992165i | \(0.539873\pi\) | |||||||
\(272\) | 3.96075 | 0.240156 | ||||||||
\(273\) | 0.752426 | 0.0455389 | ||||||||
\(274\) | −7.39220 | −0.446579 | ||||||||
\(275\) | 14.3371 | 0.864558 | ||||||||
\(276\) | −11.8312 | −0.712155 | ||||||||
\(277\) | −10.6252 | −0.638409 | −0.319205 | − | 0.947686i | \(-0.603416\pi\) | ||||
−0.319205 | + | 0.947686i | \(0.603416\pi\) | |||||||
\(278\) | −26.8850 | −1.61246 | ||||||||
\(279\) | −6.52595 | −0.390698 | ||||||||
\(280\) | 0.153829 | 0.00919303 | ||||||||
\(281\) | 14.6100 | 0.871558 | 0.435779 | − | 0.900054i | \(-0.356473\pi\) | ||||
0.435779 | + | 0.900054i | \(0.356473\pi\) | |||||||
\(282\) | 6.82299 | 0.406303 | ||||||||
\(283\) | 32.4691 | 1.93009 | 0.965043 | − | 0.262093i | \(-0.0844126\pi\) | ||||
0.965043 | + | 0.262093i | \(0.0844126\pi\) | |||||||
\(284\) | 2.28449 | 0.135559 | ||||||||
\(285\) | −15.7102 | −0.930593 | ||||||||
\(286\) | 4.88148 | 0.288648 | ||||||||
\(287\) | −6.41133 | −0.378449 | ||||||||
\(288\) | 8.01865 | 0.472504 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −8.22857 | −0.483198 | ||||||||
\(291\) | −10.3137 | −0.604600 | ||||||||
\(292\) | −26.7045 | −1.56276 | ||||||||
\(293\) | 5.62523 | 0.328629 | 0.164315 | − | 0.986408i | \(-0.447459\pi\) | ||||
0.164315 | + | 0.986408i | \(0.447459\pi\) | |||||||
\(294\) | 10.2314 | 0.596705 | ||||||||
\(295\) | 40.7819 | 2.37441 | ||||||||
\(296\) | −0.0826190 | −0.00480213 | ||||||||
\(297\) | 4.45661 | 0.258599 | ||||||||
\(298\) | −7.19567 | −0.416834 | ||||||||
\(299\) | 3.20084 | 0.185109 | ||||||||
\(300\) | 6.49660 | 0.375081 | ||||||||
\(301\) | 4.96688 | 0.286286 | ||||||||
\(302\) | 5.77250 | 0.332170 | ||||||||
\(303\) | −8.96292 | −0.514906 | ||||||||
\(304\) | 21.7071 | 1.24499 | ||||||||
\(305\) | −12.0029 | −0.687284 | ||||||||
\(306\) | 2.00485 | 0.114610 | ||||||||
\(307\) | 1.44141 | 0.0822656 | 0.0411328 | − | 0.999154i | \(-0.486903\pi\) | ||||
0.0411328 | + | 0.999154i | \(0.486903\pi\) | |||||||
\(308\) | −12.3946 | −0.706250 | ||||||||
\(309\) | 0.659899 | 0.0375403 | ||||||||
\(310\) | 37.5045 | 2.13011 | ||||||||
\(311\) | −8.16060 | −0.462745 | −0.231373 | − | 0.972865i | \(-0.574322\pi\) | ||||
−0.231373 | + | 0.972865i | \(0.574322\pi\) | |||||||
\(312\) | 0.0212885 | 0.00120522 | ||||||||
\(313\) | 8.94216 | 0.505441 | 0.252720 | − | 0.967539i | \(-0.418675\pi\) | ||||
0.252720 | + | 0.967539i | \(0.418675\pi\) | |||||||
\(314\) | −2.00485 | −0.113140 | ||||||||
\(315\) | −3.94782 | −0.222434 | ||||||||
\(316\) | −9.70224 | −0.545794 | ||||||||
\(317\) | −24.7048 | −1.38756 | −0.693781 | − | 0.720186i | \(-0.744056\pi\) | ||||
−0.693781 | + | 0.720186i | \(0.744056\pi\) | |||||||
\(318\) | 6.15132 | 0.344949 | ||||||||
\(319\) | 6.38100 | 0.357267 | ||||||||
\(320\) | −23.3758 | −1.30675 | ||||||||
\(321\) | 6.63959 | 0.370586 | ||||||||
\(322\) | −16.1764 | −0.901474 | ||||||||
\(323\) | 5.48056 | 0.304946 | ||||||||
\(324\) | 2.01944 | 0.112191 | ||||||||
\(325\) | −1.75760 | −0.0974942 | ||||||||
\(326\) | −6.07367 | −0.336389 | ||||||||
\(327\) | 3.59660 | 0.198893 | ||||||||
\(328\) | −0.181397 | −0.0100159 | ||||||||
\(329\) | 4.68697 | 0.258401 | ||||||||
\(330\) | −25.6121 | −1.40990 | ||||||||
\(331\) | −24.1392 | −1.32681 | −0.663404 | − | 0.748261i | \(-0.730889\pi\) | ||||
−0.663404 | + | 0.748261i | \(0.730889\pi\) | |||||||
\(332\) | 4.79696 | 0.263268 | ||||||||
\(333\) | 2.12031 | 0.116192 | ||||||||
\(334\) | 17.6876 | 0.967824 | ||||||||
\(335\) | −30.6393 | −1.67400 | ||||||||
\(336\) | 5.45478 | 0.297582 | ||||||||
\(337\) | −11.7248 | −0.638693 | −0.319347 | − | 0.947638i | \(-0.603463\pi\) | ||||
−0.319347 | + | 0.947638i | \(0.603463\pi\) | |||||||
\(338\) | 25.4647 | 1.38510 | ||||||||
\(339\) | −2.47427 | −0.134384 | ||||||||
\(340\) | −5.78879 | −0.313941 | ||||||||
\(341\) | −29.0836 | −1.57497 | ||||||||
\(342\) | 10.9877 | 0.594147 | ||||||||
\(343\) | 16.6688 | 0.900028 | ||||||||
\(344\) | 0.140529 | 0.00757680 | ||||||||
\(345\) | −16.7941 | −0.904164 | ||||||||
\(346\) | 7.79411 | 0.419014 | ||||||||
\(347\) | −5.40933 | −0.290388 | −0.145194 | − | 0.989403i | \(-0.546381\pi\) | ||||
−0.145194 | + | 0.989403i | \(0.546381\pi\) | |||||||
\(348\) | 2.89144 | 0.154997 | ||||||||
\(349\) | 24.0487 | 1.28730 | 0.643650 | − | 0.765320i | \(-0.277419\pi\) | ||||
0.643650 | + | 0.765320i | \(0.277419\pi\) | |||||||
\(350\) | 8.88256 | 0.474793 | ||||||||
\(351\) | −0.546342 | −0.0291616 | ||||||||
\(352\) | 35.7360 | 1.90474 | ||||||||
\(353\) | 9.10689 | 0.484711 | 0.242356 | − | 0.970187i | \(-0.422080\pi\) | ||||
0.242356 | + | 0.970187i | \(0.422080\pi\) | |||||||
\(354\) | −28.5228 | −1.51597 | ||||||||
\(355\) | 3.24277 | 0.172108 | ||||||||
\(356\) | −24.1573 | −1.28033 | ||||||||
\(357\) | 1.37721 | 0.0728896 | ||||||||
\(358\) | 41.1070 | 2.17257 | ||||||||
\(359\) | −3.07887 | −0.162497 | −0.0812484 | − | 0.996694i | \(-0.525891\pi\) | ||||
−0.0812484 | + | 0.996694i | \(0.525891\pi\) | |||||||
\(360\) | −0.111696 | −0.00588690 | ||||||||
\(361\) | 11.0365 | 0.580869 | ||||||||
