Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.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: | \(48.2056877002\) |
Analytic rank: | \(0\) |
Dimension: | \(259\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.42988 | −1.71818 | −0.859091 | − | 0.511823i | \(-0.828970\pi\) | ||||
−0.859091 | + | 0.511823i | \(0.828970\pi\) | |||||||
\(3\) | 0.381455 | 0.220233 | 0.110116 | − | 0.993919i | \(-0.464878\pi\) | ||||
0.110116 | + | 0.993919i | \(0.464878\pi\) | |||||||
\(4\) | 3.90430 | 1.95215 | ||||||||
\(5\) | −2.17078 | −0.970802 | −0.485401 | − | 0.874292i | \(-0.661326\pi\) | ||||
−0.485401 | + | 0.874292i | \(0.661326\pi\) | |||||||
\(6\) | −0.926887 | −0.378400 | ||||||||
\(7\) | −2.70764 | −1.02339 | −0.511696 | − | 0.859167i | \(-0.670983\pi\) | ||||
−0.511696 | + | 0.859167i | \(0.670983\pi\) | |||||||
\(8\) | −4.62721 | −1.63597 | ||||||||
\(9\) | −2.85449 | −0.951497 | ||||||||
\(10\) | 5.27472 | 1.66801 | ||||||||
\(11\) | 5.11321 | 1.54169 | 0.770845 | − | 0.637022i | \(-0.219834\pi\) | ||||
0.770845 | + | 0.637022i | \(0.219834\pi\) | |||||||
\(12\) | 1.48931 | 0.429927 | ||||||||
\(13\) | 6.54077 | 1.81408 | 0.907042 | − | 0.421040i | \(-0.138335\pi\) | ||||
0.907042 | + | 0.421040i | \(0.138335\pi\) | |||||||
\(14\) | 6.57923 | 1.75837 | ||||||||
\(15\) | −0.828053 | −0.213802 | ||||||||
\(16\) | 3.43495 | 0.858738 | ||||||||
\(17\) | −0.0279003 | −0.00676683 | −0.00338341 | − | 0.999994i | \(-0.501077\pi\) | ||||
−0.00338341 | + | 0.999994i | \(0.501077\pi\) | |||||||
\(18\) | 6.93606 | 1.63485 | ||||||||
\(19\) | 7.94119 | 1.82183 | 0.910917 | − | 0.412590i | \(-0.135376\pi\) | ||||
0.910917 | + | 0.412590i | \(0.135376\pi\) | |||||||
\(20\) | −8.47537 | −1.89515 | ||||||||
\(21\) | −1.03284 | −0.225385 | ||||||||
\(22\) | −12.4245 | −2.64891 | ||||||||
\(23\) | 7.01359 | 1.46244 | 0.731218 | − | 0.682144i | \(-0.238952\pi\) | ||||
0.731218 | + | 0.682144i | \(0.238952\pi\) | |||||||
\(24\) | −1.76507 | −0.360294 | ||||||||
\(25\) | −0.287719 | −0.0575438 | ||||||||
\(26\) | −15.8933 | −3.11693 | ||||||||
\(27\) | −2.23322 | −0.429784 | ||||||||
\(28\) | −10.5714 | −1.99781 | ||||||||
\(29\) | 8.51367 | 1.58095 | 0.790474 | − | 0.612495i | \(-0.209834\pi\) | ||||
0.790474 | + | 0.612495i | \(0.209834\pi\) | |||||||
\(30\) | 2.01207 | 0.367352 | ||||||||
\(31\) | 3.77239 | 0.677541 | 0.338770 | − | 0.940869i | \(-0.389989\pi\) | ||||
0.338770 | + | 0.940869i | \(0.389989\pi\) | |||||||
\(32\) | 0.907913 | 0.160498 | ||||||||
\(33\) | 1.95046 | 0.339531 | ||||||||
\(34\) | 0.0677944 | 0.0116266 | ||||||||
\(35\) | 5.87769 | 0.993511 | ||||||||
\(36\) | −11.1448 | −1.85747 | ||||||||
\(37\) | −0.838138 | −0.137789 | −0.0688946 | − | 0.997624i | \(-0.521947\pi\) | ||||
−0.0688946 | + | 0.997624i | \(0.521947\pi\) | |||||||
\(38\) | −19.2961 | −3.13024 | ||||||||
\(39\) | 2.49501 | 0.399521 | ||||||||
\(40\) | 10.0447 | 1.58820 | ||||||||
\(41\) | −8.68434 | −1.35627 | −0.678133 | − | 0.734939i | \(-0.737211\pi\) | ||||
−0.678133 | + | 0.734939i | \(0.737211\pi\) | |||||||
\(42\) | 2.50968 | 0.387252 | ||||||||
\(43\) | 3.58105 | 0.546104 | 0.273052 | − | 0.961999i | \(-0.411967\pi\) | ||||
0.273052 | + | 0.961999i | \(0.411967\pi\) | |||||||
\(44\) | 19.9635 | 3.00961 | ||||||||
\(45\) | 6.19647 | 0.923715 | ||||||||
\(46\) | −17.0422 | −2.51273 | ||||||||
\(47\) | 7.68087 | 1.12037 | 0.560185 | − | 0.828368i | \(-0.310730\pi\) | ||||
0.560185 | + | 0.828368i | \(0.310730\pi\) | |||||||
\(48\) | 1.31028 | 0.189122 | ||||||||
\(49\) | 0.331317 | 0.0473311 | ||||||||
\(50\) | 0.699122 | 0.0988708 | ||||||||
\(51\) | −0.0106427 | −0.00149028 | ||||||||
\(52\) | 25.5371 | 3.54136 | ||||||||
\(53\) | 13.0055 | 1.78645 | 0.893223 | − | 0.449613i | \(-0.148438\pi\) | ||||
0.893223 | + | 0.449613i | \(0.148438\pi\) | |||||||
\(54\) | 5.42645 | 0.738447 | ||||||||
\(55\) | −11.0996 | −1.49668 | ||||||||
\(56\) | 12.5288 | 1.67423 | ||||||||
\(57\) | 3.02920 | 0.401228 | ||||||||
\(58\) | −20.6872 | −2.71636 | ||||||||
\(59\) | 10.0502 | 1.30843 | 0.654215 | − | 0.756309i | \(-0.272999\pi\) | ||||
0.654215 | + | 0.756309i | \(0.272999\pi\) | |||||||
\(60\) | −3.23297 | −0.417374 | ||||||||
\(61\) | 5.26980 | 0.674729 | 0.337364 | − | 0.941374i | \(-0.390465\pi\) | ||||
0.337364 | + | 0.941374i | \(0.390465\pi\) | |||||||
\(62\) | −9.16644 | −1.16414 | ||||||||
\(63\) | 7.72894 | 0.973755 | ||||||||
\(64\) | −9.07602 | −1.13450 | ||||||||
\(65\) | −14.1986 | −1.76112 | ||||||||
\(66\) | −4.73937 | −0.583376 | ||||||||
\(67\) | −12.6218 | −1.54200 | −0.770999 | − | 0.636837i | \(-0.780243\pi\) | ||||
−0.770999 | + | 0.636837i | \(0.780243\pi\) | |||||||
\(68\) | −0.108931 | −0.0132099 | ||||||||
\(69\) | 2.67537 | 0.322076 | ||||||||
\(70\) | −14.2821 | −1.70703 | ||||||||
\(71\) | −11.1737 | −1.32607 | −0.663036 | − | 0.748587i | \(-0.730733\pi\) | ||||
−0.663036 | + | 0.748587i | \(0.730733\pi\) | |||||||
\(72\) | 13.2083 | 1.55662 | ||||||||
\(73\) | 5.14509 | 0.602187 | 0.301094 | − | 0.953595i | \(-0.402648\pi\) | ||||
0.301094 | + | 0.953595i | \(0.402648\pi\) | |||||||
\(74\) | 2.03657 | 0.236747 | ||||||||
\(75\) | −0.109752 | −0.0126730 | ||||||||
\(76\) | 31.0048 | 3.55649 | ||||||||
\(77\) | −13.8447 | −1.57775 | ||||||||
\(78\) | −6.06256 | −0.686450 | ||||||||
\(79\) | −9.63964 | −1.08454 | −0.542272 | − | 0.840203i | \(-0.682436\pi\) | ||||
−0.542272 | + | 0.840203i | \(0.682436\pi\) | |||||||
\(80\) | −7.45652 | −0.833664 | ||||||||
\(81\) | 7.71160 | 0.856845 | ||||||||
\(82\) | 21.1019 | 2.33031 | ||||||||
\(83\) | 9.70275 | 1.06502 | 0.532508 | − | 0.846425i | \(-0.321250\pi\) | ||||
0.532508 | + | 0.846425i | \(0.321250\pi\) | |||||||
\(84\) | −4.03252 | −0.439984 | ||||||||
\(85\) | 0.0605655 | 0.00656925 | ||||||||
\(86\) | −8.70150 | −0.938307 | ||||||||
\(87\) | 3.24758 | 0.348177 | ||||||||
\(88\) | −23.6599 | −2.52215 | ||||||||
\(89\) | 0.517760 | 0.0548824 | 0.0274412 | − | 0.999623i | \(-0.491264\pi\) | ||||
0.0274412 | + | 0.999623i | \(0.491264\pi\) | |||||||
\(90\) | −15.0567 | −1.58711 | ||||||||
\(91\) | −17.7101 | −1.85652 | ||||||||
\(92\) | 27.3832 | 2.85489 | ||||||||
\(93\) | 1.43899 | 0.149217 | ||||||||
\(94\) | −18.6636 | −1.92500 | ||||||||
\(95\) | −17.2386 | −1.76864 | ||||||||
\(96\) | 0.346327 | 0.0353469 | ||||||||
\(97\) | −6.38286 | −0.648081 | −0.324041 | − | 0.946043i | \(-0.605041\pi\) | ||||
−0.324041 | + | 0.946043i | \(0.605041\pi\) | |||||||
\(98\) | −0.805060 | −0.0813234 | ||||||||
\(99\) | −14.5956 | −1.46691 | ||||||||
\(100\) | −1.12334 | −0.112334 | ||||||||
\(101\) | −3.42167 | −0.340469 | −0.170234 | − | 0.985404i | \(-0.554453\pi\) | ||||
−0.170234 | + | 0.985404i | \(0.554453\pi\) | |||||||
\(102\) | 0.0258605 | 0.00256057 | ||||||||
\(103\) | 10.9741 | 1.08131 | 0.540654 | − | 0.841245i | \(-0.318177\pi\) | ||||
0.540654 | + | 0.841245i | \(0.318177\pi\) | |||||||
\(104\) | −30.2655 | −2.96778 | ||||||||
\(105\) | 2.24207 | 0.218804 | ||||||||
\(106\) | −31.6018 | −3.06944 | ||||||||
\(107\) | −1.70405 | −0.164737 | −0.0823684 | − | 0.996602i | \(-0.526248\pi\) | ||||
−0.0823684 | + | 0.996602i | \(0.526248\pi\) | |||||||
