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: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.48 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.79853 | 1.27175 | 0.635876 | − | 0.771791i | \(-0.280639\pi\) | ||||
0.635876 | + | 0.771791i | \(0.280639\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.23470 | 0.617352 | ||||||||
\(5\) | 4.43407 | 1.98298 | 0.991488 | − | 0.130202i | \(-0.0415625\pi\) | ||||
0.991488 | + | 0.130202i | \(0.0415625\pi\) | |||||||
\(6\) | −1.79853 | −0.734246 | ||||||||
\(7\) | −4.49904 | −1.70048 | −0.850239 | − | 0.526397i | \(-0.823543\pi\) | ||||
−0.850239 | + | 0.526397i | \(0.823543\pi\) | |||||||
\(8\) | −1.37641 | −0.486633 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 7.97480 | 2.52185 | ||||||||
\(11\) | −4.62856 | −1.39556 | −0.697782 | − | 0.716310i | \(-0.745830\pi\) | ||||
−0.697782 | + | 0.716310i | \(0.745830\pi\) | |||||||
\(12\) | −1.23470 | −0.356428 | ||||||||
\(13\) | −2.91661 | −0.808923 | −0.404462 | − | 0.914555i | \(-0.632541\pi\) | ||||
−0.404462 | + | 0.914555i | \(0.632541\pi\) | |||||||
\(14\) | −8.09166 | −2.16259 | ||||||||
\(15\) | −4.43407 | −1.14487 | ||||||||
\(16\) | −4.94491 | −1.23623 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 1.79853 | 0.423917 | ||||||||
\(19\) | −0.480190 | −0.110163 | −0.0550816 | − | 0.998482i | \(-0.517542\pi\) | ||||
−0.0550816 | + | 0.998482i | \(0.517542\pi\) | |||||||
\(20\) | 5.47476 | 1.22419 | ||||||||
\(21\) | 4.49904 | 0.981772 | ||||||||
\(22\) | −8.32460 | −1.77481 | ||||||||
\(23\) | 3.05235 | 0.636460 | 0.318230 | − | 0.948014i | \(-0.396912\pi\) | ||||
0.318230 | + | 0.948014i | \(0.396912\pi\) | |||||||
\(24\) | 1.37641 | 0.280958 | ||||||||
\(25\) | 14.6610 | 2.93219 | ||||||||
\(26\) | −5.24561 | −1.02875 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −5.55499 | −1.04979 | ||||||||
\(29\) | 9.94458 | 1.84666 | 0.923332 | − | 0.384004i | \(-0.125455\pi\) | ||||
0.923332 | + | 0.384004i | \(0.125455\pi\) | |||||||
\(30\) | −7.97480 | −1.45599 | ||||||||
\(31\) | 3.58031 | 0.643043 | 0.321521 | − | 0.946902i | \(-0.395806\pi\) | ||||
0.321521 | + | 0.946902i | \(0.395806\pi\) | |||||||
\(32\) | −6.14076 | −1.08554 | ||||||||
\(33\) | 4.62856 | 0.805729 | ||||||||
\(34\) | 1.79853 | 0.308445 | ||||||||
\(35\) | −19.9491 | −3.37201 | ||||||||
\(36\) | 1.23470 | 0.205784 | ||||||||
\(37\) | −4.58724 | −0.754137 | −0.377069 | − | 0.926185i | \(-0.623068\pi\) | ||||
−0.377069 | + | 0.926185i | \(0.623068\pi\) | |||||||
\(38\) | −0.863636 | −0.140100 | ||||||||
\(39\) | 2.91661 | 0.467032 | ||||||||
\(40\) | −6.10308 | −0.964981 | ||||||||
\(41\) | 5.50600 | 0.859892 | 0.429946 | − | 0.902855i | \(-0.358533\pi\) | ||||
0.429946 | + | 0.902855i | \(0.358533\pi\) | |||||||
\(42\) | 8.09166 | 1.24857 | ||||||||
\(43\) | 6.63207 | 1.01138 | 0.505691 | − | 0.862715i | \(-0.331238\pi\) | ||||
0.505691 | + | 0.862715i | \(0.331238\pi\) | |||||||
\(44\) | −5.71491 | −0.861555 | ||||||||
\(45\) | 4.43407 | 0.660992 | ||||||||
\(46\) | 5.48974 | 0.809419 | ||||||||
\(47\) | −5.29067 | −0.771724 | −0.385862 | − | 0.922556i | \(-0.626096\pi\) | ||||
−0.385862 | + | 0.922556i | \(0.626096\pi\) | |||||||
\(48\) | 4.94491 | 0.713737 | ||||||||
\(49\) | 13.2414 | 1.89163 | ||||||||
\(50\) | 26.3681 | 3.72902 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −3.60116 | −0.499391 | ||||||||
\(53\) | 7.85674 | 1.07921 | 0.539603 | − | 0.841920i | \(-0.318574\pi\) | ||||
0.539603 | + | 0.841920i | \(0.318574\pi\) | |||||||
\(54\) | −1.79853 | −0.244749 | ||||||||
\(55\) | −20.5234 | −2.76737 | ||||||||
\(56\) | 6.19251 | 0.827509 | ||||||||
\(57\) | 0.480190 | 0.0636028 | ||||||||
\(58\) | 17.8856 | 2.34850 | ||||||||
\(59\) | −11.4881 | −1.49563 | −0.747814 | − | 0.663908i | \(-0.768897\pi\) | ||||
−0.747814 | + | 0.663908i | \(0.768897\pi\) | |||||||
\(60\) | −5.47476 | −0.706789 | ||||||||
\(61\) | −15.0640 | −1.92875 | −0.964376 | − | 0.264536i | \(-0.914781\pi\) | ||||
−0.964376 | + | 0.264536i | \(0.914781\pi\) | |||||||
\(62\) | 6.43929 | 0.817791 | ||||||||
\(63\) | −4.49904 | −0.566826 | ||||||||
\(64\) | −1.15450 | −0.144312 | ||||||||
\(65\) | −12.9325 | −1.60407 | ||||||||
\(66\) | 8.32460 | 1.02469 | ||||||||
\(67\) | 5.55181 | 0.678262 | 0.339131 | − | 0.940739i | \(-0.389867\pi\) | ||||
0.339131 | + | 0.940739i | \(0.389867\pi\) | |||||||
\(68\) | 1.23470 | 0.149730 | ||||||||
\(69\) | −3.05235 | −0.367460 | ||||||||
\(70\) | −35.8789 | −4.28835 | ||||||||
\(71\) | 7.98950 | 0.948179 | 0.474089 | − | 0.880477i | \(-0.342777\pi\) | ||||
0.474089 | + | 0.880477i | \(0.342777\pi\) | |||||||
\(72\) | −1.37641 | −0.162211 | ||||||||
\(73\) | 2.71710 | 0.318012 | 0.159006 | − | 0.987278i | \(-0.449171\pi\) | ||||
0.159006 | + | 0.987278i | \(0.449171\pi\) | |||||||
\(74\) | −8.25028 | −0.959075 | ||||||||
\(75\) | −14.6610 | −1.69290 | ||||||||
\(76\) | −0.592893 | −0.0680095 | ||||||||
\(77\) | 20.8241 | 2.37313 | ||||||||
\(78\) | 5.24561 | 0.593949 | ||||||||
\(79\) | 13.5994 | 1.53005 | 0.765023 | − | 0.644002i | \(-0.222727\pi\) | ||||
0.765023 | + | 0.644002i | \(0.222727\pi\) | |||||||
\(80\) | −21.9261 | −2.45141 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.90269 | 1.09357 | ||||||||