\(362\) | −7.80208 | −0.410068 | ||||||||
\(363\) | 8.86138 | 0.465102 | ||||||||
\(364\) | 1.51948 | 0.0796422 | ||||||||
\(365\) | −37.9063 | −1.98411 | ||||||||
\(366\) | 8.39482 | 0.438804 | ||||||||
\(367\) | 26.9074 | 1.40455 | 0.702276 | − | 0.711904i | \(-0.252167\pi\) | ||||
0.702276 | + | 0.711904i | \(0.252167\pi\) | |||||||
\(368\) | 23.2047 | 1.20963 | ||||||||
\(369\) | 4.65531 | 0.242346 | ||||||||
\(370\) | −12.1854 | −0.633488 | ||||||||
\(371\) | 4.22557 | 0.219381 | ||||||||
\(372\) | −13.1787 | −0.683285 | ||||||||
\(373\) | 10.9041 | 0.564593 | 0.282296 | − | 0.959327i | \(-0.408904\pi\) | ||||
0.282296 | + | 0.959327i | \(0.408904\pi\) | |||||||
\(374\) | 8.93485 | 0.462010 | ||||||||
\(375\) | −5.11093 | −0.263927 | ||||||||
\(376\) | 0.132609 | 0.00683879 | ||||||||
\(377\) | −0.782255 | −0.0402882 | ||||||||
\(378\) | 2.76110 | 0.142016 | ||||||||
\(379\) | −13.3333 | −0.684888 | −0.342444 | − | 0.939538i | \(-0.611255\pi\) | ||||
−0.342444 | + | 0.939538i | \(0.611255\pi\) | |||||||
\(380\) | −31.7258 | −1.62750 | ||||||||
\(381\) | −8.77605 | −0.449611 | ||||||||
\(382\) | −13.1800 | −0.674348 | ||||||||
\(383\) | −14.6781 | −0.750016 | −0.375008 | − | 0.927022i | \(-0.622360\pi\) | ||||
−0.375008 | + | 0.927022i | \(0.622360\pi\) | |||||||
\(384\) | 0.311710 | 0.0159069 | ||||||||
\(385\) | −17.5939 | −0.896667 | ||||||||
\(386\) | 34.9554 | 1.77918 | ||||||||
\(387\) | −3.60649 | −0.183328 | ||||||||
\(388\) | −20.8279 | −1.05738 | ||||||||
\(389\) | −25.0472 | −1.26994 | −0.634972 | − | 0.772535i | \(-0.718988\pi\) | ||||
−0.634972 | + | 0.772535i | \(0.718988\pi\) | |||||||
\(390\) | 3.13982 | 0.158991 | ||||||||
\(391\) | 5.85867 | 0.296286 | ||||||||
\(392\) | 0.198853 | 0.0100436 | ||||||||
\(393\) | −8.43184 | −0.425330 | ||||||||
\(394\) | −1.47053 | −0.0740841 | ||||||||
\(395\) | −13.7721 | −0.692949 | ||||||||
\(396\) | 8.99984 | 0.452259 | ||||||||
\(397\) | −2.41395 | −0.121153 | −0.0605764 | − | 0.998164i | \(-0.519294\pi\) | ||||
−0.0605764 | + | 0.998164i | \(0.519294\pi\) | |||||||
\(398\) | −36.7580 | −1.84251 | ||||||||
\(399\) | 7.54787 | 0.377866 | ||||||||
\(400\) | −12.7419 | −0.637094 | ||||||||
\(401\) | −1.35431 | −0.0676313 | −0.0338156 | − | 0.999428i | \(-0.510766\pi\) | ||||
−0.0338156 | + | 0.999428i | \(0.510766\pi\) | |||||||
\(402\) | 21.4291 | 1.06879 | ||||||||
\(403\) | 3.56540 | 0.177605 | ||||||||
\(404\) | −18.1000 | −0.900510 | ||||||||
\(405\) | 2.86654 | 0.142439 | ||||||||
\(406\) | 3.95336 | 0.196202 | ||||||||
\(407\) | 9.44939 | 0.468389 | ||||||||
\(408\) | 0.0389655 | 0.00192908 | ||||||||
\(409\) | −25.6765 | −1.26962 | −0.634811 | − | 0.772667i | \(-0.718922\pi\) | ||||
−0.634811 | + | 0.772667i | \(0.718922\pi\) | |||||||
\(410\) | −26.7540 | −1.32129 | ||||||||
\(411\) | 3.68715 | 0.181874 | ||||||||
\(412\) | 1.33262 | 0.0656537 | ||||||||
\(413\) | −19.5934 | −0.964127 | ||||||||
\(414\) | 11.7458 | 0.577274 | ||||||||
\(415\) | 6.80917 | 0.334249 | ||||||||
\(416\) | −4.38093 | −0.214793 | ||||||||
\(417\) | 13.4100 | 0.656689 | ||||||||
\(418\) | 48.9680 | 2.39510 | ||||||||
\(419\) | −8.36614 | −0.408713 | −0.204356 | − | 0.978897i | \(-0.565510\pi\) | ||||
−0.204356 | + | 0.978897i | \(0.565510\pi\) | |||||||
\(420\) | −7.97236 | −0.389011 | ||||||||
\(421\) | 31.3435 | 1.52759 | 0.763795 | − | 0.645459i | \(-0.223334\pi\) | ||||
0.763795 | + | 0.645459i | \(0.223334\pi\) | |||||||
\(422\) | −27.6045 | −1.34377 | ||||||||
\(423\) | −3.40324 | −0.165471 | ||||||||
\(424\) | 0.119555 | 0.00580609 | ||||||||
\(425\) | −3.21704 | −0.156049 | ||||||||
\(426\) | −2.26799 | −0.109884 | ||||||||
\(427\) | 5.76671 | 0.279071 | ||||||||
\(428\) | 13.4082 | 0.648111 | ||||||||
\(429\) | −2.43483 | −0.117555 | ||||||||
\(430\) | 20.7264 | 0.999517 | ||||||||
\(431\) | 28.8096 | 1.38771 | 0.693855 | − | 0.720114i | \(-0.255911\pi\) | ||||
0.693855 | + | 0.720114i | \(0.255911\pi\) | |||||||
\(432\) | −3.96075 | −0.190562 | ||||||||
\(433\) | −16.4592 | −0.790977 | −0.395489 | − | 0.918471i | \(-0.629425\pi\) | ||||
−0.395489 | + | 0.918471i | \(0.629425\pi\) | |||||||
\(434\) | −18.0188 | −0.864929 | ||||||||
\(435\) | 4.10432 | 0.196787 | ||||||||
\(436\) | 7.26311 | 0.347840 | ||||||||
\(437\) | 32.1088 | 1.53597 | ||||||||
\(438\) | 26.5116 | 1.26677 | ||||||||
\(439\) | 35.5319 | 1.69584 | 0.847922 | − | 0.530121i | \(-0.177854\pi\) | ||||
0.847922 | + | 0.530121i | \(0.177854\pi\) | |||||||
\(440\) | −0.497786 | −0.0237310 | ||||||||
\(441\) | −5.10330 | −0.243014 | ||||||||
\(442\) | −1.09533 | −0.0520998 | ||||||||
\(443\) | 18.6524 | 0.886201 | 0.443100 | − | 0.896472i | \(-0.353878\pi\) | ||||
0.443100 | + | 0.896472i | \(0.353878\pi\) | |||||||
\(444\) | 4.28183 | 0.203207 | ||||||||
\(445\) | −34.2907 | −1.62553 | ||||||||
\(446\) | −57.8492 | −2.73924 | ||||||||
\(447\) | 3.58913 | 0.169760 | ||||||||
\(448\) | 11.2307 | 0.530603 | ||||||||
\(449\) | 17.3506 | 0.818826 | 0.409413 | − | 0.912349i | \(-0.365734\pi\) | ||||
0.409413 | + | 0.912349i | \(0.365734\pi\) | |||||||
\(450\) | −6.44969 | −0.304041 | ||||||||