\(108\) | −8.71917 | −0.839002 | ||||||||
\(109\) | −7.63030 | −0.730850 | −0.365425 | − | 0.930841i | \(-0.619076\pi\) | ||||
−0.365425 | + | 0.930841i | \(0.619076\pi\) | |||||||
\(110\) | 26.9708 | 2.57156 | ||||||||
\(111\) | −0.319712 | −0.0303457 | ||||||||
\(112\) | −9.30062 | −0.878826 | ||||||||
\(113\) | −11.9116 | −1.12055 | −0.560274 | − | 0.828307i | \(-0.689304\pi\) | ||||
−0.560274 | + | 0.828307i | \(0.689304\pi\) | |||||||
\(114\) | −7.36059 | −0.689382 | ||||||||
\(115\) | −15.2250 | −1.41973 | ||||||||
\(116\) | 33.2399 | 3.08625 | ||||||||
\(117\) | −18.6706 | −1.72610 | ||||||||
\(118\) | −24.4208 | −2.24812 | ||||||||
\(119\) | 0.0755441 | 0.00692511 | ||||||||
\(120\) | 3.83158 | 0.349774 | ||||||||
\(121\) | 15.1449 | 1.37681 | ||||||||
\(122\) | −12.8050 | −1.15931 | ||||||||
\(123\) | −3.31268 | −0.298694 | ||||||||
\(124\) | 14.7285 | 1.32266 | ||||||||
\(125\) | 11.4785 | 1.02667 | ||||||||
\(126\) | −18.7804 | −1.67309 | ||||||||
\(127\) | −19.0225 | −1.68797 | −0.843985 | − | 0.536366i | \(-0.819797\pi\) | ||||
−0.843985 | + | 0.536366i | \(0.819797\pi\) | |||||||
\(128\) | 20.2378 | 1.78878 | ||||||||
\(129\) | 1.36601 | 0.120270 | ||||||||
\(130\) | 34.5008 | 3.02592 | ||||||||
\(131\) | −12.8748 | −1.12488 | −0.562439 | − | 0.826839i | \(-0.690137\pi\) | ||||
−0.562439 | + | 0.826839i | \(0.690137\pi\) | |||||||
\(132\) | 7.61517 | 0.662815 | ||||||||
\(133\) | −21.5019 | −1.86445 | ||||||||
\(134\) | 30.6694 | 2.64943 | ||||||||
\(135\) | 4.84783 | 0.417235 | ||||||||
\(136\) | 0.129101 | 0.0110703 | ||||||||
\(137\) | 7.15901 | 0.611636 | 0.305818 | − | 0.952090i | \(-0.401070\pi\) | ||||
0.305818 | + | 0.952090i | \(0.401070\pi\) | |||||||
\(138\) | −6.50081 | −0.553386 | ||||||||
\(139\) | 1.79961 | 0.152641 | 0.0763206 | − | 0.997083i | \(-0.475683\pi\) | ||||
0.0763206 | + | 0.997083i | \(0.475683\pi\) | |||||||
\(140\) | 22.9483 | 1.93948 | ||||||||
\(141\) | 2.92990 | 0.246742 | ||||||||
\(142\) | 27.1507 | 2.27843 | ||||||||
\(143\) | 33.4444 | 2.79676 | ||||||||
\(144\) | −9.80505 | −0.817087 | ||||||||
\(145\) | −18.4813 | −1.53479 | ||||||||
\(146\) | −12.5019 | −1.03467 | ||||||||
\(147\) | 0.126383 | 0.0104239 | ||||||||
\(148\) | −3.27234 | −0.268985 | ||||||||
\(149\) | 3.26256 | 0.267279 | 0.133640 | − | 0.991030i | \(-0.457334\pi\) | ||||
0.133640 | + | 0.991030i | \(0.457334\pi\) | |||||||
\(150\) | 0.266683 | 0.0217746 | ||||||||
\(151\) | −7.50807 | −0.610998 | −0.305499 | − | 0.952192i | \(-0.598823\pi\) | ||||
−0.305499 | + | 0.952192i | \(0.598823\pi\) | |||||||
\(152\) | −36.7455 | −2.98046 | ||||||||
\(153\) | 0.0796413 | 0.00643862 | ||||||||
\(154\) | 33.6410 | 2.71087 | ||||||||
\(155\) | −8.18902 | −0.657758 | ||||||||
\(156\) | 9.74126 | 0.779925 | ||||||||
\(157\) | 17.4635 | 1.39374 | 0.696870 | − | 0.717198i | \(-0.254576\pi\) | ||||
0.696870 | + | 0.717198i | \(0.254576\pi\) | |||||||
\(158\) | 23.4231 | 1.86344 | ||||||||
\(159\) | 4.96102 | 0.393434 | ||||||||
\(160\) | −1.97088 | −0.155812 | ||||||||
\(161\) | −18.9903 | −1.49664 | ||||||||
\(162\) | −18.7382 | −1.47222 | ||||||||
\(163\) | −4.63131 | −0.362752 | −0.181376 | − | 0.983414i | \(-0.558055\pi\) | ||||
−0.181376 | + | 0.983414i | \(0.558055\pi\) | |||||||
\(164\) | −33.9063 | −2.64763 | ||||||||
\(165\) | −4.23401 | −0.329617 | ||||||||
\(166\) | −23.5765 | −1.82989 | ||||||||
\(167\) | −4.60701 | −0.356501 | −0.178251 | − | 0.983985i | \(-0.557044\pi\) | ||||
−0.178251 | + | 0.983985i | \(0.557044\pi\) | |||||||
\(168\) | 4.77918 | 0.368721 | ||||||||
\(169\) | 29.7817 | 2.29090 | ||||||||
\(170\) | −0.147167 | −0.0112872 | ||||||||
\(171\) | −22.6681 | −1.73347 | ||||||||
\(172\) | 13.9815 | 1.06608 | ||||||||
\(173\) | −3.85338 | −0.292967 | −0.146483 | − | 0.989213i | \(-0.546795\pi\) | ||||
−0.146483 | + | 0.989213i | \(0.546795\pi\) | |||||||
\(174\) | −7.89121 | −0.598231 | ||||||||
\(175\) | 0.779040 | 0.0588899 | ||||||||
\(176\) | 17.5636 | 1.32391 | ||||||||
\(177\) | 3.83371 | 0.288159 | ||||||||
\(178\) | −1.25809 | −0.0942980 | ||||||||
\(179\) | −10.1651 | −0.759778 | −0.379889 | − | 0.925032i | \(-0.624038\pi\) | ||||
−0.379889 | + | 0.925032i | \(0.624038\pi\) | |||||||
\(180\) | 24.1929 | 1.80323 | ||||||||
\(181\) | 3.73076 | 0.277305 | 0.138653 | − | 0.990341i | \(-0.455723\pi\) | ||||
0.138653 | + | 0.990341i | \(0.455723\pi\) | |||||||
\(182\) | 43.0333 | 3.18984 | ||||||||
\(183\) | 2.01019 | 0.148597 | ||||||||
\(184\) | −32.4534 | −2.39249 | ||||||||
\(185\) | 1.81941 | 0.133766 | ||||||||
\(186\) | −3.49658 | −0.256382 | ||||||||
\(187\) | −0.142660 | −0.0104324 | ||||||||
\(188\) | 29.9884 | 2.18713 | ||||||||
\(189\) | 6.04676 | 0.439837 | ||||||||
\(190\) | 41.8876 | 3.03884 | ||||||||
\(191\) | 24.5691 | 1.77776 | 0.888880 | − | 0.458140i | \(-0.151484\pi\) | ||||
0.888880 | + | 0.458140i | \(0.151484\pi\) | |||||||
\(192\) | −3.46209 | −0.249855 | ||||||||
\(193\) | −1.32536 | −0.0954014 | −0.0477007 | − | 0.998862i | \(-0.515189\pi\) | ||||
−0.0477007 | + | 0.998862i | \(0.515189\pi\) | |||||||
\(194\) | 15.5096 | 1.11352 | ||||||||
\(195\) | −5.41611 | −0.387856 | ||||||||
\(196\) | 1.29356 | 0.0923973 | ||||||||
\(197\) | 27.2035 | 1.93817 | 0.969086 | − | 0.246724i | \(-0.0793541\pi\) | ||||
0.969086 | + | 0.246724i | \(0.0793541\pi\) | |||||||
\(198\) | 35.4655 | 2.52043 | ||||||||
\(199\) | 10.4326 | 0.739547 | 0.369773 | − | 0.929122i | \(-0.379435\pi\) | ||||
0.369773 | + | 0.929122i | \(0.379435\pi\) | |||||||
\(200\) | 1.33134 | 0.0941398 | ||||||||
\(201\) | −4.81464 | −0.339599 | ||||||||
\(202\) | 8.31424 | 0.584988 | ||||||||
\(203\) | −23.0520 | −1.61793 | ||||||||
\(204\) | −0.0415523 | −0.00290924 | ||||||||
\(205\) | 18.8518 | 1.31667 | ||||||||
\(206\) | −26.6656 | −1.85788 | ||||||||
\(207\) | −20.0202 | −1.39150 | ||||||||
\(208\) | 22.4672 | 1.55782 | ||||||||
\(209\) | 40.6050 | 2.80870 | ||||||||
\(210\) | −5.44796 | −0.375945 | ||||||||
\(211\) | −13.3026 | −0.915790 | −0.457895 | − | 0.889006i | \(-0.651396\pi\) | ||||
−0.457895 | + | 0.889006i | \(0.651396\pi\) | |||||||
\(212\) | 50.7775 | 3.48741 | ||||||||
\(213\) | −4.26225 | −0.292045 | ||||||||
\(214\) | 4.14063 | 0.283048 | ||||||||
\(215\) | −7.77366 | −0.530159 | ||||||||
\(216\) | 10.3336 | 0.703112 | ||||||||
\(217\) | −10.2143 | −0.693390 | ||||||||
\(218\) | 18.5407 | 1.25573 | ||||||||
\(219\) | 1.96262 | 0.132621 | ||||||||
\(220\) | −43.3363 | −2.92174 | ||||||||
\(221\) | −0.182490 | −0.0122756 | ||||||||
\(222\) | 0.776860 | 0.0521394 | ||||||||
\(223\) | −16.7060 | −1.11872 | −0.559358 | − | 0.828926i | \(-0.688952\pi\) | ||||
−0.559358 | + | 0.828926i | \(0.688952\pi\) | |||||||
\(224\) | −2.45830 | −0.164252 | ||||||||
\(225\) | 0.821292 | 0.0547528 | ||||||||
\(226\) | 28.9437 | 1.92531 | ||||||||
\(227\) | 19.5423 | 1.29707 | 0.648533 | − | 0.761186i | \(-0.275383\pi\) | ||||
0.648533 | + | 0.761186i | \(0.275383\pi\) | |||||||
\(228\) | 11.8269 | 0.783256 | ||||||||
\(229\) | 10.7710 | 0.711769 | 0.355884 | − | 0.934530i | \(-0.384180\pi\) | ||||
0.355884 | + | 0.934530i | \(0.384180\pi\) | |||||||
\(230\) | 36.9948 | 2.43936 | ||||||||
\(231\) | −5.28114 | −0.347473 | ||||||||