\(83\) | 4.67665 | 0.513329 | 0.256665 | − | 0.966501i | \(-0.417376\pi\) | ||||
0.256665 | + | 0.966501i | \(0.417376\pi\) | |||||||
\(84\) | 5.55499 | 0.606099 | ||||||||
\(85\) | 4.43407 | 0.480942 | ||||||||
\(86\) | 11.9280 | 1.28623 | ||||||||
\(87\) | −9.94458 | −1.06617 | ||||||||
\(88\) | 6.37078 | 0.679128 | ||||||||
\(89\) | −9.95473 | −1.05520 | −0.527600 | − | 0.849493i | \(-0.676908\pi\) | ||||
−0.527600 | + | 0.849493i | \(0.676908\pi\) | |||||||
\(90\) | 7.97480 | 0.840617 | ||||||||
\(91\) | 13.1220 | 1.37556 | ||||||||
\(92\) | 3.76875 | 0.392920 | ||||||||
\(93\) | −3.58031 | −0.371261 | ||||||||
\(94\) | −9.51543 | −0.981441 | ||||||||
\(95\) | −2.12920 | −0.218451 | ||||||||
\(96\) | 6.14076 | 0.626738 | ||||||||
\(97\) | 14.9666 | 1.51963 | 0.759816 | − | 0.650138i | \(-0.225289\pi\) | ||||
0.759816 | + | 0.650138i | \(0.225289\pi\) | |||||||
\(98\) | 23.8150 | 2.40568 | ||||||||
\(99\) | −4.62856 | −0.465188 | ||||||||
\(100\) | 18.1019 | 1.81019 | ||||||||
\(101\) | 9.97039 | 0.992090 | 0.496045 | − | 0.868297i | \(-0.334785\pi\) | ||||
0.496045 | + | 0.868297i | \(0.334785\pi\) | |||||||
\(102\) | −1.79853 | −0.178081 | ||||||||
\(103\) | 4.71678 | 0.464758 | 0.232379 | − | 0.972625i | \(-0.425349\pi\) | ||||
0.232379 | + | 0.972625i | \(0.425349\pi\) | |||||||
\(104\) | 4.01445 | 0.393649 | ||||||||
\(105\) | 19.9491 | 1.94683 | ||||||||
\(106\) | 14.1306 | 1.37248 | ||||||||
\(107\) | 17.4959 | 1.69140 | 0.845698 | − | 0.533661i | \(-0.179184\pi\) | ||||
0.845698 | + | 0.533661i | \(0.179184\pi\) | |||||||
\(108\) | −1.23470 | −0.118809 | ||||||||
\(109\) | 9.60614 | 0.920102 | 0.460051 | − | 0.887893i | \(-0.347831\pi\) | ||||
0.460051 | + | 0.887893i | \(0.347831\pi\) | |||||||
\(110\) | −36.9118 | −3.51941 | ||||||||
\(111\) | 4.58724 | 0.435401 | ||||||||
\(112\) | 22.2474 | 2.10218 | ||||||||
\(113\) | 7.49558 | 0.705125 | 0.352562 | − | 0.935788i | \(-0.385310\pi\) | ||||
0.352562 | + | 0.935788i | \(0.385310\pi\) | |||||||
\(114\) | 0.863636 | 0.0808869 | ||||||||
\(115\) | 13.5343 | 1.26208 | ||||||||
\(116\) | 12.2786 | 1.14004 | ||||||||
\(117\) | −2.91661 | −0.269641 | ||||||||
\(118\) | −20.6617 | −1.90207 | ||||||||
\(119\) | −4.49904 | −0.412427 | ||||||||
\(120\) | 6.10308 | 0.557132 | ||||||||
\(121\) | 10.4236 | 0.947599 | ||||||||
\(122\) | −27.0931 | −2.45289 | ||||||||
\(123\) | −5.50600 | −0.496459 | ||||||||
\(124\) | 4.42063 | 0.396984 | ||||||||
\(125\) | 42.8373 | 3.83148 | ||||||||
\(126\) | −8.09166 | −0.720862 | ||||||||
\(127\) | 0.893378 | 0.0792745 | 0.0396372 | − | 0.999214i | \(-0.487380\pi\) | ||||
0.0396372 | + | 0.999214i | \(0.487380\pi\) | |||||||
\(128\) | 10.2051 | 0.902013 | ||||||||
\(129\) | −6.63207 | −0.583921 | ||||||||
\(130\) | −23.2594 | −2.03998 | ||||||||
\(131\) | −7.91024 | −0.691121 | −0.345560 | − | 0.938397i | \(-0.612311\pi\) | ||||
−0.345560 | + | 0.938397i | \(0.612311\pi\) | |||||||
\(132\) | 5.71491 | 0.497419 | ||||||||
\(133\) | 2.16040 | 0.187330 | ||||||||
\(134\) | 9.98509 | 0.862581 | ||||||||
\(135\) | −4.43407 | −0.381624 | ||||||||
\(136\) | −1.37641 | −0.118026 | ||||||||
\(137\) | 7.49347 | 0.640210 | 0.320105 | − | 0.947382i | \(-0.396282\pi\) | ||||
0.320105 | + | 0.947382i | \(0.396282\pi\) | |||||||
\(138\) | −5.48974 | −0.467318 | ||||||||
\(139\) | −14.4874 | −1.22881 | −0.614404 | − | 0.788991i | \(-0.710604\pi\) | ||||
−0.614404 | + | 0.788991i | \(0.710604\pi\) | |||||||
\(140\) | −24.6312 | −2.08172 | ||||||||
\(141\) | 5.29067 | 0.445555 | ||||||||
\(142\) | 14.3693 | 1.20585 | ||||||||
\(143\) | 13.4997 | 1.12890 | ||||||||
\(144\) | −4.94491 | −0.412076 | ||||||||
\(145\) | 44.0950 | 3.66189 | ||||||||
\(146\) | 4.88677 | 0.404432 | ||||||||
\(147\) | −13.2414 | −1.09213 | ||||||||
\(148\) | −5.66388 | −0.465568 | ||||||||
\(149\) | −14.9281 | −1.22295 | −0.611477 | − | 0.791262i | \(-0.709424\pi\) | ||||
−0.611477 | + | 0.791262i | \(0.709424\pi\) | |||||||
\(150\) | −26.3681 | −2.15295 | ||||||||
\(151\) | 21.4229 | 1.74337 | 0.871687 | − | 0.490064i | \(-0.163027\pi\) | ||||
0.871687 | + | 0.490064i | \(0.163027\pi\) | |||||||
\(152\) | 0.660937 | 0.0536091 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 37.4527 | 3.01803 | ||||||||
\(155\) | 15.8753 | 1.27514 | ||||||||
\(156\) | 3.60116 | 0.288323 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 24.4588 | 1.94584 | ||||||||
\(159\) | −7.85674 | −0.623080 | ||||||||
\(160\) | −27.2285 | −2.15260 | ||||||||
\(161\) | −13.7327 | −1.08229 | ||||||||
\(162\) | 1.79853 | 0.141306 | ||||||||
\(163\) | −19.7354 | −1.54579 | −0.772897 | − | 0.634531i | \(-0.781193\pi\) | ||||
−0.772897 | + | 0.634531i | \(0.781193\pi\) | |||||||
\(164\) | 6.79828 | 0.530856 | ||||||||
\(165\) | 20.5234 | 1.59774 | ||||||||
\(166\) | 8.41109 | 0.652827 | ||||||||
\(167\) | 5.51825 | 0.427015 | 0.213508 | − | 0.976941i | \(-0.431511\pi\) | ||||
0.213508 | + | 0.976941i | \(0.431511\pi\) | |||||||
\(168\) | −6.19251 | −0.477762 | ||||||||
\(169\) | −4.49336 | −0.345643 | ||||||||
\(170\) | 7.97480 | 0.611639 | ||||||||
\(171\) | −0.480190 | −0.0367211 | ||||||||
\(172\) | 8.18864 | 0.624378 | ||||||||