\(451\) | 20.7469 | 0.976933 | ||||||||
\(452\) | −4.99663 | −0.235022 | ||||||||
\(453\) | −2.87926 | −0.135280 | ||||||||
\(454\) | −11.0715 | −0.519611 | ||||||||
\(455\) | 2.15686 | 0.101115 | ||||||||
\(456\) | 0.213553 | 0.0100005 | ||||||||
\(457\) | 30.0523 | 1.40579 | 0.702893 | − | 0.711295i | \(-0.251891\pi\) | ||||
0.702893 | + | 0.711295i | \(0.251891\pi\) | |||||||
\(458\) | 35.7124 | 1.66873 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −33.9146 | −1.58128 | ||||||||
\(461\) | 14.4897 | 0.674854 | 0.337427 | − | 0.941352i | \(-0.390443\pi\) | ||||
0.337427 | + | 0.941352i | \(0.390443\pi\) | |||||||
\(462\) | 12.3051 | 0.572487 | ||||||||
\(463\) | −4.00974 | −0.186348 | −0.0931742 | − | 0.995650i | \(-0.529701\pi\) | ||||
−0.0931742 | + | 0.995650i | \(0.529701\pi\) | |||||||
\(464\) | −5.67103 | −0.263271 | ||||||||
\(465\) | −18.7069 | −0.867510 | ||||||||
\(466\) | 29.6788 | 1.37484 | ||||||||
\(467\) | 23.4089 | 1.08323 | 0.541617 | − | 0.840625i | \(-0.317812\pi\) | ||||
0.541617 | + | 0.840625i | \(0.317812\pi\) | |||||||
\(468\) | −1.10330 | −0.0510001 | ||||||||
\(469\) | 14.7204 | 0.679726 | ||||||||
\(470\) | 19.5584 | 0.902160 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −0.554358 | −0.0255164 | ||||||||
\(473\) | −16.0727 | −0.739024 | ||||||||
\(474\) | 9.63218 | 0.442421 | ||||||||
\(475\) | −17.6312 | −0.808973 | ||||||||
\(476\) | 2.78118 | 0.127475 | ||||||||
\(477\) | −3.06822 | −0.140484 | ||||||||
\(478\) | −58.3619 | −2.66941 | ||||||||
\(479\) | −11.7932 | −0.538844 | −0.269422 | − | 0.963022i | \(-0.586833\pi\) | ||||
−0.269422 | + | 0.963022i | \(0.586833\pi\) | |||||||
\(480\) | 22.9858 | 1.04915 | ||||||||
\(481\) | −1.15841 | −0.0528191 | ||||||||
\(482\) | 27.4062 | 1.24832 | ||||||||
\(483\) | 8.06861 | 0.367134 | ||||||||
\(484\) | 17.8950 | 0.813408 | ||||||||
\(485\) | −29.5646 | −1.34246 | ||||||||
\(486\) | −2.00485 | −0.0909420 | ||||||||
\(487\) | −11.9864 | −0.543155 | −0.271578 | − | 0.962417i | \(-0.587545\pi\) | ||||
−0.271578 | + | 0.962417i | \(0.587545\pi\) | |||||||
\(488\) | 0.163158 | 0.00738583 | ||||||||
\(489\) | 3.02948 | 0.136998 | ||||||||
\(490\) | 29.3286 | 1.32493 | ||||||||
\(491\) | 18.8930 | 0.852631 | 0.426315 | − | 0.904575i | \(-0.359811\pi\) | ||||
0.426315 | + | 0.904575i | \(0.359811\pi\) | |||||||
\(492\) | 9.40109 | 0.423834 | ||||||||
\(493\) | −1.43181 | −0.0644853 | ||||||||
\(494\) | −6.00305 | −0.270090 | ||||||||
\(495\) | 12.7750 | 0.574195 | ||||||||
\(496\) | 25.8476 | 1.16059 | ||||||||
\(497\) | −1.55797 | −0.0698843 | ||||||||
\(498\) | −4.76232 | −0.213405 | ||||||||
\(499\) | 16.6378 | 0.744810 | 0.372405 | − | 0.928070i | \(-0.378533\pi\) | ||||
0.372405 | + | 0.928070i | \(0.378533\pi\) | |||||||
\(500\) | −10.3212 | −0.461578 | ||||||||
\(501\) | −8.82241 | −0.394156 | ||||||||
\(502\) | −11.3062 | −0.504622 | ||||||||
\(503\) | 37.0162 | 1.65047 | 0.825235 | − | 0.564790i | \(-0.191043\pi\) | ||||
0.825235 | + | 0.564790i | \(0.191043\pi\) | |||||||
\(504\) | 0.0536636 | 0.00239037 | ||||||||
\(505\) | −25.6925 | −1.14330 | ||||||||
\(506\) | 52.3464 | 2.32708 | ||||||||
\(507\) | −12.7015 | −0.564094 | ||||||||
\(508\) | −17.7227 | −0.786317 | ||||||||
\(509\) | 14.9314 | 0.661823 | 0.330912 | − | 0.943662i | \(-0.392644\pi\) | ||||
0.330912 | + | 0.943662i | \(0.392644\pi\) | |||||||
\(510\) | 5.74699 | 0.254481 | ||||||||
\(511\) | 18.2118 | 0.805643 | ||||||||
\(512\) | −32.0686 | −1.41724 | ||||||||
\(513\) | −5.48056 | −0.241973 | ||||||||
\(514\) | −4.85640 | −0.214207 | ||||||||
\(515\) | 1.89163 | 0.0833550 | ||||||||
\(516\) | −7.28307 | −0.320619 | ||||||||
\(517\) | −15.1669 | −0.667040 | ||||||||
\(518\) | 5.85438 | 0.257227 | ||||||||
\(519\) | −3.88762 | −0.170648 | ||||||||
\(520\) | 0.0610243 | 0.00267609 | ||||||||
\(521\) | 40.1220 | 1.75778 | 0.878889 | − | 0.477027i | \(-0.158285\pi\) | ||||
0.878889 | + | 0.477027i | \(0.158285\pi\) | |||||||
\(522\) | −2.87056 | −0.125641 | ||||||||
\(523\) | −18.5668 | −0.811870 | −0.405935 | − | 0.913902i | \(-0.633054\pi\) | ||||
−0.405935 | + | 0.913902i | \(0.633054\pi\) | |||||||
\(524\) | −17.0275 | −0.743852 | ||||||||
\(525\) | −4.43053 | −0.193364 | ||||||||
\(526\) | 39.4086 | 1.71830 | ||||||||
\(527\) | 6.52595 | 0.284275 | ||||||||
\(528\) | −17.6515 | −0.768184 | ||||||||
\(529\) | 11.3241 | 0.492350 | ||||||||
\(530\) | 17.6330 | 0.765928 | ||||||||
\(531\) | 14.2269 | 0.617394 | ||||||||
\(532\) | 15.2424 | 0.660843 | ||||||||
\(533\) | −2.54339 | −0.110166 | ||||||||
\(534\) | 23.9828 | 1.03784 | ||||||||
\(535\) | 19.0326 | 0.822852 | ||||||||
\(536\) | 0.416487 | 0.0179895 | ||||||||
\(537\) | −20.5037 | −0.884802 | ||||||||
\(538\) | 43.4308 | 1.87243 | ||||||||
\(539\) | −22.7434 | −0.979628 | ||||||||
\(540\) | 5.78879 | 0.249110 | ||||||||
\(541\) | 10.4847 | 0.450772 | 0.225386 | − | 0.974269i | \(-0.427636\pi\) | ||||
0.225386 | + | 0.974269i | \(0.427636\pi\) | |||||||
\(542\) | 8.24686 | 0.354233 | ||||||||
\(543\) | 3.89160 | 0.167004 | ||||||||
\(544\) | −8.01865 | −0.343797 | ||||||||