\(232\) | −39.3945 | −2.58638 | ||||||||
\(233\) | 17.3009 | 1.13342 | 0.566710 | − | 0.823917i | \(-0.308216\pi\) | ||||
0.566710 | + | 0.823917i | \(0.308216\pi\) | |||||||
\(234\) | 45.3672 | 2.96575 | ||||||||
\(235\) | −16.6735 | −1.08766 | ||||||||
\(236\) | 39.2392 | 2.55425 | ||||||||
\(237\) | −3.67708 | −0.238852 | ||||||||
\(238\) | −0.183563 | −0.0118986 | ||||||||
\(239\) | 8.99359 | 0.581747 | 0.290874 | − | 0.956761i | \(-0.406054\pi\) | ||||
0.290874 | + | 0.956761i | \(0.406054\pi\) | |||||||
\(240\) | −2.84432 | −0.183600 | ||||||||
\(241\) | −0.747944 | −0.0481793 | −0.0240896 | − | 0.999710i | \(-0.507669\pi\) | ||||
−0.0240896 | + | 0.999710i | \(0.507669\pi\) | |||||||
\(242\) | −36.8003 | −2.36561 | ||||||||
\(243\) | 9.64129 | 0.618489 | ||||||||
\(244\) | 20.5749 | 1.31717 | ||||||||
\(245\) | −0.719217 | −0.0459491 | ||||||||
\(246\) | 8.04941 | 0.513211 | ||||||||
\(247\) | 51.9415 | 3.30496 | ||||||||
\(248\) | −17.4556 | −1.10843 | ||||||||
\(249\) | 3.70116 | 0.234551 | ||||||||
\(250\) | −27.8913 | −1.76400 | ||||||||
\(251\) | 3.19751 | 0.201825 | 0.100913 | − | 0.994895i | \(-0.467824\pi\) | ||||
0.100913 | + | 0.994895i | \(0.467824\pi\) | |||||||
\(252\) | 30.1761 | 1.90092 | ||||||||
\(253\) | 35.8620 | 2.25462 | ||||||||
\(254\) | 46.2222 | 2.90024 | ||||||||
\(255\) | 0.0231030 | 0.00144676 | ||||||||
\(256\) | −31.0233 | −1.93895 | ||||||||
\(257\) | 2.11386 | 0.131859 | 0.0659293 | − | 0.997824i | \(-0.478999\pi\) | ||||
0.0659293 | + | 0.997824i | \(0.478999\pi\) | |||||||
\(258\) | −3.31923 | −0.206646 | ||||||||
\(259\) | 2.26938 | 0.141012 | ||||||||
\(260\) | −55.4355 | −3.43796 | ||||||||
\(261\) | −24.3022 | −1.50427 | ||||||||
\(262\) | 31.2842 | 1.93275 | ||||||||
\(263\) | −10.2742 | −0.633534 | −0.316767 | − | 0.948503i | \(-0.602597\pi\) | ||||
−0.316767 | + | 0.948503i | \(0.602597\pi\) | |||||||
\(264\) | −9.02518 | −0.555461 | ||||||||
\(265\) | −28.2321 | −1.73429 | ||||||||
\(266\) | 52.2469 | 3.20346 | ||||||||
\(267\) | 0.197502 | 0.0120869 | ||||||||
\(268\) | −49.2793 | −3.01021 | ||||||||
\(269\) | −8.18748 | −0.499199 | −0.249600 | − | 0.968349i | \(-0.580299\pi\) | ||||
−0.249600 | + | 0.968349i | \(0.580299\pi\) | |||||||
\(270\) | −11.7796 | −0.716886 | ||||||||
\(271\) | −8.44352 | −0.512907 | −0.256454 | − | 0.966557i | \(-0.582554\pi\) | ||||
−0.256454 | + | 0.966557i | \(0.582554\pi\) | |||||||
\(272\) | −0.0958363 | −0.00581093 | ||||||||
\(273\) | −6.75558 | −0.408867 | ||||||||
\(274\) | −17.3955 | −1.05090 | ||||||||
\(275\) | −1.47117 | −0.0887148 | ||||||||
\(276\) | 10.4454 | 0.628741 | ||||||||
\(277\) | −8.86079 | −0.532393 | −0.266197 | − | 0.963919i | \(-0.585767\pi\) | ||||
−0.266197 | + | 0.963919i | \(0.585767\pi\) | |||||||
\(278\) | −4.37284 | −0.262265 | ||||||||
\(279\) | −10.7683 | −0.644678 | ||||||||
\(280\) | −27.1973 | −1.62535 | ||||||||
\(281\) | −15.8292 | −0.944291 | −0.472146 | − | 0.881521i | \(-0.656520\pi\) | ||||
−0.472146 | + | 0.881521i | \(0.656520\pi\) | |||||||
\(282\) | −7.11930 | −0.423948 | ||||||||
\(283\) | −2.83901 | −0.168761 | −0.0843807 | − | 0.996434i | \(-0.526891\pi\) | ||||
−0.0843807 | + | 0.996434i | \(0.526891\pi\) | |||||||
\(284\) | −43.6254 | −2.58869 | ||||||||
\(285\) | −6.57573 | −0.389512 | ||||||||
\(286\) | −81.2656 | −4.80534 | ||||||||
\(287\) | 23.5141 | 1.38799 | ||||||||
\(288\) | −2.59163 | −0.152713 | ||||||||
\(289\) | −16.9992 | −0.999954 | ||||||||
\(290\) | 44.9073 | 2.63704 | ||||||||
\(291\) | −2.43477 | −0.142729 | ||||||||
\(292\) | 20.0880 | 1.17556 | ||||||||
\(293\) | −3.38920 | −0.197999 | −0.0989997 | − | 0.995087i | \(-0.531564\pi\) | ||||
−0.0989997 | + | 0.995087i | \(0.531564\pi\) | |||||||
\(294\) | −0.307094 | −0.0179101 | ||||||||
\(295\) | −21.8169 | −1.27023 | ||||||||
\(296\) | 3.87824 | 0.225418 | ||||||||
\(297\) | −11.4189 | −0.662594 | ||||||||
\(298\) | −7.92761 | −0.459234 | ||||||||
\(299\) | 45.8743 | 2.65298 | ||||||||
\(300\) | −0.428504 | −0.0247397 | ||||||||
\(301\) | −9.69619 | −0.558879 | ||||||||
\(302\) | 18.2437 | 1.04981 | ||||||||
\(303\) | −1.30521 | −0.0749825 | ||||||||
\(304\) | 27.2776 | 1.56448 | ||||||||
\(305\) | −11.4396 | −0.655028 | ||||||||
\(306\) | −0.193518 | −0.0110627 | ||||||||
\(307\) | 20.9825 | 1.19754 | 0.598768 | − | 0.800923i | \(-0.295657\pi\) | ||||
0.598768 | + | 0.800923i | \(0.295657\pi\) | |||||||
\(308\) | −54.0540 | −3.08001 | ||||||||
\(309\) | 4.18611 | 0.238139 | ||||||||
\(310\) | 19.8983 | 1.13015 | ||||||||
\(311\) | −34.0275 | −1.92952 | −0.964761 | − | 0.263129i | \(-0.915245\pi\) | ||||
−0.964761 | + | 0.263129i | \(0.915245\pi\) | |||||||
\(312\) | −11.5449 | −0.653603 | ||||||||
\(313\) | 20.6352 | 1.16637 | 0.583186 | − | 0.812339i | \(-0.301806\pi\) | ||||
0.583186 | + | 0.812339i | \(0.301806\pi\) | |||||||
\(314\) | −42.4342 | −2.39470 | ||||||||
\(315\) | −16.7778 | −0.945323 | ||||||||
\(316\) | −37.6360 | −2.11719 | ||||||||
\(317\) | −7.59523 | −0.426591 | −0.213295 | − | 0.976988i | \(-0.568420\pi\) | ||||
−0.213295 | + | 0.976988i | \(0.568420\pi\) | |||||||
\(318\) | −12.0547 | −0.675992 | ||||||||
\(319\) | 43.5322 | 2.43733 | ||||||||
\(320\) | 19.7020 | 1.10138 | ||||||||
\(321\) | −0.650018 | −0.0362805 | ||||||||
\(322\) | 46.1440 | 2.57151 | ||||||||
\(323\) | −0.221562 | −0.0123280 | ||||||||
\(324\) | 30.1084 | 1.67269 | ||||||||
\(325\) | −1.88191 | −0.104389 | ||||||||
\(326\) | 11.2535 | 0.623275 | ||||||||
\(327\) | −2.91061 | −0.160957 | ||||||||
\(328\) | 40.1843 | 2.21881 | ||||||||
\(329\) | −20.7970 | −1.14658 | ||||||||
\(330\) | 10.2881 | 0.566343 | ||||||||
\(331\) | −6.91192 | −0.379913 | −0.189957 | − | 0.981792i | \(-0.560835\pi\) | ||||
−0.189957 | + | 0.981792i | \(0.560835\pi\) | |||||||
\(332\) | 37.8824 | 2.07907 | ||||||||
\(333\) | 2.39246 | 0.131106 | ||||||||
\(334\) | 11.1945 | 0.612534 | ||||||||
\(335\) | 27.3991 | 1.49697 | ||||||||
\(336\) | −3.54776 | −0.193546 | ||||||||
\(337\) | −6.84462 | −0.372850 | −0.186425 | − | 0.982469i | \(-0.559690\pi\) | ||||
−0.186425 | + | 0.982469i | \(0.559690\pi\) | |||||||
\(338\) | −72.3659 | −3.93619 | ||||||||
\(339\) | −4.54373 | −0.246782 | ||||||||
\(340\) | 0.236466 | 0.0128242 | ||||||||
\(341\) | 19.2890 | 1.04456 | ||||||||
\(342\) | 55.0806 | 2.97842 | ||||||||
\(343\) | 18.0564 | 0.974954 | ||||||||
\(344\) | −16.5703 | −0.893408 | ||||||||
\(345\) | −5.80763 | −0.312672 | ||||||||
\(346\) | 9.36323 | 0.503370 | ||||||||
\(347\) | 10.6196 | 0.570091 | 0.285045 | − | 0.958514i | \(-0.407991\pi\) | ||||
0.285045 | + | 0.958514i | \(0.407991\pi\) | |||||||
\(348\) | 12.6795 | 0.679693 | ||||||||
\(349\) | −0.592091 | −0.0316939 | −0.0158470 | − | 0.999874i | \(-0.505044\pi\) | ||||
−0.0158470 | + | 0.999874i | \(0.505044\pi\) | |||||||
\(350\) | −1.89297 | −0.101184 | ||||||||
\(351\) | −14.6070 | −0.779664 | ||||||||
\(352\) | 4.64235 | 0.247438 | ||||||||
\(353\) | −13.3053 | −0.708169 | −0.354084 | − | 0.935213i | \(-0.615207\pi\) | ||||
−0.354084 | + | 0.935213i | \(0.615207\pi\) | |||||||
\(354\) | −9.31544 | −0.495110 | ||||||||
\(355\) | 24.2556 | 1.28735 | ||||||||
\(356\) | 2.02149 | 0.107139 | ||||||||