\(173\) | −19.2886 | −1.46648 | −0.733241 | − | 0.679969i | \(-0.761993\pi\) | ||||
−0.733241 | + | 0.679969i | \(0.761993\pi\) | |||||||
\(174\) | −17.8856 | −1.35591 | ||||||||
\(175\) | −65.9602 | −4.98613 | ||||||||
\(176\) | 22.8878 | 1.72524 | ||||||||
\(177\) | 11.4881 | 0.863501 | ||||||||
\(178\) | −17.9039 | −1.34195 | ||||||||
\(179\) | 11.0243 | 0.823993 | 0.411997 | − | 0.911185i | \(-0.364832\pi\) | ||||
0.411997 | + | 0.911185i | \(0.364832\pi\) | |||||||
\(180\) | 5.47476 | 0.408065 | ||||||||
\(181\) | −12.2257 | −0.908727 | −0.454363 | − | 0.890816i | \(-0.650133\pi\) | ||||
−0.454363 | + | 0.890816i | \(0.650133\pi\) | |||||||
\(182\) | 23.6002 | 1.74937 | ||||||||
\(183\) | 15.0640 | 1.11357 | ||||||||
\(184\) | −4.20128 | −0.309722 | ||||||||
\(185\) | −20.3401 | −1.49543 | ||||||||
\(186\) | −6.43929 | −0.472152 | ||||||||
\(187\) | −4.62856 | −0.338474 | ||||||||
\(188\) | −6.53242 | −0.476426 | ||||||||
\(189\) | 4.49904 | 0.327257 | ||||||||
\(190\) | −3.82942 | −0.277815 | ||||||||
\(191\) | 18.8444 | 1.36353 | 0.681765 | − | 0.731571i | \(-0.261213\pi\) | ||||
0.681765 | + | 0.731571i | \(0.261213\pi\) | |||||||
\(192\) | 1.15450 | 0.0833186 | ||||||||
\(193\) | −25.5147 | −1.83659 | −0.918295 | − | 0.395897i | \(-0.870434\pi\) | ||||
−0.918295 | + | 0.395897i | \(0.870434\pi\) | |||||||
\(194\) | 26.9179 | 1.93260 | ||||||||
\(195\) | 12.9325 | 0.926113 | ||||||||
\(196\) | 16.3492 | 1.16780 | ||||||||
\(197\) | 5.86540 | 0.417892 | 0.208946 | − | 0.977927i | \(-0.432997\pi\) | ||||
0.208946 | + | 0.977927i | \(0.432997\pi\) | |||||||
\(198\) | −8.32460 | −0.591604 | ||||||||
\(199\) | −19.4004 | −1.37526 | −0.687629 | − | 0.726063i | \(-0.741348\pi\) | ||||
−0.687629 | + | 0.726063i | \(0.741348\pi\) | |||||||
\(200\) | −20.1794 | −1.42690 | ||||||||
\(201\) | −5.55181 | −0.391595 | ||||||||
\(202\) | 17.9320 | 1.26169 | ||||||||
\(203\) | −44.7411 | −3.14021 | ||||||||
\(204\) | −1.23470 | −0.0864466 | ||||||||
\(205\) | 24.4140 | 1.70514 | ||||||||
\(206\) | 8.48327 | 0.591057 | ||||||||
\(207\) | 3.05235 | 0.212153 | ||||||||
\(208\) | 14.4224 | 1.00001 | ||||||||
\(209\) | 2.22259 | 0.153740 | ||||||||
\(210\) | 35.8789 | 2.47588 | ||||||||
\(211\) | 12.5811 | 0.866121 | 0.433061 | − | 0.901365i | \(-0.357434\pi\) | ||||
0.433061 | + | 0.901365i | \(0.357434\pi\) | |||||||
\(212\) | 9.70075 | 0.666250 | ||||||||
\(213\) | −7.98950 | −0.547431 | ||||||||
\(214\) | 31.4670 | 2.15104 | ||||||||
\(215\) | 29.4070 | 2.00554 | ||||||||
\(216\) | 1.37641 | 0.0936526 | ||||||||
\(217\) | −16.1080 | −1.09348 | ||||||||
\(218\) | 17.2769 | 1.17014 | ||||||||
\(219\) | −2.71710 | −0.183604 | ||||||||
\(220\) | −25.3403 | −1.70844 | ||||||||
\(221\) | −2.91661 | −0.196193 | ||||||||
\(222\) | 8.25028 | 0.553722 | ||||||||
\(223\) | −21.5299 | −1.44175 | −0.720875 | − | 0.693065i | \(-0.756260\pi\) | ||||
−0.720875 | + | 0.693065i | \(0.756260\pi\) | |||||||
\(224\) | 27.6275 | 1.84594 | ||||||||
\(225\) | 14.6610 | 0.977397 | ||||||||
\(226\) | 13.4810 | 0.896743 | ||||||||
\(227\) | −12.9210 | −0.857596 | −0.428798 | − | 0.903401i | \(-0.641063\pi\) | ||||
−0.428798 | + | 0.903401i | \(0.641063\pi\) | |||||||
\(228\) | 0.592893 | 0.0392653 | ||||||||
\(229\) | 19.0280 | 1.25741 | 0.628703 | − | 0.777645i | \(-0.283586\pi\) | ||||
0.628703 | + | 0.777645i | \(0.283586\pi\) | |||||||
\(230\) | 24.3419 | 1.60506 | ||||||||
\(231\) | −20.8241 | −1.37013 | ||||||||
\(232\) | −13.6878 | −0.898647 | ||||||||
\(233\) | 18.8820 | 1.23700 | 0.618501 | − | 0.785784i | \(-0.287740\pi\) | ||||
0.618501 | + | 0.785784i | \(0.287740\pi\) | |||||||
\(234\) | −5.24561 | −0.342917 | ||||||||
\(235\) | −23.4592 | −1.53031 | ||||||||
\(236\) | −14.1845 | −0.923329 | ||||||||
\(237\) | −13.5994 | −0.883373 | ||||||||
\(238\) | −8.09166 | −0.524504 | ||||||||
\(239\) | −16.2674 | −1.05225 | −0.526126 | − | 0.850407i | \(-0.676356\pi\) | ||||
−0.526126 | + | 0.850407i | \(0.676356\pi\) | |||||||
\(240\) | 21.9261 | 1.41532 | ||||||||
\(241\) | 4.33551 | 0.279274 | 0.139637 | − | 0.990203i | \(-0.455406\pi\) | ||||
0.139637 | + | 0.990203i | \(0.455406\pi\) | |||||||
\(242\) | 18.7471 | 1.20511 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −18.5996 | −1.19072 | ||||||||
\(245\) | 58.7132 | 3.75105 | ||||||||
\(246\) | −9.90269 | −0.631373 | ||||||||
\(247\) | 1.40053 | 0.0891136 | ||||||||
\(248\) | −4.92796 | −0.312926 | ||||||||
\(249\) | −4.67665 | −0.296371 | ||||||||
\(250\) | 77.0441 | 4.87270 | ||||||||
\(251\) | 6.99084 | 0.441258 | 0.220629 | − | 0.975358i | \(-0.429189\pi\) | ||||
0.220629 | + | 0.975358i | \(0.429189\pi\) | |||||||
\(252\) | −5.55499 | −0.349931 | ||||||||
\(253\) | −14.1280 | −0.888220 | ||||||||
\(254\) | 1.60677 | 0.100817 | ||||||||
\(255\) | −4.43407 | −0.277672 | ||||||||
\(256\) | 20.6632 | 1.29145 | ||||||||
\(257\) | 18.7213 | 1.16780 | 0.583901 | − | 0.811825i | \(-0.301526\pi\) | ||||
0.583901 | + | 0.811825i | \(0.301526\pi\) | |||||||
\(258\) | −11.9280 | −0.742603 | ||||||||
\(259\) | 20.6382 | 1.28239 | ||||||||
\(260\) | −15.9678 | −0.990279 | ||||||||
\(261\) | 9.94458 | 0.615554 | ||||||||
\(262\) | −14.2268 | −0.878934 | ||||||||