\(545\) | 10.3098 | 0.441623 | ||||||||
\(546\) | −1.50850 | −0.0645580 | ||||||||
\(547\) | 40.1637 | 1.71727 | 0.858637 | − | 0.512584i | \(-0.171312\pi\) | ||||
0.858637 | + | 0.512584i | \(0.171312\pi\) | |||||||
\(548\) | 7.44597 | 0.318076 | ||||||||
\(549\) | −4.18725 | −0.178707 | ||||||||
\(550\) | −28.7437 | −1.22564 | ||||||||
\(551\) | −7.84709 | −0.334297 | ||||||||
\(552\) | 0.228286 | 0.00971651 | ||||||||
\(553\) | 6.61670 | 0.281371 | ||||||||
\(554\) | 21.3021 | 0.905038 | ||||||||
\(555\) | 6.07795 | 0.257994 | ||||||||
\(556\) | 27.0806 | 1.14847 | ||||||||
\(557\) | −12.9624 | −0.549236 | −0.274618 | − | 0.961553i | \(-0.588551\pi\) | ||||
−0.274618 | + | 0.961553i | \(0.588551\pi\) | |||||||
\(558\) | 13.0836 | 0.553871 | ||||||||
\(559\) | 1.97037 | 0.0833380 | ||||||||
\(560\) | 15.6363 | 0.660755 | ||||||||
\(561\) | −4.45661 | −0.188158 | ||||||||
\(562\) | −29.2909 | −1.23556 | ||||||||
\(563\) | 0.331680 | 0.0139786 | 0.00698931 | − | 0.999976i | \(-0.497775\pi\) | ||||
0.00698931 | + | 0.999976i | \(0.497775\pi\) | |||||||
\(564\) | −6.87262 | −0.289390 | ||||||||
\(565\) | −7.09258 | −0.298387 | ||||||||
\(566\) | −65.0957 | −2.73618 | ||||||||
\(567\) | −1.37721 | −0.0578373 | ||||||||
\(568\) | −0.0440797 | −0.00184955 | ||||||||
\(569\) | 22.7960 | 0.955658 | 0.477829 | − | 0.878453i | \(-0.341424\pi\) | ||||
0.477829 | + | 0.878453i | \(0.341424\pi\) | |||||||
\(570\) | 31.4967 | 1.31925 | ||||||||
\(571\) | 8.61150 | 0.360380 | 0.180190 | − | 0.983632i | \(-0.442329\pi\) | ||||
0.180190 | + | 0.983632i | \(0.442329\pi\) | |||||||
\(572\) | −4.91699 | −0.205590 | ||||||||
\(573\) | 6.57405 | 0.274635 | ||||||||
\(574\) | 12.8538 | 0.536506 | ||||||||
\(575\) | −18.8476 | −0.785998 | ||||||||
\(576\) | −8.15472 | −0.339780 | ||||||||
\(577\) | −34.1100 | −1.42002 | −0.710009 | − | 0.704193i | \(-0.751309\pi\) | ||||
−0.710009 | + | 0.704193i | \(0.751309\pi\) | |||||||
\(578\) | −2.00485 | −0.0833909 | ||||||||
\(579\) | −17.4354 | −0.724591 | ||||||||
\(580\) | 8.28842 | 0.344158 | ||||||||
\(581\) | −3.27142 | −0.135721 | ||||||||
\(582\) | 20.6775 | 0.857109 | ||||||||
\(583\) | −13.6738 | −0.566313 | ||||||||
\(584\) | 0.515270 | 0.0213220 | ||||||||
\(585\) | −1.56611 | −0.0647506 | ||||||||
\(586\) | −11.2778 | −0.465880 | ||||||||
\(587\) | −45.3401 | −1.87139 | −0.935693 | − | 0.352814i | \(-0.885225\pi\) | ||||
−0.935693 | + | 0.352814i | \(0.885225\pi\) | |||||||
\(588\) | −10.3058 | −0.425003 | ||||||||
\(589\) | 35.7658 | 1.47371 | ||||||||
\(590\) | −81.7617 | −3.36608 | ||||||||
\(591\) | 0.733484 | 0.0301715 | ||||||||
\(592\) | −8.39802 | −0.345156 | ||||||||
\(593\) | −25.1697 | −1.03360 | −0.516799 | − | 0.856107i | \(-0.672876\pi\) | ||||
−0.516799 | + | 0.856107i | \(0.672876\pi\) | |||||||
\(594\) | −8.93485 | −0.366601 | ||||||||
\(595\) | 3.94782 | 0.161845 | ||||||||
\(596\) | 7.24801 | 0.296890 | ||||||||
\(597\) | 18.3345 | 0.750381 | ||||||||
\(598\) | −6.41721 | −0.262419 | ||||||||
\(599\) | 15.3010 | 0.625181 | 0.312590 | − | 0.949888i | \(-0.398803\pi\) | ||||
0.312590 | + | 0.949888i | \(0.398803\pi\) | |||||||
\(600\) | −0.125354 | −0.00511754 | ||||||||
\(601\) | −5.36129 | −0.218692 | −0.109346 | − | 0.994004i | \(-0.534876\pi\) | ||||
−0.109346 | + | 0.994004i | \(0.534876\pi\) | |||||||
\(602\) | −9.95787 | −0.405852 | ||||||||
\(603\) | −10.6886 | −0.435274 | ||||||||
\(604\) | −5.81449 | −0.236588 | ||||||||
\(605\) | 25.4015 | 1.03272 | ||||||||
\(606\) | 17.9693 | 0.729954 | ||||||||
\(607\) | −43.3910 | −1.76119 | −0.880593 | − | 0.473874i | \(-0.842855\pi\) | ||||
−0.880593 | + | 0.473874i | \(0.842855\pi\) | |||||||
\(608\) | −43.9467 | −1.78227 | ||||||||
\(609\) | −1.97189 | −0.0799052 | ||||||||
\(610\) | 24.0641 | 0.974325 | ||||||||
\(611\) | 1.85933 | 0.0752205 | ||||||||
\(612\) | −2.01944 | −0.0816308 | ||||||||
\(613\) | −0.0395570 | −0.00159769 | −0.000798847 | − | 1.00000i | \(-0.500254\pi\) | ||||
−0.000798847 | 1.00000i | \(0.500254\pi\) | ||||||||
\(614\) | −2.88981 | −0.116623 | ||||||||
\(615\) | 13.3446 | 0.538107 | ||||||||
\(616\) | 0.239158 | 0.00963594 | ||||||||
\(617\) | 21.8066 | 0.877902 | 0.438951 | − | 0.898511i | \(-0.355350\pi\) | ||||
0.438951 | + | 0.898511i | \(0.355350\pi\) | |||||||
\(618\) | −1.32300 | −0.0532189 | ||||||||
\(619\) | −21.0830 | −0.847396 | −0.423698 | − | 0.905804i | \(-0.639268\pi\) | ||||
−0.423698 | + | 0.905804i | \(0.639268\pi\) | |||||||
\(620\) | −37.7773 | −1.51717 | ||||||||
\(621\) | −5.85867 | −0.235100 | ||||||||
\(622\) | 16.3608 | 0.656008 | ||||||||
\(623\) | 16.4747 | 0.660045 | ||||||||
\(624\) | 2.16392 | 0.0866263 | ||||||||
\(625\) | −30.7359 | −1.22943 | ||||||||
\(626\) | −17.9277 | −0.716536 | ||||||||
\(627\) | −24.4247 | −0.975429 | ||||||||
\(628\) | 2.01944 | 0.0805843 | ||||||||
\(629\) | −2.12031 | −0.0845423 | ||||||||
\(630\) | 7.91479 | 0.315333 | ||||||||
\(631\) | −8.49757 | −0.338283 | −0.169141 | − | 0.985592i | \(-0.554099\pi\) | ||||
−0.169141 | + | 0.985592i | \(0.554099\pi\) | |||||||
\(632\) | 0.187207 | 0.00744671 | ||||||||