\(357\) | 0.0288166 | 0.00152514 | ||||||||
\(358\) | 24.7000 | 1.30544 | ||||||||
\(359\) | −7.21305 | −0.380690 | −0.190345 | − | 0.981717i | \(-0.560961\pi\) | ||||
−0.190345 | + | 0.981717i | \(0.560961\pi\) | |||||||
\(360\) | −28.6724 | −1.51117 | ||||||||
\(361\) | 44.0625 | 2.31908 | ||||||||
\(362\) | −9.06529 | −0.476461 | ||||||||
\(363\) | 5.77710 | 0.303219 | ||||||||
\(364\) | −69.1454 | −3.62420 | ||||||||
\(365\) | −11.1688 | −0.584604 | ||||||||
\(366\) | −4.88451 | −0.255317 | ||||||||
\(367\) | −6.54698 | −0.341749 | −0.170875 | − | 0.985293i | \(-0.554659\pi\) | ||||
−0.170875 | + | 0.985293i | \(0.554659\pi\) | |||||||
\(368\) | 24.0914 | 1.25585 | ||||||||
\(369\) | 24.7894 | 1.29048 | ||||||||
\(370\) | −4.42095 | −0.229834 | ||||||||
\(371\) | −35.2143 | −1.82824 | ||||||||
\(372\) | 5.61826 | 0.291293 | ||||||||
\(373\) | −21.7384 | −1.12557 | −0.562786 | − | 0.826602i | \(-0.690271\pi\) | ||||
−0.562786 | + | 0.826602i | \(0.690271\pi\) | |||||||
\(374\) | 0.346647 | 0.0179247 | ||||||||
\(375\) | 4.37851 | 0.226105 | ||||||||
\(376\) | −35.5410 | −1.83289 | ||||||||
\(377\) | 55.6860 | 2.86797 | ||||||||
\(378\) | −14.6929 | −0.755721 | ||||||||
\(379\) | −31.4655 | −1.61628 | −0.808138 | − | 0.588994i | \(-0.799524\pi\) | ||||
−0.808138 | + | 0.588994i | \(0.799524\pi\) | |||||||
\(380\) | −67.3045 | −3.45265 | ||||||||
\(381\) | −7.25620 | −0.371747 | ||||||||
\(382\) | −59.7000 | −3.05452 | ||||||||
\(383\) | 27.5479 | 1.40763 | 0.703816 | − | 0.710382i | \(-0.251478\pi\) | ||||
0.703816 | + | 0.710382i | \(0.251478\pi\) | |||||||
\(384\) | 7.71979 | 0.393949 | ||||||||
\(385\) | 30.0539 | 1.53169 | ||||||||
\(386\) | 3.22046 | 0.163917 | ||||||||
\(387\) | −10.2221 | −0.519617 | ||||||||
\(388\) | −24.9206 | −1.26515 | ||||||||
\(389\) | 10.9966 | 0.557548 | 0.278774 | − | 0.960357i | \(-0.410072\pi\) | ||||
0.278774 | + | 0.960357i | \(0.410072\pi\) | |||||||
\(390\) | 13.1605 | 0.666407 | ||||||||
\(391\) | −0.195682 | −0.00989604 | ||||||||
\(392\) | −1.53308 | −0.0774320 | ||||||||
\(393\) | −4.91116 | −0.247735 | ||||||||
\(394\) | −66.1012 | −3.33013 | ||||||||
\(395\) | 20.9255 | 1.05288 | ||||||||
\(396\) | −56.9857 | −2.86364 | ||||||||
\(397\) | −39.5138 | −1.98314 | −0.991571 | − | 0.129561i | \(-0.958643\pi\) | ||||
−0.991571 | + | 0.129561i | \(0.958643\pi\) | |||||||
\(398\) | −25.3499 | −1.27068 | ||||||||
\(399\) | −8.20199 | −0.410613 | ||||||||
\(400\) | −0.988302 | −0.0494151 | ||||||||
\(401\) | 33.7732 | 1.68656 | 0.843278 | − | 0.537478i | \(-0.180623\pi\) | ||||
0.843278 | + | 0.537478i | \(0.180623\pi\) | |||||||
\(402\) | 11.6990 | 0.583492 | ||||||||
\(403\) | 24.6743 | 1.22912 | ||||||||
\(404\) | −13.3592 | −0.664646 | ||||||||
\(405\) | −16.7402 | −0.831827 | ||||||||
\(406\) | 56.0134 | 2.77990 | ||||||||
\(407\) | −4.28558 | −0.212428 | ||||||||
\(408\) | 0.0492461 | 0.00243804 | ||||||||
\(409\) | 25.7484 | 1.27317 | 0.636587 | − | 0.771205i | \(-0.280345\pi\) | ||||
0.636587 | + | 0.771205i | \(0.280345\pi\) | |||||||
\(410\) | −45.8075 | −2.26227 | ||||||||
\(411\) | 2.73084 | 0.134702 | ||||||||
\(412\) | 42.8461 | 2.11087 | ||||||||
\(413\) | −27.2124 | −1.33904 | ||||||||
\(414\) | 48.6467 | 2.39086 | ||||||||
\(415\) | −21.0625 | −1.03392 | ||||||||
\(416\) | 5.93845 | 0.291157 | ||||||||
\(417\) | 0.686471 | 0.0336166 | ||||||||
\(418\) | −98.6650 | −4.82586 | ||||||||
\(419\) | −29.0944 | −1.42135 | −0.710677 | − | 0.703518i | \(-0.751611\pi\) | ||||
−0.710677 | + | 0.703518i | \(0.751611\pi\) | |||||||
\(420\) | 8.75372 | 0.427138 | ||||||||
\(421\) | −30.4606 | −1.48456 | −0.742278 | − | 0.670092i | \(-0.766255\pi\) | ||||
−0.742278 | + | 0.670092i | \(0.766255\pi\) | |||||||
\(422\) | 32.3237 | 1.57349 | ||||||||
\(423\) | −21.9250 | −1.06603 | ||||||||
\(424\) | −60.1793 | −2.92257 | ||||||||
\(425\) | 0.00802746 | 0.000389389 0 | ||||||||
\(426\) | 10.3567 | 0.501786 | ||||||||
\(427\) | −14.2687 | −0.690512 | ||||||||
\(428\) | −6.65312 | −0.321591 | ||||||||
\(429\) | 12.7575 | 0.615938 | ||||||||
\(430\) | 18.8890 | 0.910910 | ||||||||
\(431\) | −35.1939 | −1.69523 | −0.847616 | − | 0.530610i | \(-0.821963\pi\) | ||||
−0.847616 | + | 0.530610i | \(0.821963\pi\) | |||||||
\(432\) | −7.67101 | −0.369072 | ||||||||
\(433\) | 37.1689 | 1.78622 | 0.893110 | − | 0.449837i | \(-0.148518\pi\) | ||||
0.893110 | + | 0.449837i | \(0.148518\pi\) | |||||||
\(434\) | 24.8194 | 1.19137 | ||||||||
\(435\) | −7.04977 | −0.338011 | ||||||||
\(436\) | −29.7910 | −1.42673 | ||||||||
\(437\) | 55.6962 | 2.66431 | ||||||||
\(438\) | −4.76892 | −0.227868 | ||||||||
\(439\) | −33.8850 | −1.61724 | −0.808622 | − | 0.588329i | \(-0.799786\pi\) | ||||
−0.808622 | + | 0.588329i | \(0.799786\pi\) | |||||||
\(440\) | 51.3604 | 2.44851 | ||||||||
\(441\) | −0.945743 | −0.0450354 | ||||||||
\(442\) | 0.443428 | 0.0210917 | ||||||||
\(443\) | 24.6304 | 1.17022 | 0.585112 | − | 0.810952i | \(-0.301050\pi\) | ||||
0.585112 | + | 0.810952i | \(0.301050\pi\) | |||||||
\(444\) | −1.24825 | −0.0592393 | ||||||||
\(445\) | −1.12394 | −0.0532800 | ||||||||
\(446\) | 40.5935 | 1.92216 | ||||||||
\(447\) | 1.24452 | 0.0588637 | ||||||||
\(448\) | 24.5746 | 1.16104 | ||||||||
\(449\) | −31.3391 | −1.47898 | −0.739491 | − | 0.673166i | \(-0.764934\pi\) | ||||
−0.739491 | + | 0.673166i | \(0.764934\pi\) | |||||||
\(450\) | −1.99564 | −0.0940753 | ||||||||
\(451\) | −44.4049 | −2.09094 | ||||||||
\(452\) | −46.5064 | −2.18748 | ||||||||
\(453\) | −2.86399 | −0.134562 | ||||||||
\(454\) | −47.4853 | −2.22860 | ||||||||
\(455\) | 38.4446 | 1.80231 | ||||||||
\(456\) | −14.0168 | −0.656395 | ||||||||
\(457\) | −5.27861 | −0.246923 | −0.123461 | − | 0.992349i | \(-0.539400\pi\) | ||||
−0.123461 | + | 0.992349i | \(0.539400\pi\) | |||||||
\(458\) | −26.1722 | −1.22295 | ||||||||
\(459\) | 0.0623077 | 0.00290827 | ||||||||
\(460\) | −59.4428 | −2.77153 | ||||||||
\(461\) | 1.04519 | 0.0486793 | 0.0243397 | − | 0.999704i | \(-0.492252\pi\) | ||||
0.0243397 | + | 0.999704i | \(0.492252\pi\) | |||||||
\(462\) | 12.8325 | 0.597022 | ||||||||
\(463\) | 12.7165 | 0.590985 | 0.295492 | − | 0.955345i | \(-0.404516\pi\) | ||||
0.295492 | + | 0.955345i | \(0.404516\pi\) | |||||||
\(464\) | 29.2440 | 1.35762 | ||||||||
\(465\) | −3.12374 | −0.144860 | ||||||||
\(466\) | −42.0391 | −1.94742 | ||||||||
\(467\) | 42.9765 | 1.98871 | 0.994357 | − | 0.106083i | \(-0.0338309\pi\) | ||||
0.994357 | + | 0.106083i | \(0.0338309\pi\) | |||||||
\(468\) | −72.8956 | −3.36960 | ||||||||
\(469\) | 34.1753 | 1.57807 | ||||||||
\(470\) | 40.5145 | 1.86879 | ||||||||
\(471\) | 6.66153 | 0.306947 | ||||||||
\(472\) | −46.5046 | −2.14055 | ||||||||
\(473\) | 18.3106 | 0.841924 | ||||||||
\(474\) | 8.93486 | 0.410392 | ||||||||
\(475\) | −2.28483 | −0.104835 | ||||||||
\(476\) | 0.294947 | 0.0135189 | ||||||||
\(477\) | −37.1242 | −1.69980 | ||||||||
\(478\) | −21.8533 | −0.999548 | ||||||||
\(479\) | 14.7895 | 0.675750 | 0.337875 | − | 0.941191i | \(-0.390292\pi\) | ||||
0.337875 | + | 0.941191i | \(0.390292\pi\) | |||||||
\(480\) | −0.751800 | −0.0343148 | ||||||||
\(481\) | −5.48207 | −0.249961 | ||||||||