\(263\) | 12.9078 | 0.795928 | 0.397964 | − | 0.917401i | \(-0.369717\pi\) | ||||
0.397964 | + | 0.917401i | \(0.369717\pi\) | |||||||
\(264\) | −6.37078 | −0.392094 | ||||||||
\(265\) | 34.8373 | 2.14004 | ||||||||
\(266\) | 3.88554 | 0.238238 | ||||||||
\(267\) | 9.95473 | 0.609219 | ||||||||
\(268\) | 6.85485 | 0.418726 | ||||||||
\(269\) | 4.68577 | 0.285697 | 0.142848 | − | 0.989745i | \(-0.454374\pi\) | ||||
0.142848 | + | 0.989745i | \(0.454374\pi\) | |||||||
\(270\) | −7.97480 | −0.485331 | ||||||||
\(271\) | −3.35006 | −0.203502 | −0.101751 | − | 0.994810i | \(-0.532444\pi\) | ||||
−0.101751 | + | 0.994810i | \(0.532444\pi\) | |||||||
\(272\) | −4.94491 | −0.299829 | ||||||||
\(273\) | −13.1220 | −0.794178 | ||||||||
\(274\) | 13.4772 | 0.814189 | ||||||||
\(275\) | −67.8591 | −4.09206 | ||||||||
\(276\) | −3.76875 | −0.226852 | ||||||||
\(277\) | 28.3758 | 1.70494 | 0.852469 | − | 0.522778i | \(-0.175104\pi\) | ||||
0.852469 | + | 0.522778i | \(0.175104\pi\) | |||||||
\(278\) | −26.0561 | −1.56274 | ||||||||
\(279\) | 3.58031 | 0.214348 | ||||||||
\(280\) | 27.4580 | 1.64093 | ||||||||
\(281\) | −16.2369 | −0.968613 | −0.484307 | − | 0.874898i | \(-0.660928\pi\) | ||||
−0.484307 | + | 0.874898i | \(0.660928\pi\) | |||||||
\(282\) | 9.51543 | 0.566636 | ||||||||
\(283\) | −10.7145 | −0.636909 | −0.318455 | − | 0.947938i | \(-0.603164\pi\) | ||||
−0.318455 | + | 0.947938i | \(0.603164\pi\) | |||||||
\(284\) | 9.86467 | 0.585360 | ||||||||
\(285\) | 2.12920 | 0.126123 | ||||||||
\(286\) | 24.2797 | 1.43569 | ||||||||
\(287\) | −24.7717 | −1.46223 | ||||||||
\(288\) | −6.14076 | −0.361848 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 79.3060 | 4.65701 | ||||||||
\(291\) | −14.9666 | −0.877360 | ||||||||
\(292\) | 3.35481 | 0.196325 | ||||||||
\(293\) | −26.3958 | −1.54206 | −0.771028 | − | 0.636801i | \(-0.780257\pi\) | ||||
−0.771028 | + | 0.636801i | \(0.780257\pi\) | |||||||
\(294\) | −23.8150 | −1.38892 | ||||||||
\(295\) | −50.9392 | −2.96579 | ||||||||
\(296\) | 6.31390 | 0.366988 | ||||||||
\(297\) | 4.62856 | 0.268576 | ||||||||
\(298\) | −26.8485 | −1.55529 | ||||||||
\(299\) | −8.90254 | −0.514847 | ||||||||
\(300\) | −18.1019 | −1.04512 | ||||||||
\(301\) | −29.8380 | −1.71983 | ||||||||
\(302\) | 38.5297 | 2.21714 | ||||||||
\(303\) | −9.97039 | −0.572784 | ||||||||
\(304\) | 2.37450 | 0.136187 | ||||||||
\(305\) | −66.7949 | −3.82467 | ||||||||
\(306\) | 1.79853 | 0.102815 | ||||||||
\(307\) | −19.1507 | −1.09299 | −0.546493 | − | 0.837464i | \(-0.684037\pi\) | ||||
−0.546493 | + | 0.837464i | \(0.684037\pi\) | |||||||
\(308\) | 25.7116 | 1.46505 | ||||||||
\(309\) | −4.71678 | −0.268328 | ||||||||
\(310\) | 28.5522 | 1.62166 | ||||||||
\(311\) | 1.52003 | 0.0861929 | 0.0430965 | − | 0.999071i | \(-0.486278\pi\) | ||||
0.0430965 | + | 0.999071i | \(0.486278\pi\) | |||||||
\(312\) | −4.01445 | −0.227273 | ||||||||
\(313\) | 8.83884 | 0.499601 | 0.249800 | − | 0.968297i | \(-0.419635\pi\) | ||||
0.249800 | + | 0.968297i | \(0.419635\pi\) | |||||||
\(314\) | −1.79853 | −0.101497 | ||||||||
\(315\) | −19.9491 | −1.12400 | ||||||||
\(316\) | 16.7912 | 0.944578 | ||||||||
\(317\) | −0.200835 | −0.0112800 | −0.00564000 | − | 0.999984i | \(-0.501795\pi\) | ||||
−0.00564000 | + | 0.999984i | \(0.501795\pi\) | |||||||
\(318\) | −14.1306 | −0.792403 | ||||||||
\(319\) | −46.0291 | −2.57714 | ||||||||
\(320\) | −5.11912 | −0.286167 | ||||||||
\(321\) | −17.4959 | −0.976528 | ||||||||
\(322\) | −24.6986 | −1.37640 | ||||||||
\(323\) | −0.480190 | −0.0267185 | ||||||||
\(324\) | 1.23470 | 0.0685947 | ||||||||
\(325\) | −42.7603 | −2.37192 | ||||||||
\(326\) | −35.4947 | −1.96587 | ||||||||
\(327\) | −9.60614 | −0.531221 | ||||||||
\(328\) | −7.57849 | −0.418452 | ||||||||
\(329\) | 23.8030 | 1.31230 | ||||||||
\(330\) | 36.9118 | 2.03193 | ||||||||
\(331\) | 17.9318 | 0.985620 | 0.492810 | − | 0.870137i | \(-0.335970\pi\) | ||||
0.492810 | + | 0.870137i | \(0.335970\pi\) | |||||||
\(332\) | 5.77428 | 0.316905 | ||||||||
\(333\) | −4.58724 | −0.251379 | ||||||||
\(334\) | 9.92473 | 0.543057 | ||||||||
\(335\) | 24.6171 | 1.34498 | ||||||||
\(336\) | −22.2474 | −1.21369 | ||||||||
\(337\) | 3.11678 | 0.169782 | 0.0848910 | − | 0.996390i | \(-0.472946\pi\) | ||||
0.0848910 | + | 0.996390i | \(0.472946\pi\) | |||||||
\(338\) | −8.08144 | −0.439572 | ||||||||
\(339\) | −7.49558 | −0.407104 | ||||||||
\(340\) | 5.47476 | 0.296911 | ||||||||
\(341\) | −16.5717 | −0.897408 | ||||||||
\(342\) | −0.863636 | −0.0467001 | ||||||||
\(343\) | −28.0803 | −1.51619 | ||||||||
\(344\) | −9.12842 | −0.492171 | ||||||||
\(345\) | −13.5343 | −0.728664 | ||||||||
\(346\) | −34.6910 | −1.86500 | ||||||||
\(347\) | 17.4388 | 0.936162 | 0.468081 | − | 0.883686i | \(-0.344946\pi\) | ||||
0.468081 | + | 0.883686i | \(0.344946\pi\) | |||||||
\(348\) | −12.2786 | −0.658203 | ||||||||
\(349\) | 1.72202 | 0.0921775 | 0.0460888 | − | 0.998937i | \(-0.485324\pi\) | ||||
0.0460888 | + | 0.998937i | \(0.485324\pi\) | |||||||
\(350\) | −118.631 | −6.34111 | ||||||||
\(351\) | 2.91661 | 0.155677 | ||||||||
\(352\) | 28.4229 | 1.51494 | ||||||||
\(353\) | 34.7628 | 1.85024 | 0.925119 | − | 0.379678i | \(-0.123965\pi\) | ||||