\(633\) | 13.7689 | 0.547263 | ||||||||
\(634\) | 49.5295 | 1.96707 | ||||||||
\(635\) | −25.1569 | −0.998321 | ||||||||
\(636\) | −6.19606 | −0.245690 | ||||||||
\(637\) | 2.78815 | 0.110470 | ||||||||
\(638\) | −12.7930 | −0.506478 | ||||||||
\(639\) | 1.13125 | 0.0447515 | ||||||||
\(640\) | 0.893527 | 0.0353198 | ||||||||
\(641\) | −25.7301 | −1.01628 | −0.508138 | − | 0.861276i | \(-0.669666\pi\) | ||||
−0.508138 | + | 0.861276i | \(0.669666\pi\) | |||||||
\(642\) | −13.3114 | −0.525359 | ||||||||
\(643\) | 19.3315 | 0.762362 | 0.381181 | − | 0.924500i | \(-0.375518\pi\) | ||||
0.381181 | + | 0.924500i | \(0.375518\pi\) | |||||||
\(644\) | 16.2940 | 0.642075 | ||||||||
\(645\) | −10.3381 | −0.407064 | ||||||||
\(646\) | −10.9877 | −0.432306 | ||||||||
\(647\) | −5.53680 | −0.217674 | −0.108837 | − | 0.994060i | \(-0.534713\pi\) | ||||
−0.108837 | + | 0.994060i | \(0.534713\pi\) | |||||||
\(648\) | −0.0389655 | −0.00153071 | ||||||||
\(649\) | 63.4037 | 2.48881 | ||||||||
\(650\) | 3.52373 | 0.138212 | ||||||||
\(651\) | 8.98758 | 0.352251 | ||||||||
\(652\) | 6.11785 | 0.239593 | ||||||||
\(653\) | 16.0385 | 0.627633 | 0.313817 | − | 0.949484i | \(-0.398392\pi\) | ||||
0.313817 | + | 0.949484i | \(0.398392\pi\) | |||||||
\(654\) | −7.21066 | −0.281959 | ||||||||
\(655\) | −24.1702 | −0.944407 | ||||||||
\(656\) | −18.4385 | −0.719903 | ||||||||
\(657\) | −13.2237 | −0.515907 | ||||||||
\(658\) | −9.39668 | −0.366321 | ||||||||
\(659\) | 8.96517 | 0.349234 | 0.174617 | − | 0.984636i | \(-0.444131\pi\) | ||||
0.174617 | + | 0.984636i | \(0.444131\pi\) | |||||||
\(660\) | 25.7984 | 1.00420 | ||||||||
\(661\) | −40.7448 | −1.58479 | −0.792395 | − | 0.610008i | \(-0.791166\pi\) | ||||
−0.792395 | + | 0.610008i | \(0.791166\pi\) | |||||||
\(662\) | 48.3955 | 1.88094 | ||||||||
\(663\) | 0.546342 | 0.0212182 | ||||||||
\(664\) | −0.0925586 | −0.00359197 | ||||||||
\(665\) | 21.6362 | 0.839017 | ||||||||
\(666\) | −4.25091 | −0.164719 | ||||||||
\(667\) | −8.38848 | −0.324803 | ||||||||
\(668\) | −17.8163 | −0.689333 | ||||||||
\(669\) | 28.8546 | 1.11558 | ||||||||
\(670\) | 61.4273 | 2.37314 | ||||||||
\(671\) | −18.6609 | −0.720397 | ||||||||
\(672\) | −11.0434 | −0.426007 | ||||||||
\(673\) | −49.4249 | −1.90519 | −0.952596 | − | 0.304239i | \(-0.901598\pi\) | ||||
−0.952596 | + | 0.304239i | \(0.901598\pi\) | |||||||
\(674\) | 23.5066 | 0.905440 | ||||||||
\(675\) | 3.21704 | 0.123824 | ||||||||
\(676\) | −25.6499 | −0.986534 | ||||||||
\(677\) | −0.821016 | −0.0315542 | −0.0157771 | − | 0.999876i | \(-0.505022\pi\) | ||||
−0.0157771 | + | 0.999876i | \(0.505022\pi\) | |||||||
\(678\) | 4.96054 | 0.190509 | ||||||||
\(679\) | 14.2041 | 0.545104 | ||||||||
\(680\) | 0.111696 | 0.00428335 | ||||||||
\(681\) | 5.52235 | 0.211617 | ||||||||
\(682\) | 58.3083 | 2.23274 | ||||||||
\(683\) | −12.9695 | −0.496264 | −0.248132 | − | 0.968726i | \(-0.579817\pi\) | ||||
−0.248132 | + | 0.968726i | \(0.579817\pi\) | |||||||
\(684\) | −11.0676 | −0.423182 | ||||||||
\(685\) | 10.5694 | 0.403834 | ||||||||
\(686\) | −33.4184 | −1.27592 | ||||||||
\(687\) | −17.8130 | −0.679607 | ||||||||
\(688\) | 14.2844 | 0.544588 | ||||||||
\(689\) | 1.67629 | 0.0638617 | ||||||||
\(690\) | 33.6697 | 1.28178 | ||||||||
\(691\) | 14.8609 | 0.565335 | 0.282667 | − | 0.959218i | \(-0.408781\pi\) | ||||
0.282667 | + | 0.959218i | \(0.408781\pi\) | |||||||
\(692\) | −7.85080 | −0.298443 | ||||||||
\(693\) | −6.13768 | −0.233151 | ||||||||
\(694\) | 10.8449 | 0.411667 | ||||||||
\(695\) | 38.4402 | 1.45812 | ||||||||
\(696\) | −0.0557911 | −0.00211476 | ||||||||
\(697\) | −4.65531 | −0.176332 | ||||||||
\(698\) | −48.2142 | −1.82493 | ||||||||
\(699\) | −14.8035 | −0.559918 | ||||||||
\(700\) | −8.94716 | −0.338171 | ||||||||
\(701\) | 43.2251 | 1.63259 | 0.816296 | − | 0.577634i | \(-0.196024\pi\) | ||||
0.816296 | + | 0.577634i | \(0.196024\pi\) | |||||||
\(702\) | 1.09533 | 0.0413407 | ||||||||
\(703\) | −11.6205 | −0.438275 | ||||||||
\(704\) | −36.3424 | −1.36971 | ||||||||
\(705\) | −9.75551 | −0.367414 | ||||||||
\(706\) | −18.2580 | −0.687148 | ||||||||
\(707\) | 12.3438 | 0.464236 | ||||||||
\(708\) | 28.7303 | 1.07975 | ||||||||
\(709\) | −43.8415 | −1.64650 | −0.823250 | − | 0.567678i | \(-0.807842\pi\) | ||||
−0.823250 | + | 0.567678i | \(0.807842\pi\) | |||||||
\(710\) | −6.50128 | −0.243989 | ||||||||
\(711\) | −4.80443 | −0.180180 | ||||||||
\(712\) | 0.466121 | 0.0174686 | ||||||||
\(713\) | 38.2334 | 1.43185 | ||||||||
\(714\) | −2.76110 | −0.103332 | ||||||||
\(715\) | −6.97954 | −0.261020 | ||||||||
\(716\) | −41.4060 | −1.54741 | ||||||||
\(717\) | 29.1103 | 1.08714 | ||||||||
\(718\) | 6.17269 | 0.230363 | ||||||||
\(719\) | −34.1706 | −1.27435 | −0.637174 | − | 0.770720i | \(-0.719897\pi\) | ||||
−0.637174 | + | 0.770720i | \(0.719897\pi\) | |||||||
\(720\) | −11.3536 | −0.423125 | ||||||||
\(721\) | −0.908818 | −0.0338461 | ||||||||
\(722\) | −22.1266 | −0.823466 | ||||||||
\(723\) | −13.6700 | −0.508391 | ||||||||
\(724\) | 7.85883 | 0.292071 | ||||||||
\(725\) | 4.60617 | 0.171069 | ||||||||