\(482\) | 1.81741 | 0.0827808 | ||||||||
\(483\) | −7.24393 | −0.329610 | ||||||||
\(484\) | 59.1303 | 2.68774 | ||||||||
\(485\) | 13.8558 | 0.629158 | ||||||||
\(486\) | −23.4272 | −1.06268 | ||||||||
\(487\) | 7.61778 | 0.345195 | 0.172597 | − | 0.984992i | \(-0.444784\pi\) | ||||
0.172597 | + | 0.984992i | \(0.444784\pi\) | |||||||
\(488\) | −24.3845 | −1.10383 | ||||||||
\(489\) | −1.76664 | −0.0798900 | ||||||||
\(490\) | 1.74761 | 0.0789489 | ||||||||
\(491\) | −3.95144 | −0.178326 | −0.0891630 | − | 0.996017i | \(-0.528419\pi\) | ||||
−0.0891630 | + | 0.996017i | \(0.528419\pi\) | |||||||
\(492\) | −12.9337 | −0.583096 | ||||||||
\(493\) | −0.237534 | −0.0106980 | ||||||||
\(494\) | −126.211 | −5.67852 | ||||||||
\(495\) | 31.6839 | 1.42408 | ||||||||
\(496\) | 12.9580 | 0.581830 | ||||||||
\(497\) | 30.2543 | 1.35709 | ||||||||
\(498\) | −8.99336 | −0.403002 | ||||||||
\(499\) | 9.77167 | 0.437440 | 0.218720 | − | 0.975788i | \(-0.429812\pi\) | ||||
0.218720 | + | 0.975788i | \(0.429812\pi\) | |||||||
\(500\) | 44.8154 | 2.00420 | ||||||||
\(501\) | −1.75737 | −0.0785133 | ||||||||
\(502\) | −7.76955 | −0.346772 | ||||||||
\(503\) | 11.9231 | 0.531625 | 0.265812 | − | 0.964025i | \(-0.414360\pi\) | ||||
0.265812 | + | 0.964025i | \(0.414360\pi\) | |||||||
\(504\) | −35.7634 | −1.59303 | ||||||||
\(505\) | 7.42769 | 0.330528 | ||||||||
\(506\) | −87.1402 | −3.87385 | ||||||||
\(507\) | 11.3604 | 0.504532 | ||||||||
\(508\) | −74.2694 | −3.29517 | ||||||||
\(509\) | 12.1535 | 0.538693 | 0.269346 | − | 0.963043i | \(-0.413192\pi\) | ||||
0.269346 | + | 0.963043i | \(0.413192\pi\) | |||||||
\(510\) | −0.0561374 | −0.00248580 | ||||||||
\(511\) | −13.9311 | −0.616273 | ||||||||
\(512\) | 34.9071 | 1.54269 | ||||||||
\(513\) | −17.7344 | −0.782995 | ||||||||
\(514\) | −5.13641 | −0.226557 | ||||||||
\(515\) | −23.8223 | −1.04974 | ||||||||
\(516\) | 5.33330 | 0.234785 | ||||||||
\(517\) | 39.2739 | 1.72726 | ||||||||
\(518\) | −5.51431 | −0.242285 | ||||||||
\(519\) | −1.46989 | −0.0645209 | ||||||||
\(520\) | 65.6998 | 2.88113 | ||||||||
\(521\) | 37.3354 | 1.63569 | 0.817847 | − | 0.575435i | \(-0.195167\pi\) | ||||
0.817847 | + | 0.575435i | \(0.195167\pi\) | |||||||
\(522\) | 59.0513 | 2.58461 | ||||||||
\(523\) | 11.8713 | 0.519095 | 0.259548 | − | 0.965730i | \(-0.416427\pi\) | ||||
0.259548 | + | 0.965730i | \(0.416427\pi\) | |||||||
\(524\) | −50.2672 | −2.19593 | ||||||||
\(525\) | 0.297168 | 0.0129695 | ||||||||
\(526\) | 24.9650 | 1.08853 | ||||||||
\(527\) | −0.105251 | −0.00458480 | ||||||||
\(528\) | 6.69973 | 0.291568 | ||||||||
\(529\) | 26.1905 | 1.13872 | ||||||||
\(530\) | 68.6006 | 2.97982 | ||||||||
\(531\) | −28.6883 | −1.24497 | ||||||||
\(532\) | −83.9498 | −3.63968 | ||||||||
\(533\) | −56.8023 | −2.46038 | ||||||||
\(534\) | −0.479905 | −0.0207675 | ||||||||
\(535\) | 3.69912 | 0.159927 | ||||||||
\(536\) | 58.4037 | 2.52266 | ||||||||
\(537\) | −3.87754 | −0.167328 | ||||||||
\(538\) | 19.8946 | 0.857715 | ||||||||
\(539\) | 1.69410 | 0.0729699 | ||||||||
\(540\) | 18.9274 | 0.814505 | ||||||||
\(541\) | −1.58914 | −0.0683225 | −0.0341612 | − | 0.999416i | \(-0.510876\pi\) | ||||
−0.0341612 | + | 0.999416i | \(0.510876\pi\) | |||||||
\(542\) | 20.5167 | 0.881268 | ||||||||
\(543\) | 1.42312 | 0.0610718 | ||||||||
\(544\) | −0.0253311 | −0.00108606 | ||||||||
\(545\) | 16.5637 | 0.709511 | ||||||||
\(546\) | 16.4152 | 0.702507 | ||||||||
\(547\) | −40.2811 | −1.72230 | −0.861148 | − | 0.508354i | \(-0.830254\pi\) | ||||
−0.861148 | + | 0.508354i | \(0.830254\pi\) | |||||||
\(548\) | 27.9509 | 1.19400 | ||||||||
\(549\) | −15.0426 | −0.642003 | ||||||||
\(550\) | 3.57476 | 0.152428 | ||||||||
\(551\) | 67.6086 | 2.88022 | ||||||||
\(552\) | −12.3795 | −0.526906 | ||||||||
\(553\) | 26.1007 | 1.10991 | ||||||||
\(554\) | 21.5306 | 0.914749 | ||||||||
\(555\) | 0.694023 | 0.0294597 | ||||||||
\(556\) | 7.02623 | 0.297979 | ||||||||
\(557\) | 17.6685 | 0.748640 | 0.374320 | − | 0.927300i | \(-0.377876\pi\) | ||||
0.374320 | + | 0.927300i | \(0.377876\pi\) | |||||||
\(558\) | 26.1655 | 1.10767 | ||||||||
\(559\) | 23.4228 | 0.990680 | ||||||||
\(560\) | 20.1896 | 0.853166 | ||||||||
\(561\) | −0.0544184 | −0.00229755 | ||||||||
\(562\) | 38.4630 | 1.62246 | ||||||||
\(563\) | −23.4192 | −0.987001 | −0.493500 | − | 0.869746i | \(-0.664283\pi\) | ||||
−0.493500 | + | 0.869746i | \(0.664283\pi\) | |||||||
\(564\) | 11.4392 | 0.481678 | ||||||||
\(565\) | 25.8574 | 1.08783 | ||||||||
\(566\) | 6.89843 | 0.289963 | ||||||||
\(567\) | −20.8803 | −0.876888 | ||||||||
\(568\) | 51.7030 | 2.16941 | ||||||||
\(569\) | 3.60300 | 0.151045 | 0.0755227 | − | 0.997144i | \(-0.475937\pi\) | ||||
0.0755227 | + | 0.997144i | \(0.475937\pi\) | |||||||
\(570\) | 15.9782 | 0.669253 | ||||||||
\(571\) | 7.82842 | 0.327609 | 0.163805 | − | 0.986493i | \(-0.447623\pi\) | ||||
0.163805 | + | 0.986493i | \(0.447623\pi\) | |||||||
\(572\) | 130.577 | 5.45969 | ||||||||
\(573\) | 9.37201 | 0.391521 | ||||||||
\(574\) | −57.1363 | −2.38482 | ||||||||
\(575\) | −2.01794 | −0.0841541 | ||||||||
\(576\) | 25.9074 | 1.07948 | ||||||||
\(577\) | −8.78037 | −0.365532 | −0.182766 | − | 0.983156i | \(-0.558505\pi\) | ||||
−0.182766 | + | 0.983156i | \(0.558505\pi\) | |||||||
\(578\) | 41.3060 | 1.71810 | ||||||||
\(579\) | −0.505564 | −0.0210105 | ||||||||
\(580\) | −72.1565 | −2.99614 | ||||||||
\(581\) | −26.2716 | −1.08993 | ||||||||
\(582\) | 5.91619 | 0.245234 | ||||||||
\(583\) | 66.5000 | 2.75415 | ||||||||
\(584\) | −23.8074 | −0.985158 | ||||||||
\(585\) | 40.5297 | 1.67570 | ||||||||
\(586\) | 8.23534 | 0.340199 | ||||||||
\(587\) | 26.3610 | 1.08803 | 0.544017 | − | 0.839074i | \(-0.316903\pi\) | ||||
0.544017 | + | 0.839074i | \(0.316903\pi\) | |||||||
\(588\) | 0.493435 | 0.0203489 | ||||||||
\(589\) | 29.9572 | 1.23437 | ||||||||
\(590\) | 53.0123 | 2.18248 | ||||||||
\(591\) | 10.3769 | 0.426849 | ||||||||
\(592\) | −2.87897 | −0.118325 | ||||||||
\(593\) | −22.3609 | −0.918252 | −0.459126 | − | 0.888371i | \(-0.651837\pi\) | ||||
−0.459126 | + | 0.888371i | \(0.651837\pi\) | |||||||
\(594\) | 27.7466 | 1.13846 | ||||||||
\(595\) | −0.163989 | −0.00672291 | ||||||||
\(596\) | 12.7380 | 0.521769 | ||||||||
\(597\) | 3.97956 | 0.162872 | ||||||||
\(598\) | −111.469 | −4.55830 | ||||||||
\(599\) | −9.04870 | −0.369720 | −0.184860 | − | 0.982765i | \(-0.559183\pi\) | ||||
−0.184860 | + | 0.982765i | \(0.559183\pi\) | |||||||
\(600\) | 0.507845 | 0.0207327 | ||||||||
\(601\) | 16.9125 | 0.689876 | 0.344938 | − | 0.938625i | \(-0.387900\pi\) | ||||
0.344938 | + | 0.938625i | \(0.387900\pi\) | |||||||
\(602\) | 23.5605 | 0.960256 | ||||||||
\(603\) | 36.0288 | 1.46721 | ||||||||
\(604\) | −29.3138 | −1.19276 | ||||||||
\(605\) | −32.8763 | −1.33661 | ||||||||
\(606\) | 3.17150 | 0.128833 | ||||||||
\(607\) | −33.3170 | −1.35230 | −0.676148 | − | 0.736766i | \(-0.736352\pi\) | ||||
−0.676148 | + | 0.736766i | \(0.736352\pi\) | |||||||
\(608\) | 7.20990 | 0.292400 | ||||||||
\(609\) | −8.79327 | −0.356321 | ||||||||
\(610\) | 27.7967 | 1.12546 | ||||||||
\(611\) | 50.2388 | 2.03245 | ||||||||
\(612\) | 0.310943 | 0.0125691 | ||||||||