0.925119 | + | 0.379678i | \(0.123965\pi\) | |||||||
\(354\) | 20.6617 | 1.09816 | ||||||||
\(355\) | 35.4260 | 1.88021 | ||||||||
\(356\) | −12.2911 | −0.651429 | ||||||||
\(357\) | 4.49904 | 0.238115 | ||||||||
\(358\) | 19.8275 | 1.04791 | ||||||||
\(359\) | 21.8667 | 1.15408 | 0.577041 | − | 0.816715i | \(-0.304207\pi\) | ||||
0.577041 | + | 0.816715i | \(0.304207\pi\) | |||||||
\(360\) | −6.10308 | −0.321660 | ||||||||
\(361\) | −18.7694 | −0.987864 | ||||||||
\(362\) | −21.9882 | −1.15567 | ||||||||
\(363\) | −10.4236 | −0.547097 | ||||||||
\(364\) | 16.2018 | 0.849203 | ||||||||
\(365\) | 12.0478 | 0.630610 | ||||||||
\(366\) | 27.0931 | 1.41618 | ||||||||
\(367\) | −22.8011 | −1.19021 | −0.595104 | − | 0.803648i | \(-0.702889\pi\) | ||||
−0.595104 | + | 0.803648i | \(0.702889\pi\) | |||||||
\(368\) | −15.0936 | −0.786810 | ||||||||
\(369\) | 5.50600 | 0.286631 | ||||||||
\(370\) | −36.5823 | −1.90182 | ||||||||
\(371\) | −35.3478 | −1.83517 | ||||||||
\(372\) | −4.42063 | −0.229199 | ||||||||
\(373\) | 2.51016 | 0.129971 | 0.0649855 | − | 0.997886i | \(-0.479300\pi\) | ||||
0.0649855 | + | 0.997886i | \(0.479300\pi\) | |||||||
\(374\) | −8.32460 | −0.430455 | ||||||||
\(375\) | −42.8373 | −2.21211 | ||||||||
\(376\) | 7.28212 | 0.375546 | ||||||||
\(377\) | −29.0045 | −1.49381 | ||||||||
\(378\) | 8.09166 | 0.416190 | ||||||||
\(379\) | −27.5901 | −1.41721 | −0.708605 | − | 0.705606i | \(-0.750675\pi\) | ||||
−0.708605 | + | 0.705606i | \(0.750675\pi\) | |||||||
\(380\) | −2.62893 | −0.134861 | ||||||||
\(381\) | −0.893378 | −0.0457691 | ||||||||
\(382\) | 33.8921 | 1.73407 | ||||||||
\(383\) | 26.7908 | 1.36894 | 0.684472 | − | 0.729039i | \(-0.260033\pi\) | ||||
0.684472 | + | 0.729039i | \(0.260033\pi\) | |||||||
\(384\) | −10.2051 | −0.520778 | ||||||||
\(385\) | 92.3355 | 4.70585 | ||||||||
\(386\) | −45.8890 | −2.33569 | ||||||||
\(387\) | 6.63207 | 0.337127 | ||||||||
\(388\) | 18.4794 | 0.938149 | ||||||||
\(389\) | 15.6700 | 0.794501 | 0.397251 | − | 0.917710i | \(-0.369964\pi\) | ||||
0.397251 | + | 0.917710i | \(0.369964\pi\) | |||||||
\(390\) | 23.2594 | 1.17779 | ||||||||
\(391\) | 3.05235 | 0.154364 | ||||||||
\(392\) | −18.2255 | −0.920528 | ||||||||
\(393\) | 7.91024 | 0.399019 | ||||||||
\(394\) | 10.5491 | 0.531455 | ||||||||
\(395\) | 60.3005 | 3.03404 | ||||||||
\(396\) | −5.71491 | −0.287185 | ||||||||
\(397\) | −1.79232 | −0.0899539 | −0.0449769 | − | 0.998988i | \(-0.514321\pi\) | ||||
−0.0449769 | + | 0.998988i | \(0.514321\pi\) | |||||||
\(398\) | −34.8921 | −1.74899 | ||||||||
\(399\) | −2.16040 | −0.108155 | ||||||||
\(400\) | −72.4971 | −3.62486 | ||||||||
\(401\) | 22.9717 | 1.14715 | 0.573577 | − | 0.819152i | \(-0.305555\pi\) | ||||
0.573577 | + | 0.819152i | \(0.305555\pi\) | |||||||
\(402\) | −9.98509 | −0.498011 | ||||||||
\(403\) | −10.4424 | −0.520172 | ||||||||
\(404\) | 12.3105 | 0.612469 | ||||||||
\(405\) | 4.43407 | 0.220331 | ||||||||
\(406\) | −80.4682 | −3.99357 | ||||||||
\(407\) | 21.2323 | 1.05245 | ||||||||
\(408\) | 1.37641 | 0.0681422 | ||||||||
\(409\) | −21.0186 | −1.03930 | −0.519650 | − | 0.854379i | \(-0.673938\pi\) | ||||
−0.519650 | + | 0.854379i | \(0.673938\pi\) | |||||||
\(410\) | 43.9092 | 2.16852 | ||||||||
\(411\) | −7.49347 | −0.369626 | ||||||||
\(412\) | 5.82383 | 0.286920 | ||||||||
\(413\) | 51.6856 | 2.54328 | ||||||||
\(414\) | 5.48974 | 0.269806 | ||||||||
\(415\) | 20.7366 | 1.01792 | ||||||||
\(416\) | 17.9102 | 0.878121 | ||||||||
\(417\) | 14.4874 | 0.709453 | ||||||||
\(418\) | 3.99739 | 0.195519 | ||||||||
\(419\) | −11.4970 | −0.561667 | −0.280833 | − | 0.959757i | \(-0.590611\pi\) | ||||
−0.280833 | + | 0.959757i | \(0.590611\pi\) | |||||||
\(420\) | 24.6312 | 1.20188 | ||||||||
\(421\) | −7.29663 | −0.355616 | −0.177808 | − | 0.984065i | \(-0.556901\pi\) | ||||
−0.177808 | + | 0.984065i | \(0.556901\pi\) | |||||||
\(422\) | 22.6275 | 1.10149 | ||||||||
\(423\) | −5.29067 | −0.257241 | ||||||||
\(424\) | −10.8141 | −0.525177 | ||||||||
\(425\) | 14.6610 | 0.711161 | ||||||||
\(426\) | −14.3693 | −0.696197 | ||||||||
\(427\) | 67.7737 | 3.27980 | ||||||||
\(428\) | 21.6023 | 1.04419 | ||||||||
\(429\) | −13.4997 | −0.651773 | ||||||||
\(430\) | 52.8894 | 2.55055 | ||||||||
\(431\) | 18.1705 | 0.875244 | 0.437622 | − | 0.899159i | \(-0.355821\pi\) | ||||
0.437622 | + | 0.899159i | \(0.355821\pi\) | |||||||
\(432\) | 4.94491 | 0.237912 | ||||||||
\(433\) | 40.7831 | 1.95991 | 0.979956 | − | 0.199215i | \(-0.0638393\pi\) | ||||
0.979956 | + | 0.199215i | \(0.0638393\pi\) | |||||||
\(434\) | −28.9706 | −1.39064 | ||||||||
\(435\) | −44.0950 | −2.11419 | ||||||||
\(436\) | 11.8607 | 0.568027 | ||||||||
\(437\) | −1.46571 | −0.0701145 | ||||||||
\(438\) | −4.88677 | −0.233499 | ||||||||
\(439\) | 5.50731 | 0.262850 | 0.131425 | − | 0.991326i | \(-0.458045\pi\) | ||||
0.131425 | + | 0.991326i | \(0.458045\pi\) | |||||||
\(440\) | 28.2485 | 1.34669 | ||||||||
\(441\) | 13.2414 | 0.630542 | ||||||||
\(442\) | −5.24561 | −0.249508 | ||||||||
\(443\) | 5.92484 | 0.281498 | 0.140749 | − | 0.990045i | \(-0.455049\pi\) | ||||
0.140749 | + | 0.990045i | \(0.455049\pi\) | |||||||
\(444\) | 5.66388 | 0.268796 | ||||||||