\(726\) | −17.7658 | −0.659349 | ||||||||
\(727\) | −20.5519 | −0.762228 | −0.381114 | − | 0.924528i | \(-0.624459\pi\) | ||||
−0.381114 | + | 0.924528i | \(0.624459\pi\) | |||||||
\(728\) | −0.0293187 | −0.00108662 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 75.9966 | 2.81276 | ||||||||
\(731\) | 3.60649 | 0.133391 | ||||||||
\(732\) | −8.45588 | −0.312538 | ||||||||
\(733\) | 49.0781 | 1.81274 | 0.906371 | − | 0.422482i | \(-0.138841\pi\) | ||||
0.906371 | + | 0.422482i | \(0.138841\pi\) | |||||||
\(734\) | −53.9453 | −1.99116 | ||||||||
\(735\) | −14.6288 | −0.539591 | ||||||||
\(736\) | −46.9787 | −1.73166 | ||||||||
\(737\) | −47.6349 | −1.75466 | ||||||||
\(738\) | −9.33321 | −0.343560 | ||||||||
\(739\) | −21.7901 | −0.801563 | −0.400782 | − | 0.916174i | \(-0.631261\pi\) | ||||
−0.400782 | + | 0.916174i | \(0.631261\pi\) | |||||||
\(740\) | 12.2740 | 0.451202 | ||||||||
\(741\) | 2.99426 | 0.109997 | ||||||||
\(742\) | −8.47165 | −0.311004 | ||||||||
\(743\) | −14.1776 | −0.520124 | −0.260062 | − | 0.965592i | \(-0.583743\pi\) | ||||
−0.260062 | + | 0.965592i | \(0.583743\pi\) | |||||||
\(744\) | 0.254287 | 0.00932261 | ||||||||
\(745\) | 10.2884 | 0.376937 | ||||||||
\(746\) | −21.8611 | −0.800392 | ||||||||
\(747\) | 2.37540 | 0.0869113 | ||||||||
\(748\) | −8.99984 | −0.329067 | ||||||||
\(749\) | −9.14409 | −0.334118 | ||||||||
\(750\) | 10.2467 | 0.374155 | ||||||||
\(751\) | 12.7769 | 0.466235 | 0.233118 | − | 0.972449i | \(-0.425107\pi\) | ||||
0.233118 | + | 0.972449i | \(0.425107\pi\) | |||||||
\(752\) | 13.4794 | 0.491542 | ||||||||
\(753\) | 5.63943 | 0.205512 | ||||||||
\(754\) | 1.56831 | 0.0571144 | ||||||||
\(755\) | −8.25352 | −0.300376 | ||||||||
\(756\) | −2.78118 | −0.101151 | ||||||||
\(757\) | 19.2523 | 0.699739 | 0.349869 | − | 0.936799i | \(-0.386226\pi\) | ||||
0.349869 | + | 0.936799i | \(0.386226\pi\) | |||||||
\(758\) | 26.7314 | 0.970928 | ||||||||
\(759\) | −26.1098 | −0.947727 | ||||||||
\(760\) | 0.612157 | 0.0222053 | ||||||||
\(761\) | −40.4457 | −1.46616 | −0.733078 | − | 0.680144i | \(-0.761917\pi\) | ||||
−0.733078 | + | 0.680144i | \(0.761917\pi\) | |||||||
\(762\) | 17.5947 | 0.637389 | ||||||||
\(763\) | −4.95327 | −0.179320 | ||||||||
\(764\) | 13.2759 | 0.480304 | ||||||||
\(765\) | −2.86654 | −0.103640 | ||||||||
\(766\) | 29.4274 | 1.06326 | ||||||||
\(767\) | −7.77274 | −0.280657 | ||||||||
\(768\) | 15.6845 | 0.565966 | ||||||||
\(769\) | −31.1093 | −1.12183 | −0.560916 | − | 0.827873i | \(-0.689551\pi\) | ||||
−0.560916 | + | 0.827873i | \(0.689551\pi\) | |||||||
\(770\) | 35.2731 | 1.27116 | ||||||||
\(771\) | 2.42232 | 0.0872378 | ||||||||
\(772\) | −35.2097 | −1.26722 | ||||||||
\(773\) | −49.4489 | −1.77855 | −0.889277 | − | 0.457370i | \(-0.848792\pi\) | ||||
−0.889277 | + | 0.457370i | \(0.848792\pi\) | |||||||
\(774\) | 7.23048 | 0.259894 | ||||||||
\(775\) | −20.9942 | −0.754134 | ||||||||
\(776\) | 0.401879 | 0.0144266 | ||||||||
\(777\) | −2.92011 | −0.104758 | ||||||||
\(778\) | 50.2160 | 1.80033 | ||||||||
\(779\) | −25.5137 | −0.914123 | ||||||||
\(780\) | −3.16266 | −0.113241 | ||||||||
\(781\) | 5.04154 | 0.180400 | ||||||||
\(782\) | −11.7458 | −0.420028 | ||||||||
\(783\) | 1.43181 | 0.0511686 | ||||||||
\(784\) | 20.2129 | 0.721889 | ||||||||
\(785\) | 2.86654 | 0.102311 | ||||||||
\(786\) | 16.9046 | 0.602967 | ||||||||
\(787\) | −34.2957 | −1.22251 | −0.611255 | − | 0.791434i | \(-0.709335\pi\) | ||||
−0.611255 | + | 0.791434i | \(0.709335\pi\) | |||||||
\(788\) | 1.48122 | 0.0527664 | ||||||||
\(789\) | −19.6566 | −0.699793 | ||||||||
\(790\) | 27.6110 | 0.982356 | ||||||||
\(791\) | 3.40758 | 0.121160 | ||||||||
\(792\) | −0.173654 | −0.00617053 | ||||||||
\(793\) | 2.28767 | 0.0812375 | ||||||||
\(794\) | 4.83962 | 0.171752 | ||||||||
\(795\) | −8.79516 | −0.311932 | ||||||||
\(796\) | 37.0253 | 1.31233 | ||||||||
\(797\) | 35.4137 | 1.25442 | 0.627208 | − | 0.778851i | \(-0.284197\pi\) | ||||
0.627208 | + | 0.778851i | \(0.284197\pi\) | |||||||
\(798\) | −15.1324 | −0.535680 | ||||||||
\(799\) | 3.40324 | 0.120398 | ||||||||
\(800\) | 25.7963 | 0.912037 | ||||||||
\(801\) | −11.9624 | −0.422671 | ||||||||
\(802\) | 2.71520 | 0.0958771 | ||||||||
\(803\) | −58.9330 | −2.07970 | ||||||||
\(804\) | −21.5849 | −0.761242 | ||||||||
\(805\) | 23.1290 | 0.815189 | ||||||||
\(806\) | −7.14810 | −0.251781 | ||||||||
\(807\) | −21.6628 | −0.762567 | ||||||||
\(808\) | 0.349245 | 0.0122864 | ||||||||
\(809\) | 5.09425 | 0.179104 | 0.0895522 | − | 0.995982i | \(-0.471456\pi\) | ||||
0.0895522 | + | 0.995982i | \(0.471456\pi\) | |||||||
\(810\) | −5.74699 | −0.201929 | ||||||||
\(811\) | −22.7353 | −0.798346 | −0.399173 | − | 0.916876i | \(-0.630703\pi\) | ||||
−0.399173 | + | 0.916876i | \(0.630703\pi\) | |||||||
\(812\) | −3.98211 | −0.139745 | ||||||||
\(813\) | −4.11345 | −0.144265 | ||||||||
\(814\) | −18.9446 | −0.664010 | ||||||||
\(815\) | 8.68413 | 0.304192 | ||||||||
\(816\) | 3.96075 | 0.138654 | ||||||||
\(817\) | 19.7656 | 0.691509 | ||||||||
\(818\) | 51.4777 | 1.79987 | ||||||||
\(819\) | 0.752426 | 0.0262919 | ||||||||