\(613\) | 45.4364 | 1.83516 | 0.917580 | − | 0.397550i | \(-0.130140\pi\) | ||||
0.917580 | + | 0.397550i | \(0.130140\pi\) | |||||||
\(614\) | −50.9849 | −2.05758 | ||||||||
\(615\) | 7.19110 | 0.289973 | ||||||||
\(616\) | 64.0625 | 2.58115 | ||||||||
\(617\) | −26.2290 | −1.05594 | −0.527970 | − | 0.849263i | \(-0.677047\pi\) | ||||
−0.527970 | + | 0.849263i | \(0.677047\pi\) | |||||||
\(618\) | −10.1717 | −0.409167 | ||||||||
\(619\) | −27.5434 | −1.10706 | −0.553531 | − | 0.832828i | \(-0.686720\pi\) | ||||
−0.553531 | + | 0.832828i | \(0.686720\pi\) | |||||||
\(620\) | −31.9724 | −1.28404 | ||||||||
\(621\) | −15.6629 | −0.628531 | ||||||||
\(622\) | 82.6826 | 3.31527 | ||||||||
\(623\) | −1.40191 | −0.0561662 | ||||||||
\(624\) | 8.57023 | 0.343084 | ||||||||
\(625\) | −23.4786 | −0.939145 | ||||||||
\(626\) | −50.1410 | −2.00404 | ||||||||
\(627\) | 15.4889 | 0.618569 | ||||||||
\(628\) | 68.1828 | 2.72079 | ||||||||
\(629\) | 0.0233843 | 0.000932395 0 | ||||||||
\(630\) | 40.7680 | 1.62424 | ||||||||
\(631\) | 33.7132 | 1.34210 | 0.671050 | − | 0.741412i | \(-0.265844\pi\) | ||||
0.671050 | + | 0.741412i | \(0.265844\pi\) | |||||||
\(632\) | 44.6046 | 1.77428 | ||||||||
\(633\) | −5.07435 | −0.201687 | ||||||||
\(634\) | 18.4555 | 0.732960 | ||||||||
\(635\) | 41.2936 | 1.63868 | ||||||||
\(636\) | 19.3693 | 0.768043 | ||||||||
\(637\) | 2.16707 | 0.0858625 | ||||||||
\(638\) | −105.778 | −4.18778 | ||||||||
\(639\) | 31.8952 | 1.26175 | ||||||||
\(640\) | −43.9317 | −1.73655 | ||||||||
\(641\) | −17.4400 | −0.688838 | −0.344419 | − | 0.938816i | \(-0.611924\pi\) | ||||
−0.344419 | + | 0.938816i | \(0.611924\pi\) | |||||||
\(642\) | 1.57946 | 0.0623364 | ||||||||
\(643\) | −13.5358 | −0.533798 | −0.266899 | − | 0.963724i | \(-0.585999\pi\) | ||||
−0.266899 | + | 0.963724i | \(0.585999\pi\) | |||||||
\(644\) | −74.1438 | −2.92167 | ||||||||
\(645\) | −2.96530 | −0.116758 | ||||||||
\(646\) | 0.538368 | 0.0211818 | ||||||||
\(647\) | −2.40965 | −0.0947332 | −0.0473666 | − | 0.998878i | \(-0.515083\pi\) | ||||
−0.0473666 | + | 0.998878i | \(0.515083\pi\) | |||||||
\(648\) | −35.6832 | −1.40177 | ||||||||
\(649\) | 51.3890 | 2.01719 | ||||||||
\(650\) | 4.57280 | 0.179360 | ||||||||
\(651\) | −3.89628 | −0.152707 | ||||||||
\(652\) | −18.0820 | −0.708147 | ||||||||
\(653\) | −44.3138 | −1.73413 | −0.867066 | − | 0.498193i | \(-0.833997\pi\) | ||||
−0.867066 | + | 0.498193i | \(0.833997\pi\) | |||||||
\(654\) | 7.07243 | 0.276554 | ||||||||
\(655\) | 27.9484 | 1.09203 | ||||||||
\(656\) | −29.8303 | −1.16468 | ||||||||
\(657\) | −14.6866 | −0.572979 | ||||||||
\(658\) | 50.5342 | 1.97003 | ||||||||
\(659\) | 16.6422 | 0.648290 | 0.324145 | − | 0.946007i | \(-0.394923\pi\) | ||||
0.324145 | + | 0.946007i | \(0.394923\pi\) | |||||||
\(660\) | −16.5308 | −0.643462 | ||||||||
\(661\) | 2.68299 | 0.104356 | 0.0521781 | − | 0.998638i | \(-0.483384\pi\) | ||||
0.0521781 | + | 0.998638i | \(0.483384\pi\) | |||||||
\(662\) | 16.7951 | 0.652760 | ||||||||
\(663\) | −0.0696116 | −0.00270349 | ||||||||
\(664\) | −44.8967 | −1.74233 | ||||||||
\(665\) | 46.6758 | 1.81001 | ||||||||
\(666\) | −5.81338 | −0.225264 | ||||||||
\(667\) | 59.7114 | 2.31203 | ||||||||
\(668\) | −17.9872 | −0.695944 | ||||||||
\(669\) | −6.37258 | −0.246378 | ||||||||
\(670\) | −66.5765 | −2.57207 | ||||||||
\(671\) | 26.9456 | 1.04022 | ||||||||
\(672\) | −0.937730 | −0.0361737 | ||||||||
\(673\) | 4.65760 | 0.179537 | 0.0897686 | − | 0.995963i | \(-0.471387\pi\) | ||||
0.0897686 | + | 0.995963i | \(0.471387\pi\) | |||||||
\(674\) | 16.6316 | 0.640625 | ||||||||
\(675\) | 0.642541 | 0.0247314 | ||||||||
\(676\) | 116.277 | 4.47218 | ||||||||
\(677\) | −24.3519 | −0.935919 | −0.467959 | − | 0.883750i | \(-0.655011\pi\) | ||||
−0.467959 | + | 0.883750i | \(0.655011\pi\) | |||||||
\(678\) | 11.0407 | 0.424016 | ||||||||
\(679\) | 17.2825 | 0.663241 | ||||||||
\(680\) | −0.280249 | −0.0107471 | ||||||||
\(681\) | 7.45449 | 0.285657 | ||||||||
\(682\) | −46.8699 | −1.79474 | ||||||||
\(683\) | 48.2607 | 1.84665 | 0.923323 | − | 0.384024i | \(-0.125462\pi\) | ||||
0.923323 | + | 0.384024i | \(0.125462\pi\) | |||||||
\(684\) | −88.5029 | −3.38399 | ||||||||
\(685\) | −15.5406 | −0.593777 | ||||||||
\(686\) | −43.8748 | −1.67515 | ||||||||
\(687\) | 4.10865 | 0.156755 | ||||||||
\(688\) | 12.3007 | 0.468961 | ||||||||
\(689\) | 85.0662 | 3.24077 | ||||||||
\(690\) | 14.1118 | 0.537228 | ||||||||
\(691\) | 31.2586 | 1.18913 | 0.594566 | − | 0.804047i | \(-0.297324\pi\) | ||||
0.594566 | + | 0.804047i | \(0.297324\pi\) | |||||||
\(692\) | −15.0447 | −0.571915 | ||||||||
\(693\) | 39.5197 | 1.50123 | ||||||||
\(694\) | −25.8043 | −0.979520 | ||||||||
\(695\) | −3.90656 | −0.148184 | ||||||||
\(696\) | −15.0272 | −0.569606 | ||||||||
\(697\) | 0.242296 | 0.00917762 | ||||||||
\(698\) | 1.43871 | 0.0544559 | ||||||||
\(699\) | 6.59951 | 0.249617 | ||||||||
\(700\) | 3.04161 | 0.114962 | ||||||||
\(701\) | −41.9224 | −1.58339 | −0.791693 | − | 0.610919i | \(-0.790800\pi\) | ||||
−0.791693 | + | 0.610919i | \(0.790800\pi\) | |||||||
\(702\) | 35.4932 | 1.33961 | ||||||||
\(703\) | −6.65581 | −0.251029 | ||||||||
\(704\) | −46.4076 | −1.74905 | ||||||||
\(705\) | −6.36017 | −0.239538 | ||||||||
\(706\) | 32.3302 | 1.21676 | ||||||||
\(707\) | 9.26465 | 0.348433 | ||||||||
\(708\) | 14.9680 | 0.562530 | ||||||||
\(709\) | 13.4696 | 0.505863 | 0.252931 | − | 0.967484i | \(-0.418605\pi\) | ||||
0.252931 | + | 0.967484i | \(0.418605\pi\) | |||||||
\(710\) | −58.9381 | −2.21191 | ||||||||
\(711\) | 27.5163 | 1.03194 | ||||||||
\(712\) | −2.39578 | −0.0897858 | ||||||||
\(713\) | 26.4580 | 0.990859 | ||||||||
\(714\) | −0.0700208 | −0.00262046 | ||||||||
\(715\) | −72.6003 | −2.71510 | ||||||||
\(716\) | −39.6877 | −1.48320 | ||||||||
\(717\) | 3.43065 | 0.128120 | ||||||||
\(718\) | 17.5268 | 0.654095 | ||||||||
\(719\) | 26.7882 | 0.999030 | 0.499515 | − | 0.866305i | \(-0.333512\pi\) | ||||
0.499515 | + | 0.866305i | \(0.333512\pi\) | |||||||
\(720\) | 21.2846 | 0.793230 | ||||||||
\(721\) | −29.7138 | −1.10660 | ||||||||
\(722\) | −107.066 | −3.98460 | ||||||||
\(723\) | −0.285306 | −0.0106107 | ||||||||
\(724\) | 14.5660 | 0.541342 | ||||||||
\(725\) | −2.44955 | −0.0909738 | ||||||||
\(726\) | −14.0376 | −0.520985 | ||||||||
\(727\) | −16.9320 | −0.627973 | −0.313987 | − | 0.949427i | \(-0.601665\pi\) | ||||
−0.313987 | + | 0.949427i | \(0.601665\pi\) | |||||||
\(728\) | 81.9482 | 3.03720 | ||||||||
\(729\) | −19.4571 | −0.720633 | ||||||||
\(730\) | 27.1389 | 1.00446 | ||||||||
\(731\) | −0.0999124 | −0.00369539 | ||||||||
\(732\) | 7.84838 | 0.290084 | ||||||||
\(733\) | −15.2462 | −0.563130 | −0.281565 | − | 0.959542i | \(-0.590853\pi\) | ||||
−0.281565 | + | 0.959542i | \(0.590853\pi\) | |||||||
\(734\) | 15.9083 | 0.587188 | ||||||||
\(735\) | −0.274349 | −0.0101195 | ||||||||
\(736\) | 6.36773 | 0.234718 | ||||||||
\(737\) | −64.5379 | −2.37728 | ||||||||
\(738\) | −60.2352 | −2.21729 | ||||||||
\(739\) | −24.7430 | −0.910184 | −0.455092 | − | 0.890444i | \(-0.650394\pi\) | ||||
−0.455092 | + | 0.890444i | \(0.650394\pi\) | |||||||
\(740\) | 7.10353 | 0.261131 | ||||||||