\(445\) | −44.1399 | −2.09243 | ||||||||
\(446\) | −38.7222 | −1.83355 | ||||||||
\(447\) | 14.9281 | 0.706073 | ||||||||
\(448\) | 5.19413 | 0.245400 | ||||||||
\(449\) | 28.6750 | 1.35326 | 0.676629 | − | 0.736324i | \(-0.263440\pi\) | ||||
0.676629 | + | 0.736324i | \(0.263440\pi\) | |||||||
\(450\) | 26.3681 | 1.24301 | ||||||||
\(451\) | −25.4849 | −1.20003 | ||||||||
\(452\) | 9.25482 | 0.435310 | ||||||||
\(453\) | −21.4229 | −1.00654 | ||||||||
\(454\) | −23.2387 | −1.09065 | ||||||||
\(455\) | 58.1837 | 2.72769 | ||||||||
\(456\) | −0.660937 | −0.0309512 | ||||||||
\(457\) | −8.43914 | −0.394766 | −0.197383 | − | 0.980326i | \(-0.563244\pi\) | ||||
−0.197383 | + | 0.980326i | \(0.563244\pi\) | |||||||
\(458\) | 34.2224 | 1.59911 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 16.7109 | 0.779150 | ||||||||
\(461\) | −22.5120 | −1.04849 | −0.524244 | − | 0.851568i | \(-0.675652\pi\) | ||||
−0.524244 | + | 0.851568i | \(0.675652\pi\) | |||||||
\(462\) | −37.4527 | −1.74246 | ||||||||
\(463\) | 2.83629 | 0.131814 | 0.0659068 | − | 0.997826i | \(-0.479006\pi\) | ||||
0.0659068 | + | 0.997826i | \(0.479006\pi\) | |||||||
\(464\) | −49.1751 | −2.28290 | ||||||||
\(465\) | −15.8753 | −0.736201 | ||||||||
\(466\) | 33.9599 | 1.57316 | ||||||||
\(467\) | −8.53724 | −0.395056 | −0.197528 | − | 0.980297i | \(-0.563291\pi\) | ||||
−0.197528 | + | 0.980297i | \(0.563291\pi\) | |||||||
\(468\) | −3.60116 | −0.166464 | ||||||||
\(469\) | −24.9778 | −1.15337 | ||||||||
\(470\) | −42.1920 | −1.94617 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 15.8123 | 0.727822 | ||||||||
\(473\) | −30.6969 | −1.41145 | ||||||||
\(474\) | −24.4588 | −1.12343 | ||||||||
\(475\) | −7.04005 | −0.323020 | ||||||||
\(476\) | −5.55499 | −0.254612 | ||||||||
\(477\) | 7.85674 | 0.359735 | ||||||||
\(478\) | −29.2574 | −1.33820 | ||||||||
\(479\) | 10.4534 | 0.477630 | 0.238815 | − | 0.971065i | \(-0.423241\pi\) | ||||
0.238815 | + | 0.971065i | \(0.423241\pi\) | |||||||
\(480\) | 27.2285 | 1.24281 | ||||||||
\(481\) | 13.3792 | 0.610039 | ||||||||
\(482\) | 7.79753 | 0.355168 | ||||||||
\(483\) | 13.7327 | 0.624858 | ||||||||
\(484\) | 12.8701 | 0.585002 | ||||||||
\(485\) | 66.3631 | 3.01339 | ||||||||
\(486\) | −1.79853 | −0.0815829 | ||||||||
\(487\) | −18.6985 | −0.847311 | −0.423656 | − | 0.905823i | \(-0.639253\pi\) | ||||
−0.423656 | + | 0.905823i | \(0.639253\pi\) | |||||||
\(488\) | 20.7342 | 0.938594 | ||||||||
\(489\) | 19.7354 | 0.892465 | ||||||||
\(490\) | 105.597 | 4.77040 | ||||||||
\(491\) | −17.6434 | −0.796234 | −0.398117 | − | 0.917335i | \(-0.630336\pi\) | ||||
−0.398117 | + | 0.917335i | \(0.630336\pi\) | |||||||
\(492\) | −6.79828 | −0.306490 | ||||||||
\(493\) | 9.94458 | 0.447882 | ||||||||
\(494\) | 2.51889 | 0.113330 | ||||||||
\(495\) | −20.5234 | −0.922456 | ||||||||
\(496\) | −17.7043 | −0.794948 | ||||||||
\(497\) | −35.9451 | −1.61236 | ||||||||
\(498\) | −8.41109 | −0.376910 | ||||||||
\(499\) | −21.8744 | −0.979232 | −0.489616 | − | 0.871938i | \(-0.662863\pi\) | ||||
−0.489616 | + | 0.871938i | \(0.662863\pi\) | |||||||
\(500\) | 52.8914 | 2.36538 | ||||||||
\(501\) | −5.51825 | −0.246537 | ||||||||
\(502\) | 12.5732 | 0.561171 | ||||||||
\(503\) | 3.90620 | 0.174169 | 0.0870844 | − | 0.996201i | \(-0.472245\pi\) | ||||
0.0870844 | + | 0.996201i | \(0.472245\pi\) | |||||||
\(504\) | 6.19251 | 0.275836 | ||||||||
\(505\) | 44.2094 | 1.96729 | ||||||||
\(506\) | −25.4096 | −1.12960 | ||||||||
\(507\) | 4.49336 | 0.199557 | ||||||||
\(508\) | 1.10306 | 0.0489403 | ||||||||
\(509\) | −10.7392 | −0.476006 | −0.238003 | − | 0.971264i | \(-0.576493\pi\) | ||||
−0.238003 | + | 0.971264i | \(0.576493\pi\) | |||||||
\(510\) | −7.97480 | −0.353130 | ||||||||
\(511\) | −12.2243 | −0.540772 | ||||||||
\(512\) | 16.7531 | 0.740389 | ||||||||
\(513\) | 0.480190 | 0.0212009 | ||||||||
\(514\) | 33.6708 | 1.48515 | ||||||||
\(515\) | 20.9145 | 0.921604 | ||||||||
\(516\) | −8.18864 | −0.360485 | ||||||||
\(517\) | 24.4882 | 1.07699 | ||||||||
\(518\) | 37.1183 | 1.63089 | ||||||||
\(519\) | 19.2886 | 0.846673 | ||||||||
\(520\) | 17.8003 | 0.780596 | ||||||||
\(521\) | 30.2274 | 1.32428 | 0.662142 | − | 0.749378i | \(-0.269647\pi\) | ||||
0.662142 | + | 0.749378i | \(0.269647\pi\) | |||||||
\(522\) | 17.8856 | 0.782832 | ||||||||
\(523\) | −4.06532 | −0.177764 | −0.0888819 | − | 0.996042i | \(-0.528329\pi\) | ||||
−0.0888819 | + | 0.996042i | \(0.528329\pi\) | |||||||
\(524\) | −9.76680 | −0.426665 | ||||||||
\(525\) | 65.9602 | 2.87874 | ||||||||
\(526\) | 23.2150 | 1.01222 | ||||||||
\(527\) | 3.58031 | 0.155961 | ||||||||
\(528\) | −22.8878 | −0.996066 | ||||||||
\(529\) | −13.6831 | −0.594919 | ||||||||
\(530\) | 62.6559 | 2.72160 | ||||||||
\(531\) | −11.4881 | −0.498543 | ||||||||
\(532\) | 2.66745 | 0.115649 | ||||||||
\(533\) | −16.0589 | −0.695587 | ||||||||
\(534\) | 17.9039 | 0.774776 | ||||||||
\(535\) | 77.5782 | 3.35400 | ||||||||
\(536\) | −7.64155 | −0.330065 | ||||||||
\(537\) | −11.0243 | −0.475733 | ||||||||
\(538\) | 8.42749 | 0.363335 | ||||||||
\(539\) | −61.2886 | −2.63989 | ||||||||
\(540\) | −5.47476 | −0.235596 | ||||||||