\(820\) | 26.9486 | 0.941086 | ||||||||
\(821\) | 44.3681 | 1.54846 | 0.774229 | − | 0.632906i | \(-0.218138\pi\) | ||||
0.774229 | + | 0.632906i | \(0.218138\pi\) | |||||||
\(822\) | −7.39220 | −0.257833 | ||||||||
\(823\) | −10.2472 | −0.357196 | −0.178598 | − | 0.983922i | \(-0.557156\pi\) | ||||
−0.178598 | + | 0.983922i | \(0.557156\pi\) | |||||||
\(824\) | −0.0257133 | −0.000895766 0 | ||||||||
\(825\) | 14.3371 | 0.499153 | ||||||||
\(826\) | 39.2818 | 1.36679 | ||||||||
\(827\) | −32.0567 | −1.11472 | −0.557360 | − | 0.830271i | \(-0.688186\pi\) | ||||
−0.557360 | + | 0.830271i | \(0.688186\pi\) | |||||||
\(828\) | −11.8312 | −0.411163 | ||||||||
\(829\) | 32.8499 | 1.14092 | 0.570462 | − | 0.821324i | \(-0.306764\pi\) | ||||
0.570462 | + | 0.821324i | \(0.306764\pi\) | |||||||
\(830\) | −13.6514 | −0.473846 | ||||||||
\(831\) | −10.6252 | −0.368586 | ||||||||
\(832\) | 4.45526 | 0.154459 | ||||||||
\(833\) | 5.10330 | 0.176819 | ||||||||
\(834\) | −26.8850 | −0.930952 | ||||||||
\(835\) | −25.2898 | −0.875188 | ||||||||
\(836\) | −49.3241 | −1.70591 | ||||||||
\(837\) | −6.52595 | −0.225570 | ||||||||
\(838\) | 16.7729 | 0.579410 | ||||||||
\(839\) | −16.0044 | −0.552534 | −0.276267 | − | 0.961081i | \(-0.589097\pi\) | ||||
−0.276267 | + | 0.961081i | \(0.589097\pi\) | |||||||
\(840\) | 0.153829 | 0.00530760 | ||||||||
\(841\) | −26.9499 | −0.929308 | ||||||||
\(842\) | −62.8391 | −2.16558 | ||||||||
\(843\) | 14.6100 | 0.503195 | ||||||||
\(844\) | 27.8053 | 0.957099 | ||||||||
\(845\) | −36.4094 | −1.25252 | ||||||||
\(846\) | 6.82299 | 0.234579 | ||||||||
\(847\) | −12.2040 | −0.419333 | ||||||||
\(848\) | 12.1524 | 0.417316 | ||||||||
\(849\) | 32.4691 | 1.11434 | ||||||||
\(850\) | 6.44969 | 0.221222 | ||||||||
\(851\) | −12.4222 | −0.425828 | ||||||||
\(852\) | 2.28449 | 0.0782652 | ||||||||
\(853\) | 21.4611 | 0.734813 | 0.367406 | − | 0.930061i | \(-0.380246\pi\) | ||||
0.367406 | + | 0.930061i | \(0.380246\pi\) | |||||||
\(854\) | −11.5614 | −0.395623 | ||||||||
\(855\) | −15.7102 | −0.537278 | ||||||||
\(856\) | −0.258715 | −0.00884270 | ||||||||
\(857\) | −11.7124 | −0.400088 | −0.200044 | − | 0.979787i | \(-0.564109\pi\) | ||||
−0.200044 | + | 0.979787i | \(0.564109\pi\) | |||||||
\(858\) | 4.88148 | 0.166651 | ||||||||
\(859\) | −53.7503 | −1.83394 | −0.916968 | − | 0.398960i | \(-0.869371\pi\) | ||||
−0.916968 | + | 0.398960i | \(0.869371\pi\) | |||||||
\(860\) | −20.8772 | −0.711906 | ||||||||
\(861\) | −6.41133 | −0.218497 | ||||||||
\(862\) | −57.7591 | −1.96728 | ||||||||
\(863\) | 44.7672 | 1.52389 | 0.761947 | − | 0.647640i | \(-0.224244\pi\) | ||||
0.761947 | + | 0.647640i | \(0.224244\pi\) | |||||||
\(864\) | 8.01865 | 0.272800 | ||||||||
\(865\) | −11.1440 | −0.378908 | ||||||||
\(866\) | 32.9982 | 1.12132 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 18.1498 | 0.616046 | ||||||||
\(869\) | −21.4115 | −0.726335 | ||||||||
\(870\) | −8.22857 | −0.278975 | ||||||||
\(871\) | 5.83963 | 0.197868 | ||||||||
\(872\) | −0.140144 | −0.00474586 | ||||||||
\(873\) | −10.3137 | −0.349066 | ||||||||
\(874\) | −64.3734 | −2.17746 | ||||||||
\(875\) | 7.03881 | 0.237955 | ||||||||
\(876\) | −26.7045 | −0.902260 | ||||||||
\(877\) | 14.5576 | 0.491575 | 0.245787 | − | 0.969324i | \(-0.420954\pi\) | ||||
0.245787 | + | 0.969324i | \(0.420954\pi\) | |||||||
\(878\) | −71.2362 | −2.40410 | ||||||||
\(879\) | 5.62523 | 0.189734 | ||||||||
\(880\) | −50.5988 | −1.70568 | ||||||||
\(881\) | −24.0683 | −0.810882 | −0.405441 | − | 0.914121i | \(-0.632882\pi\) | ||||
−0.405441 | + | 0.914121i | \(0.632882\pi\) | |||||||
\(882\) | 10.2314 | 0.344508 | ||||||||
\(883\) | 11.2915 | 0.379990 | 0.189995 | − | 0.981785i | \(-0.439153\pi\) | ||||
0.189995 | + | 0.981785i | \(0.439153\pi\) | |||||||
\(884\) | 1.10330 | 0.0371081 | ||||||||
\(885\) | 40.7819 | 1.37087 | ||||||||
\(886\) | −37.3953 | −1.25632 | ||||||||
\(887\) | −36.3464 | −1.22039 | −0.610196 | − | 0.792251i | \(-0.708909\pi\) | ||||
−0.610196 | + | 0.792251i | \(0.708909\pi\) | |||||||
\(888\) | −0.0826190 | −0.00277251 | ||||||||
\(889\) | 12.0864 | 0.405366 | ||||||||
\(890\) | 68.7477 | 2.30443 | ||||||||
\(891\) | 4.45661 | 0.149302 | ||||||||
\(892\) | 58.2700 | 1.95102 | ||||||||
\(893\) | 18.6516 | 0.624153 | ||||||||
\(894\) | −7.19567 | −0.240659 | ||||||||
\(895\) | −58.7748 | −1.96462 | ||||||||
\(896\) | −0.429289 | −0.0143415 | ||||||||
\(897\) | 3.20084 | 0.106873 | ||||||||
\(898\) | −34.7854 | −1.16080 | ||||||||
\(899\) | −9.34389 | −0.311636 | ||||||||
\(900\) | 6.49660 | 0.216553 | ||||||||
\(901\) | 3.06822 | 0.102217 | ||||||||
\(902\) | −41.5945 | −1.38494 | ||||||||
\(903\) | 4.96688 | 0.165287 | ||||||||
\(904\) | 0.0964112 | 0.00320659 | ||||||||
\(905\) | 11.1554 | 0.370818 | ||||||||
\(906\) | 5.77250 | 0.191779 | ||||||||
\(907\) | −26.7496 | −0.888205 | −0.444102 | − | 0.895976i | \(-0.646477\pi\) | ||||
−0.444102 | + | 0.895976i | \(0.646477\pi\) | |||||||
\(908\) | 11.1520 | 0.370093 | ||||||||
\(909\) | −8.96292 | −0.297281 | ||||||||
\(910\) | −4.32418 | −0.143345 | ||||||||