\(741\) | 19.8133 | 0.727861 | ||||||||
\(742\) | 85.5664 | 3.14124 | ||||||||
\(743\) | 10.6923 | 0.392261 | 0.196131 | − | 0.980578i | \(-0.437162\pi\) | ||||
0.196131 | + | 0.980578i | \(0.437162\pi\) | |||||||
\(744\) | −6.65853 | −0.244114 | ||||||||
\(745\) | −7.08229 | −0.259475 | ||||||||
\(746\) | 52.8217 | 1.93394 | ||||||||
\(747\) | −27.6964 | −1.01336 | ||||||||
\(748\) | −0.556988 | −0.0203655 | ||||||||
\(749\) | 4.61396 | 0.168590 | ||||||||
\(750\) | −10.6392 | −0.388490 | ||||||||
\(751\) | 19.9609 | 0.728385 | 0.364192 | − | 0.931324i | \(-0.381345\pi\) | ||||
0.364192 | + | 0.931324i | \(0.381345\pi\) | |||||||
\(752\) | 26.3834 | 0.962104 | ||||||||
\(753\) | 1.21970 | 0.0444485 | ||||||||
\(754\) | −135.310 | −4.92770 | ||||||||
\(755\) | 16.2984 | 0.593158 | ||||||||
\(756\) | 23.6084 | 0.858628 | ||||||||
\(757\) | 5.54047 | 0.201372 | 0.100686 | − | 0.994918i | \(-0.467896\pi\) | ||||
0.100686 | + | 0.994918i | \(0.467896\pi\) | |||||||
\(758\) | 76.4573 | 2.77705 | ||||||||
\(759\) | 13.6797 | 0.496542 | ||||||||
\(760\) | 79.7665 | 2.89343 | ||||||||
\(761\) | 10.5736 | 0.383293 | 0.191646 | − | 0.981464i | \(-0.438617\pi\) | ||||
0.191646 | + | 0.981464i | \(0.438617\pi\) | |||||||
\(762\) | 17.6317 | 0.638728 | ||||||||
\(763\) | 20.6601 | 0.747946 | ||||||||
\(764\) | 95.9252 | 3.47045 | ||||||||
\(765\) | −0.172884 | −0.00625062 | ||||||||
\(766\) | −66.9380 | −2.41857 | ||||||||
\(767\) | 65.7364 | 2.37360 | ||||||||
\(768\) | −11.8340 | −0.427021 | ||||||||
\(769\) | −5.21778 | −0.188158 | −0.0940789 | − | 0.995565i | \(-0.529991\pi\) | ||||
−0.0940789 | + | 0.995565i | \(0.529991\pi\) | |||||||
\(770\) | −73.0272 | −2.63172 | ||||||||
\(771\) | 0.806340 | 0.0290396 | ||||||||
\(772\) | −5.17459 | −0.186238 | ||||||||
\(773\) | −18.8714 | −0.678756 | −0.339378 | − | 0.940650i | \(-0.610217\pi\) | ||||
−0.339378 | + | 0.940650i | \(0.610217\pi\) | |||||||
\(774\) | 24.8384 | 0.892797 | ||||||||
\(775\) | −1.08539 | −0.0389883 | ||||||||
\(776\) | 29.5348 | 1.06024 | ||||||||
\(777\) | 0.865664 | 0.0310555 | ||||||||
\(778\) | −26.7203 | −0.957969 | ||||||||
\(779\) | −68.9640 | −2.47089 | ||||||||
\(780\) | −21.1461 | −0.757152 | ||||||||
\(781\) | −57.1334 | −2.04439 | ||||||||
\(782\) | 0.475482 | 0.0170032 | ||||||||
\(783\) | −19.0129 | −0.679466 | ||||||||
\(784\) | 1.13806 | 0.0406450 | ||||||||
\(785\) | −37.9094 | −1.35305 | ||||||||
\(786\) | 11.9335 | 0.425654 | ||||||||
\(787\) | −9.14067 | −0.325830 | −0.162915 | − | 0.986640i | \(-0.552090\pi\) | ||||
−0.162915 | + | 0.986640i | \(0.552090\pi\) | |||||||
\(788\) | 106.211 | 3.78360 | ||||||||
\(789\) | −3.91914 | −0.139525 | ||||||||
\(790\) | −50.8464 | −1.80903 | ||||||||
\(791\) | 32.2523 | 1.14676 | ||||||||
\(792\) | 67.5370 | 2.39982 | ||||||||
\(793\) | 34.4686 | 1.22401 | ||||||||
\(794\) | 96.0137 | 3.40740 | ||||||||
\(795\) | −10.7693 | −0.381947 | ||||||||
\(796\) | 40.7319 | 1.44371 | ||||||||
\(797\) | −2.79399 | −0.0989680 | −0.0494840 | − | 0.998775i | \(-0.515758\pi\) | ||||
−0.0494840 | + | 0.998775i | \(0.515758\pi\) | |||||||
\(798\) | 19.9298 | 0.705508 | ||||||||
\(799\) | −0.214299 | −0.00758135 | ||||||||
\(800\) | −0.261224 | −0.00923566 | ||||||||
\(801\) | −1.47794 | −0.0522205 | ||||||||
\(802\) | −82.0648 | −2.89781 | ||||||||
\(803\) | 26.3079 | 0.928386 | ||||||||
\(804\) | −18.7978 | −0.662947 | ||||||||
\(805\) | 41.2237 | 1.45294 | ||||||||
\(806\) | −59.9556 | −2.11185 | ||||||||
\(807\) | −3.12315 | −0.109940 | ||||||||
\(808\) | 15.8328 | 0.556996 | ||||||||
\(809\) | −8.03597 | −0.282530 | −0.141265 | − | 0.989972i | \(-0.545117\pi\) | ||||
−0.141265 | + | 0.989972i | \(0.545117\pi\) | |||||||
\(810\) | 40.6766 | 1.42923 | ||||||||
\(811\) | 16.0818 | 0.564707 | 0.282354 | − | 0.959310i | \(-0.408885\pi\) | ||||
0.282354 | + | 0.959310i | \(0.408885\pi\) | |||||||
\(812\) | −90.0017 | −3.15844 | ||||||||
\(813\) | −3.22082 | −0.112959 | ||||||||
\(814\) | 10.4134 | 0.364990 | ||||||||
\(815\) | 10.0536 | 0.352161 | ||||||||
\(816\) | −0.0365572 | −0.00127976 | ||||||||
\(817\) | 28.4378 | 0.994911 | ||||||||
\(818\) | −62.5653 | −2.18755 | ||||||||
\(819\) | 50.5532 | 1.76647 | ||||||||
\(820\) | 73.6030 | 2.57033 | ||||||||
\(821\) | 22.7981 | 0.795659 | 0.397830 | − | 0.917459i | \(-0.369764\pi\) | ||||
0.397830 | + | 0.917459i | \(0.369764\pi\) | |||||||
\(822\) | −6.63560 | −0.231443 | ||||||||
\(823\) | 47.7720 | 1.66523 | 0.832613 | − | 0.553855i | \(-0.186844\pi\) | ||||
0.832613 | + | 0.553855i | \(0.186844\pi\) | |||||||
\(824\) | −50.7794 | −1.76898 | ||||||||
\(825\) | −0.561184 | −0.0195379 | ||||||||
\(826\) | 66.1229 | 2.30071 | ||||||||
\(827\) | 16.8441 | 0.585728 | 0.292864 | − | 0.956154i | \(-0.405392\pi\) | ||||
0.292864 | + | 0.956154i | \(0.405392\pi\) | |||||||
\(828\) | −78.1650 | −2.71642 | ||||||||
\(829\) | −34.0417 | −1.18232 | −0.591159 | − | 0.806555i | \(-0.701330\pi\) | ||||
−0.591159 | + | 0.806555i | \(0.701330\pi\) | |||||||
\(830\) | 51.1793 | 1.77646 | ||||||||
\(831\) | −3.37999 | −0.117251 | ||||||||
\(832\) | −59.3642 | −2.05808 | ||||||||
\(833\) | −0.00924387 | −0.000320281 0 | ||||||||
\(834\) | −1.66804 | −0.0577595 | ||||||||
\(835\) | 10.0008 | 0.346092 | ||||||||
\(836\) | 158.534 | 5.48301 | ||||||||
\(837\) | −8.42458 | −0.291196 | ||||||||
\(838\) | 70.6958 | 2.44215 | ||||||||
\(839\) | −25.2000 | −0.870002 | −0.435001 | − | 0.900430i | \(-0.643252\pi\) | ||||
−0.435001 | + | 0.900430i | \(0.643252\pi\) | |||||||
\(840\) | −10.3745 | −0.357955 | ||||||||
\(841\) | 43.4826 | 1.49940 | ||||||||
\(842\) | 74.0154 | 2.55074 | ||||||||
\(843\) | −6.03812 | −0.207964 | ||||||||
\(844\) | −51.9374 | −1.78776 | ||||||||
\(845\) | −64.6495 | −2.22401 | ||||||||
\(846\) | 53.2750 | 1.83163 | ||||||||
\(847\) | −41.0070 | −1.40902 | ||||||||
\(848\) | 44.6734 | 1.53409 | ||||||||
\(849\) | −1.08295 | −0.0371668 | ||||||||
\(850\) | −0.0195057 | −0.000669041 0 | ||||||||
\(851\) | −5.87836 | −0.201508 | ||||||||
\(852\) | −16.6411 | −0.570115 | ||||||||
\(853\) | 0.607629 | 0.0208048 | 0.0104024 | − | 0.999946i | \(-0.496689\pi\) | ||||
0.0104024 | + | 0.999946i | \(0.496689\pi\) | |||||||
\(854\) | 34.6712 | 1.18643 | ||||||||
\(855\) | 49.2073 | 1.68286 | ||||||||
\(856\) | 7.88500 | 0.269504 | ||||||||
\(857\) | 2.78457 | 0.0951191 | 0.0475595 | − | 0.998868i | \(-0.484856\pi\) | ||||
0.0475595 | + | 0.998868i | \(0.484856\pi\) | |||||||
\(858\) | −30.9991 | −1.05829 | ||||||||
\(859\) | 4.46737 | 0.152425 | 0.0762123 | − | 0.997092i | \(-0.475717\pi\) | ||||
0.0762123 | + | 0.997092i | \(0.475717\pi\) | |||||||
\(860\) | −30.3507 | −1.03495 | ||||||||
\(861\) | 8.96955 | 0.305682 | ||||||||
\(862\) | 85.5169 | 2.91272 | ||||||||
\(863\) | 47.2136 | 1.60717 | 0.803585 | − | 0.595190i | \(-0.202923\pi\) | ||||
0.803585 | + | 0.595190i | \(0.202923\pi\) | |||||||
\(864\) | −2.02757 | −0.0689794 | ||||||||
\(865\) | 8.36483 | 0.284413 | ||||||||
\(866\) | −90.3157 | −3.06905 | ||||||||
\(867\) | −6.48443 | −0.220223 | ||||||||
\(868\) | −39.8796 | −1.35360 | ||||||||
\(869\) | −49.2895 | −1.67203 | ||||||||
\(870\) | 17.1301 | 0.580764 | ||||||||