\(541\) | 28.1350 | 1.20962 | 0.604809 | − | 0.796371i | \(-0.293249\pi\) | ||||
0.604809 | + | 0.796371i | \(0.293249\pi\) | |||||||
\(542\) | −6.02518 | −0.258803 | ||||||||
\(543\) | 12.2257 | 0.524654 | ||||||||
\(544\) | −6.14076 | −0.263283 | ||||||||
\(545\) | 42.5943 | 1.82454 | ||||||||
\(546\) | −23.6002 | −1.01000 | ||||||||
\(547\) | −8.99143 | −0.384446 | −0.192223 | − | 0.981351i | \(-0.561570\pi\) | ||||
−0.192223 | + | 0.981351i | \(0.561570\pi\) | |||||||
\(548\) | 9.25222 | 0.395235 | ||||||||
\(549\) | −15.0640 | −0.642917 | ||||||||
\(550\) | −122.047 | −5.20408 | ||||||||
\(551\) | −4.77529 | −0.203434 | ||||||||
\(552\) | 4.20128 | 0.178818 | ||||||||
\(553\) | −61.1841 | −2.60181 | ||||||||
\(554\) | 51.0347 | 2.16826 | ||||||||
\(555\) | 20.3401 | 0.863390 | ||||||||
\(556\) | −17.8877 | −0.758608 | ||||||||
\(557\) | 3.12893 | 0.132577 | 0.0662886 | − | 0.997800i | \(-0.478884\pi\) | ||||
0.0662886 | + | 0.997800i | \(0.478884\pi\) | |||||||
\(558\) | 6.43929 | 0.272597 | ||||||||
\(559\) | −19.3432 | −0.818130 | ||||||||
\(560\) | 98.6464 | 4.16857 | ||||||||
\(561\) | 4.62856 | 0.195418 | ||||||||
\(562\) | −29.2025 | −1.23184 | ||||||||
\(563\) | 44.6983 | 1.88381 | 0.941905 | − | 0.335881i | \(-0.109034\pi\) | ||||
0.941905 | + | 0.335881i | \(0.109034\pi\) | |||||||
\(564\) | 6.53242 | 0.275064 | ||||||||
\(565\) | 33.2359 | 1.39824 | ||||||||
\(566\) | −19.2703 | −0.809990 | ||||||||
\(567\) | −4.49904 | −0.188942 | ||||||||
\(568\) | −10.9968 | −0.461415 | ||||||||
\(569\) | 8.69913 | 0.364686 | 0.182343 | − | 0.983235i | \(-0.441632\pi\) | ||||
0.182343 | + | 0.983235i | \(0.441632\pi\) | |||||||
\(570\) | 3.82942 | 0.160397 | ||||||||
\(571\) | −7.25869 | −0.303767 | −0.151883 | − | 0.988398i | \(-0.548534\pi\) | ||||
−0.151883 | + | 0.988398i | \(0.548534\pi\) | |||||||
\(572\) | 16.6682 | 0.696932 | ||||||||
\(573\) | −18.8444 | −0.787234 | ||||||||
\(574\) | −44.5526 | −1.85959 | ||||||||
\(575\) | 44.7504 | 1.86622 | ||||||||
\(576\) | −1.15450 | −0.0481040 | ||||||||
\(577\) | 17.7464 | 0.738790 | 0.369395 | − | 0.929272i | \(-0.379565\pi\) | ||||
0.369395 | + | 0.929272i | \(0.379565\pi\) | |||||||
\(578\) | 1.79853 | 0.0748089 | ||||||||
\(579\) | 25.5147 | 1.06036 | ||||||||
\(580\) | 54.4442 | 2.26067 | ||||||||
\(581\) | −21.0405 | −0.872905 | ||||||||
\(582\) | −26.9179 | −1.11578 | ||||||||
\(583\) | −36.3654 | −1.50610 | ||||||||
\(584\) | −3.73983 | −0.154755 | ||||||||
\(585\) | −12.9325 | −0.534692 | ||||||||
\(586\) | −47.4735 | −1.96111 | ||||||||
\(587\) | 21.6272 | 0.892652 | 0.446326 | − | 0.894871i | \(-0.352732\pi\) | ||||
0.446326 | + | 0.894871i | \(0.352732\pi\) | |||||||
\(588\) | −16.3492 | −0.674230 | ||||||||
\(589\) | −1.71923 | −0.0708397 | ||||||||
\(590\) | −91.6155 | −3.77175 | ||||||||
\(591\) | −5.86540 | −0.241270 | ||||||||
\(592\) | 22.6835 | 0.932286 | ||||||||
\(593\) | 32.8863 | 1.35048 | 0.675239 | − | 0.737599i | \(-0.264041\pi\) | ||||
0.675239 | + | 0.737599i | \(0.264041\pi\) | |||||||
\(594\) | 8.32460 | 0.341563 | ||||||||
\(595\) | −19.9491 | −0.817832 | ||||||||
\(596\) | −18.4317 | −0.754993 | ||||||||
\(597\) | 19.4004 | 0.794005 | ||||||||
\(598\) | −16.0115 | −0.654758 | ||||||||
\(599\) | 42.8417 | 1.75046 | 0.875232 | − | 0.483703i | \(-0.160708\pi\) | ||||
0.875232 | + | 0.483703i | \(0.160708\pi\) | |||||||
\(600\) | 20.1794 | 0.823821 | ||||||||
\(601\) | −16.5388 | −0.674630 | −0.337315 | − | 0.941392i | \(-0.609519\pi\) | ||||
−0.337315 | + | 0.941392i | \(0.609519\pi\) | |||||||
\(602\) | −53.6644 | −2.18720 | ||||||||
\(603\) | 5.55181 | 0.226087 | ||||||||
\(604\) | 26.4510 | 1.07628 | ||||||||
\(605\) | 46.2189 | 1.87907 | ||||||||
\(606\) | −17.9320 | −0.728439 | ||||||||
\(607\) | −8.56208 | −0.347524 | −0.173762 | − | 0.984788i | \(-0.555592\pi\) | ||||
−0.173762 | + | 0.984788i | \(0.555592\pi\) | |||||||
\(608\) | 2.94873 | 0.119587 | ||||||||
\(609\) | 44.7411 | 1.81300 | ||||||||
\(610\) | −120.133 | −4.86403 | ||||||||
\(611\) | 15.4309 | 0.624266 | ||||||||
\(612\) | 1.23470 | 0.0499100 | ||||||||
\(613\) | −3.50829 | −0.141698 | −0.0708492 | − | 0.997487i | \(-0.522571\pi\) | ||||
−0.0708492 | + | 0.997487i | \(0.522571\pi\) | |||||||
\(614\) | −34.4430 | −1.39001 | ||||||||
\(615\) | −24.4140 | −0.984466 | ||||||||
\(616\) | −28.6624 | −1.15484 | ||||||||
\(617\) | −0.200006 | −0.00805192 | −0.00402596 | − | 0.999992i | \(-0.501282\pi\) | ||||
−0.00402596 | + | 0.999992i | \(0.501282\pi\) | |||||||
\(618\) | −8.48327 | −0.341247 | ||||||||
\(619\) | −42.9788 | −1.72746 | −0.863731 | − | 0.503953i | \(-0.831879\pi\) | ||||
−0.863731 | + | 0.503953i | \(0.831879\pi\) | |||||||
\(620\) | 19.6014 | 0.787209 | ||||||||
\(621\) | −3.05235 | −0.122487 | ||||||||
\(622\) | 2.73382 | 0.109616 | ||||||||
\(623\) | 44.7868 | 1.79434 | ||||||||
\(624\) | −14.4224 | −0.577358 | ||||||||
\(625\) | 116.639 | 4.66555 | ||||||||
\(626\) | 15.8969 | 0.635368 | ||||||||
\(627\) | −2.22259 | −0.0887618 | ||||||||
\(628\) | −1.23470 | −0.0492701 | ||||||||
\(629\) | −4.58724 | −0.182905 | ||||||||
\(630\) | −35.8789 | −1.42945 | ||||||||
\(631\) | −37.2254 | −1.48192 | −0.740959 | − | 0.671550i | \(-0.765629\pi\) | ||||