\(911\) | 52.2270 | 1.73036 | 0.865178 | − | 0.501465i | \(-0.167205\pi\) | ||||
0.865178 | + | 0.501465i | \(0.167205\pi\) | |||||||
\(912\) | 21.7071 | 0.718795 | ||||||||
\(913\) | 10.5862 | 0.350353 | ||||||||
\(914\) | −60.2504 | −1.99291 | ||||||||
\(915\) | −12.0029 | −0.396804 | ||||||||
\(916\) | −35.9721 | −1.18855 | ||||||||
\(917\) | 11.6124 | 0.383475 | ||||||||
\(918\) | 2.00485 | 0.0661700 | ||||||||
\(919\) | −23.3069 | −0.768824 | −0.384412 | − | 0.923162i | \(-0.625596\pi\) | ||||
−0.384412 | + | 0.923162i | \(0.625596\pi\) | |||||||
\(920\) | 0.654391 | 0.0215746 | ||||||||
\(921\) | 1.44141 | 0.0474960 | ||||||||
\(922\) | −29.0498 | −0.956704 | ||||||||
\(923\) | −0.618049 | −0.0203433 | ||||||||
\(924\) | −12.3946 | −0.407754 | ||||||||
\(925\) | 6.82111 | 0.224277 | ||||||||
\(926\) | 8.03894 | 0.264176 | ||||||||
\(927\) | 0.659899 | 0.0216739 | ||||||||
\(928\) | 11.4812 | 0.376887 | ||||||||
\(929\) | 59.7918 | 1.96170 | 0.980852 | − | 0.194753i | \(-0.0623905\pi\) | ||||
0.980852 | + | 0.194753i | \(0.0623905\pi\) | |||||||
\(930\) | 37.5045 | 1.22982 | ||||||||
\(931\) | 27.9689 | 0.916645 | ||||||||
\(932\) | −29.8946 | −0.979231 | ||||||||
\(933\) | −8.16060 | −0.267166 | ||||||||
\(934\) | −46.9314 | −1.53564 | ||||||||
\(935\) | −12.7750 | −0.417788 | ||||||||
\(936\) | 0.0212885 | 0.000695836 0 | ||||||||
\(937\) | 3.43822 | 0.112322 | 0.0561609 | − | 0.998422i | \(-0.482114\pi\) | ||||
0.0561609 | + | 0.998422i | \(0.482114\pi\) | |||||||
\(938\) | −29.5123 | −0.963610 | ||||||||
\(939\) | 8.94216 | 0.291816 | ||||||||
\(940\) | −19.7006 | −0.642564 | ||||||||
\(941\) | 44.7685 | 1.45941 | 0.729705 | − | 0.683762i | \(-0.239657\pi\) | ||||
0.729705 | + | 0.683762i | \(0.239657\pi\) | |||||||
\(942\) | −2.00485 | −0.0653216 | ||||||||
\(943\) | −27.2739 | −0.888161 | ||||||||
\(944\) | −56.3492 | −1.83401 | ||||||||
\(945\) | −3.94782 | −0.128422 | ||||||||
\(946\) | 32.2234 | 1.04767 | ||||||||
\(947\) | −34.4910 | −1.12081 | −0.560403 | − | 0.828220i | \(-0.689354\pi\) | ||||
−0.560403 | + | 0.828220i | \(0.689354\pi\) | |||||||
\(948\) | −9.70224 | −0.315114 | ||||||||
\(949\) | 7.22467 | 0.234523 | ||||||||
\(950\) | 35.3479 | 1.14684 | ||||||||
\(951\) | −24.7048 | −0.801109 | ||||||||
\(952\) | −0.0536636 | −0.00173925 | ||||||||
\(953\) | 18.2568 | 0.591395 | 0.295698 | − | 0.955282i | \(-0.404448\pi\) | ||||
0.295698 | + | 0.955282i | \(0.404448\pi\) | |||||||
\(954\) | 6.15132 | 0.199156 | ||||||||
\(955\) | 18.8448 | 0.609802 | ||||||||
\(956\) | 58.7864 | 1.90129 | ||||||||
\(957\) | 6.38100 | 0.206268 | ||||||||
\(958\) | 23.6436 | 0.763889 | ||||||||
\(959\) | −5.07797 | −0.163976 | ||||||||
\(960\) | −23.3758 | −0.754451 | ||||||||
\(961\) | 11.5880 | 0.373806 | ||||||||
\(962\) | 2.32245 | 0.0748788 | ||||||||
\(963\) | 6.63959 | 0.213958 | ||||||||
\(964\) | −27.6056 | −0.889116 | ||||||||
\(965\) | −49.9792 | −1.60889 | ||||||||
\(966\) | −16.1764 | −0.520466 | ||||||||
\(967\) | −29.0458 | −0.934049 | −0.467024 | − | 0.884244i | \(-0.654674\pi\) | ||||
−0.467024 | + | 0.884244i | \(0.654674\pi\) | |||||||
\(968\) | −0.345288 | −0.0110980 | ||||||||
\(969\) | 5.48056 | 0.176061 | ||||||||
\(970\) | 59.2727 | 1.90313 | ||||||||
\(971\) | −14.0115 | −0.449651 | −0.224825 | − | 0.974399i | \(-0.572181\pi\) | ||||
−0.224825 | + | 0.974399i | \(0.572181\pi\) | |||||||
\(972\) | 2.01944 | 0.0647734 | ||||||||
\(973\) | −18.4683 | −0.592067 | ||||||||
\(974\) | 24.0309 | 0.770001 | ||||||||
\(975\) | −1.75760 | −0.0562883 | ||||||||
\(976\) | 16.5846 | 0.530862 | ||||||||
\(977\) | −59.4231 | −1.90111 | −0.950556 | − | 0.310552i | \(-0.899486\pi\) | ||||
−0.950556 | + | 0.310552i | \(0.899486\pi\) | |||||||
\(978\) | −6.07367 | −0.194215 | ||||||||
\(979\) | −53.3117 | −1.70385 | ||||||||
\(980\) | −29.5419 | −0.943682 | ||||||||
\(981\) | 3.59660 | 0.114831 | ||||||||
\(982\) | −37.8778 | −1.20873 | ||||||||
\(983\) | −22.4552 | −0.716210 | −0.358105 | − | 0.933681i | \(-0.616577\pi\) | ||||
−0.358105 | + | 0.933681i | \(0.616577\pi\) | |||||||
\(984\) | −0.181397 | −0.00578271 | ||||||||
\(985\) | 2.10256 | 0.0669931 | ||||||||
\(986\) | 2.87056 | 0.0914173 | ||||||||
\(987\) | 4.68697 | 0.149188 | ||||||||
\(988\) | 6.04671 | 0.192371 | ||||||||
\(989\) | 21.1292 | 0.671871 | ||||||||
\(990\) | −25.6121 | −0.814005 | ||||||||
\(991\) | 27.4415 | 0.871710 | 0.435855 | − | 0.900017i | \(-0.356446\pi\) | ||||
0.435855 | + | 0.900017i | \(0.356446\pi\) | |||||||
\(992\) | −52.3293 | −1.66146 | ||||||||
\(993\) | −24.1392 | −0.766033 | ||||||||
\(994\) | 3.12349 | 0.0990712 | ||||||||
\(995\) | 52.5565 | 1.66615 | ||||||||
\(996\) | 4.79696 | 0.151998 | ||||||||
\(997\) | −56.5822 | −1.79198 | −0.895988 | − | 0.444079i | \(-0.853531\pi\) | ||||
−0.895988 | + | 0.444079i | \(0.853531\pi\) | |||||||
\(998\) | −33.3563 | −1.05588 | ||||||||
\(999\) | 2.12031 | 0.0670836 |
(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 | 8007.2.a.e.1.9 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.e.1.9 | ✓ | 46 | 1.1 | even | 1 | trivial |