\(871\) | −82.5563 | −2.79731 | ||||||||
\(872\) | 35.3070 | 1.19565 | ||||||||
\(873\) | 18.2198 | 0.616647 | ||||||||
\(874\) | −135.335 | −4.57777 | ||||||||
\(875\) | −31.0796 | −1.05068 | ||||||||
\(876\) | 7.66264 | 0.258897 | ||||||||
\(877\) | −54.6348 | −1.84489 | −0.922443 | − | 0.386134i | \(-0.873810\pi\) | ||||
−0.922443 | + | 0.386134i | \(0.873810\pi\) | |||||||
\(878\) | 82.3364 | 2.77872 | ||||||||
\(879\) | −1.29283 | −0.0436060 | ||||||||
\(880\) | −38.1268 | −1.28525 | ||||||||
\(881\) | −10.3240 | −0.347825 | −0.173912 | − | 0.984761i | \(-0.555641\pi\) | ||||
−0.173912 | + | 0.984761i | \(0.555641\pi\) | |||||||
\(882\) | 2.29804 | 0.0773790 | ||||||||
\(883\) | −3.12060 | −0.105017 | −0.0525083 | − | 0.998620i | \(-0.516722\pi\) | ||||
−0.0525083 | + | 0.998620i | \(0.516722\pi\) | |||||||
\(884\) | −0.712495 | −0.0239638 | ||||||||
\(885\) | −8.32214 | −0.279746 | ||||||||
\(886\) | −59.8488 | −2.01066 | ||||||||
\(887\) | 10.6041 | 0.356050 | 0.178025 | − | 0.984026i | \(-0.443029\pi\) | ||||
0.178025 | + | 0.984026i | \(0.443029\pi\) | |||||||
\(888\) | 1.47937 | 0.0496445 | ||||||||
\(889\) | 51.5060 | 1.72746 | ||||||||
\(890\) | 2.73104 | 0.0915447 | ||||||||
\(891\) | 39.4311 | 1.32099 | ||||||||
\(892\) | −65.2252 | −2.18390 | ||||||||
\(893\) | 60.9952 | 2.04113 | ||||||||
\(894\) | −3.02402 | −0.101139 | ||||||||
\(895\) | 22.0663 | 0.737594 | ||||||||
\(896\) | −54.7966 | −1.83063 | ||||||||
\(897\) | 17.4990 | 0.584274 | ||||||||
\(898\) | 76.1501 | 2.54116 | ||||||||
\(899\) | 32.1169 | 1.07116 | ||||||||
\(900\) | 3.20657 | 0.106886 | ||||||||
\(901\) | −0.362859 | −0.0120886 | ||||||||
\(902\) | 107.898 | 3.59262 | ||||||||
\(903\) | −3.69865 | −0.123084 | ||||||||
\(904\) | 55.1175 | 1.83318 | ||||||||
\(905\) | −8.09866 | −0.269209 | ||||||||
\(906\) | 6.95914 | 0.231202 | ||||||||
\(907\) | −33.1586 | −1.10101 | −0.550506 | − | 0.834831i | \(-0.685565\pi\) | ||||
−0.550506 | + | 0.834831i | \(0.685565\pi\) | |||||||
\(908\) | 76.2989 | 2.53207 | ||||||||
\(909\) | 9.76713 | 0.323955 | ||||||||
\(910\) | −93.4157 | −3.09670 | ||||||||
\(911\) | −11.7842 | −0.390427 | −0.195213 | − | 0.980761i | \(-0.562540\pi\) | ||||
−0.195213 | + | 0.980761i | \(0.562540\pi\) | |||||||
\(912\) | 10.4052 | 0.344549 | ||||||||
\(913\) | 49.6122 | 1.64192 | ||||||||
\(914\) | 12.8264 | 0.424259 | ||||||||
\(915\) | −4.36368 | −0.144259 | ||||||||
\(916\) | 42.0533 | 1.38948 | ||||||||
\(917\) | 34.8604 | 1.15119 | ||||||||
\(918\) | −0.151400 | −0.00499694 | ||||||||
\(919\) | 34.9680 | 1.15349 | 0.576744 | − | 0.816925i | \(-0.304323\pi\) | ||||
0.576744 | + | 0.816925i | \(0.304323\pi\) | |||||||
\(920\) | 70.4491 | 2.32264 | ||||||||
\(921\) | 8.00387 | 0.263737 | ||||||||
\(922\) | −2.53968 | −0.0836399 | ||||||||
\(923\) | −73.0846 | −2.40561 | ||||||||
\(924\) | −20.6191 | −0.678320 | ||||||||
\(925\) | 0.241148 | 0.00792891 | ||||||||
\(926\) | −30.8995 | −1.01542 | ||||||||
\(927\) | −31.3254 | −1.02886 | ||||||||
\(928\) | 7.72967 | 0.253739 | ||||||||
\(929\) | −25.5273 | −0.837523 | −0.418762 | − | 0.908096i | \(-0.637536\pi\) | ||||
−0.418762 | + | 0.908096i | \(0.637536\pi\) | |||||||
\(930\) | 7.59030 | 0.248896 | ||||||||
\(931\) | 2.63105 | 0.0862293 | ||||||||
\(932\) | 67.5480 | 2.21261 | ||||||||
\(933\) | −12.9799 | −0.424944 | ||||||||
\(934\) | −104.428 | −3.41697 | ||||||||
\(935\) | 0.309684 | 0.0101277 | ||||||||
\(936\) | 86.3928 | 2.82384 | ||||||||
\(937\) | 52.7905 | 1.72459 | 0.862295 | − | 0.506407i | \(-0.169027\pi\) | ||||
0.862295 | + | 0.506407i | \(0.169027\pi\) | |||||||
\(938\) | −83.0417 | −2.71141 | ||||||||
\(939\) | 7.87140 | 0.256873 | ||||||||
\(940\) | −65.0982 | −2.12327 | ||||||||
\(941\) | 24.6981 | 0.805136 | 0.402568 | − | 0.915390i | \(-0.368118\pi\) | ||||
0.402568 | + | 0.915390i | \(0.368118\pi\) | |||||||
\(942\) | −16.1867 | −0.527391 | ||||||||
\(943\) | −60.9084 | −1.98345 | ||||||||
\(944\) | 34.5221 | 1.12360 | ||||||||
\(945\) | −13.1262 | −0.426995 | ||||||||
\(946\) | −44.4926 | −1.44658 | ||||||||
\(947\) | −49.7029 | −1.61513 | −0.807563 | − | 0.589782i | \(-0.799214\pi\) | ||||
−0.807563 | + | 0.589782i | \(0.799214\pi\) | |||||||
\(948\) | −14.3564 | −0.466275 | ||||||||
\(949\) | 33.6529 | 1.09242 | ||||||||
\(950\) | 5.55186 | 0.180126 | ||||||||
\(951\) | −2.89723 | −0.0939493 | ||||||||
\(952\) | −0.349558 | −0.0113293 | ||||||||
\(953\) | 2.56181 | 0.0829853 | 0.0414926 | − | 0.999139i | \(-0.486789\pi\) | ||||
0.0414926 | + | 0.999139i | \(0.486789\pi\) | |||||||
\(954\) | 90.2072 | 2.92057 | ||||||||
\(955\) | −53.3342 | −1.72585 | ||||||||
\(956\) | 35.1137 | 1.13566 | ||||||||
\(957\) | 16.6055 | 0.536781 | ||||||||
\(958\) | −35.9367 | −1.16106 | ||||||||
\(959\) | −19.3840 | −0.625943 | ||||||||
\(960\) | 7.51543 | 0.242559 | ||||||||
\(961\) | −16.7691 | −0.540938 | ||||||||
\(962\) | 13.3208 | 0.429479 | ||||||||
\(963\) | 4.86420 | 0.156747 | ||||||||
\(964\) | −2.92020 | −0.0940532 | ||||||||
\(965\) | 2.87706 | 0.0926158 | ||||||||
\(966\) | 17.6019 | 0.566330 | ||||||||
\(967\) | 5.97558 | 0.192162 | 0.0960808 | − | 0.995374i | \(-0.469369\pi\) | ||||
0.0960808 | + | 0.995374i | \(0.469369\pi\) | |||||||
\(968\) | −70.0787 | −2.25242 | ||||||||
\(969\) | −0.0845157 | −0.00271504 | ||||||||
\(970\) | −33.6678 | −1.08101 | ||||||||
\(971\) | −38.4435 | −1.23371 | −0.616855 | − | 0.787076i | \(-0.711594\pi\) | ||||
−0.616855 | + | 0.787076i | \(0.711594\pi\) | |||||||
\(972\) | 37.6425 | 1.20738 | ||||||||
\(973\) | −4.87271 | −0.156212 | ||||||||
\(974\) | −18.5103 | −0.593107 | ||||||||
\(975\) | −0.717862 | −0.0229900 | ||||||||
\(976\) | 18.1015 | 0.579415 | ||||||||
\(977\) | 24.4448 | 0.782057 | 0.391029 | − | 0.920379i | \(-0.372119\pi\) | ||||
0.391029 | + | 0.920379i | \(0.372119\pi\) | |||||||
\(978\) | 4.29271 | 0.137266 | ||||||||
\(979\) | 2.64741 | 0.0846117 | ||||||||
\(980\) | −2.80804 | −0.0896995 | ||||||||
\(981\) | 21.7806 | 0.695402 | ||||||||
\(982\) | 9.60151 | 0.306396 | ||||||||
\(983\) | −52.1539 | −1.66345 | −0.831725 | − | 0.555188i | \(-0.812646\pi\) | ||||
−0.831725 | + | 0.555188i | \(0.812646\pi\) | |||||||
\(984\) | 15.3285 | 0.488654 | ||||||||
\(985\) | −59.0529 | −1.88158 | ||||||||
\(986\) | 0.577179 | 0.0183811 | ||||||||
\(987\) | −7.93312 | −0.252514 | ||||||||
\(988\) | 202.795 | 6.45177 | ||||||||
\(989\) | 25.1160 | 0.798642 | ||||||||
\(990\) | −76.9879 | −2.44683 | ||||||||
\(991\) | 17.7836 | 0.564915 | 0.282458 | − | 0.959280i | \(-0.408850\pi\) | ||||
0.282458 | + | 0.959280i | \(0.408850\pi\) | |||||||
\(992\) | 3.42500 | 0.108744 | ||||||||
\(993\) | −2.63658 | −0.0836694 | ||||||||
\(994\) | −73.5143 | −2.33173 | ||||||||
\(995\) | −22.6468 | −0.717953 | ||||||||
\(996\) | 14.4504 | 0.457879 | ||||||||
\(997\) | −41.2168 | −1.30535 | −0.652674 | − | 0.757639i | \(-0.726353\pi\) | ||||
−0.652674 | + | 0.757639i | \(0.726353\pi\) | |||||||
\(998\) | −23.7439 | −0.751601 | ||||||||
\(999\) | 1.87175 | 0.0592195 |
(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 | 6037.2.a.b.1.17 | ✓ | 259 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.b.1.17 | ✓ | 259 | 1.1 | even | 1 | trivial |