−0.740959 | + | 0.671550i | \(0.765629\pi\) | |||||||
\(632\) | −18.7182 | −0.744571 | ||||||||
\(633\) | −12.5811 | −0.500055 | ||||||||
\(634\) | −0.361207 | −0.0143454 | ||||||||
\(635\) | 3.96130 | 0.157199 | ||||||||
\(636\) | −9.70075 | −0.384660 | ||||||||
\(637\) | −38.6200 | −1.53018 | ||||||||
\(638\) | −82.7847 | −3.27748 | ||||||||
\(639\) | 7.98950 | 0.316060 | ||||||||
\(640\) | 45.2502 | 1.78867 | ||||||||
\(641\) | −28.6641 | −1.13216 | −0.566082 | − | 0.824349i | \(-0.691542\pi\) | ||||
−0.566082 | + | 0.824349i | \(0.691542\pi\) | |||||||
\(642\) | −31.4670 | −1.24190 | ||||||||
\(643\) | −5.73294 | −0.226085 | −0.113042 | − | 0.993590i | \(-0.536060\pi\) | ||||
−0.113042 | + | 0.993590i | \(0.536060\pi\) | |||||||
\(644\) | −16.9558 | −0.668152 | ||||||||
\(645\) | −29.4070 | −1.15790 | ||||||||
\(646\) | −0.863636 | −0.0339793 | ||||||||
\(647\) | −1.19976 | −0.0471674 | −0.0235837 | − | 0.999722i | \(-0.507508\pi\) | ||||
−0.0235837 | + | 0.999722i | \(0.507508\pi\) | |||||||
\(648\) | −1.37641 | −0.0540703 | ||||||||
\(649\) | 53.1736 | 2.08724 | ||||||||
\(650\) | −76.9057 | −3.01649 | ||||||||
\(651\) | 16.1080 | 0.631321 | ||||||||
\(652\) | −24.3674 | −0.954300 | ||||||||
\(653\) | −36.5691 | −1.43106 | −0.715529 | − | 0.698583i | \(-0.753814\pi\) | ||||
−0.715529 | + | 0.698583i | \(0.753814\pi\) | |||||||
\(654\) | −17.2769 | −0.675581 | ||||||||
\(655\) | −35.0745 | −1.37047 | ||||||||
\(656\) | −27.2267 | −1.06302 | ||||||||
\(657\) | 2.71710 | 0.106004 | ||||||||
\(658\) | 42.8103 | 1.66892 | ||||||||
\(659\) | 18.2835 | 0.712224 | 0.356112 | − | 0.934443i | \(-0.384102\pi\) | ||||
0.356112 | + | 0.934443i | \(0.384102\pi\) | |||||||
\(660\) | 25.3403 | 0.986369 | ||||||||
\(661\) | −17.6781 | −0.687600 | −0.343800 | − | 0.939043i | \(-0.611714\pi\) | ||||
−0.343800 | + | 0.939043i | \(0.611714\pi\) | |||||||
\(662\) | 32.2508 | 1.25346 | ||||||||
\(663\) | 2.91661 | 0.113272 | ||||||||
\(664\) | −6.43697 | −0.249803 | ||||||||
\(665\) | 9.57935 | 0.371471 | ||||||||
\(666\) | −8.25028 | −0.319692 | ||||||||
\(667\) | 30.3544 | 1.17533 | ||||||||
\(668\) | 6.81341 | 0.263619 | ||||||||
\(669\) | 21.5299 | 0.832395 | ||||||||
\(670\) | 44.2746 | 1.71048 | ||||||||
\(671\) | 69.7248 | 2.69170 | ||||||||
\(672\) | −27.6275 | −1.06575 | ||||||||
\(673\) | −18.0466 | −0.695646 | −0.347823 | − | 0.937560i | \(-0.613079\pi\) | ||||
−0.347823 | + | 0.937560i | \(0.613079\pi\) | |||||||
\(674\) | 5.60562 | 0.215921 | ||||||||
\(675\) | −14.6610 | −0.564300 | ||||||||
\(676\) | −5.54797 | −0.213384 | ||||||||
\(677\) | −39.0457 | −1.50065 | −0.750324 | − | 0.661071i | \(-0.770102\pi\) | ||||
−0.750324 | + | 0.661071i | \(0.770102\pi\) | |||||||
\(678\) | −13.4810 | −0.517735 | ||||||||
\(679\) | −67.3356 | −2.58410 | ||||||||
\(680\) | −6.10308 | −0.234042 | ||||||||
\(681\) | 12.9210 | 0.495133 | ||||||||
\(682\) | −29.8047 | −1.14128 | ||||||||
\(683\) | −18.5600 | −0.710180 | −0.355090 | − | 0.934832i | \(-0.615550\pi\) | ||||
−0.355090 | + | 0.934832i | \(0.615550\pi\) | |||||||
\(684\) | −0.592893 | −0.0226698 | ||||||||
\(685\) | 33.2266 | 1.26952 | ||||||||
\(686\) | −50.5032 | −1.92822 | ||||||||
\(687\) | −19.0280 | −0.725964 | ||||||||
\(688\) | −32.7950 | −1.25030 | ||||||||
\(689\) | −22.9151 | −0.872995 | ||||||||
\(690\) | −24.3419 | −0.926680 | ||||||||
\(691\) | 10.7549 | 0.409137 | 0.204569 | − | 0.978852i | \(-0.434421\pi\) | ||||
0.204569 | + | 0.978852i | \(0.434421\pi\) | |||||||
\(692\) | −23.8157 | −0.905335 | ||||||||
\(693\) | 20.8241 | 0.791042 | ||||||||
\(694\) | 31.3641 | 1.19057 | ||||||||
\(695\) | −64.2383 | −2.43670 | ||||||||
\(696\) | 13.6878 | 0.518834 | ||||||||
\(697\) | 5.50600 | 0.208555 | ||||||||
\(698\) | 3.09710 | 0.117227 | ||||||||
\(699\) | −18.8820 | −0.714184 | ||||||||
\(700\) | −81.4414 | −3.07820 | ||||||||
\(701\) | 0.220501 | 0.00832820 | 0.00416410 | − | 0.999991i | \(-0.498675\pi\) | ||||
0.00416410 | + | 0.999991i | \(0.498675\pi\) | |||||||
\(702\) | 5.24561 | 0.197983 | ||||||||
\(703\) | 2.20275 | 0.0830782 | ||||||||
\(704\) | 5.34366 | 0.201397 | ||||||||
\(705\) | 23.4592 | 0.883525 | ||||||||
\(706\) | 62.5219 | 2.35304 | ||||||||
\(707\) | −44.8572 | −1.68703 | ||||||||
\(708\) | 14.1845 | 0.533084 | ||||||||
\(709\) | 14.1040 | 0.529685 | 0.264843 | − | 0.964292i | \(-0.414680\pi\) | ||||
0.264843 | + | 0.964292i | \(0.414680\pi\) | |||||||
\(710\) | 63.7146 | 2.39117 | ||||||||
\(711\) | 13.5994 | 0.510016 | ||||||||
\(712\) | 13.7017 | 0.513495 | ||||||||
\(713\) | 10.9284 | 0.409271 | ||||||||
\(714\) | 8.09166 | 0.302823 | ||||||||
\(715\) | 59.8587 | 2.23859 | ||||||||
\(716\) | 13.6117 | 0.508694 | ||||||||
\(717\) | 16.2674 | 0.607518 | ||||||||
\(718\) | 39.3279 | 1.46771 | ||||||||
\(719\) | 11.3720 | 0.424105 | 0.212053 | − | 0.977258i | \(-0.431985\pi\) | ||||
0.212053 | + | 0.977258i | \(0.431985\pi\) | |||||||
\(720\) | −21.9261 | −0.817137 | ||||||||
\(721\) | −21.2210 | −0.790312 | ||||||||
\(722\) | −33.7573 | −1.25632 | ||||||||
\(723\) | −4.33551 | −0.161239 | ||||||||
\(724\) | −15.0951 | −0.561004 | ||||||||
\(725\) | 145.797 | 5.41477 | ||||||||
\(726\) | −18.7471 | −0.695771 | ||||||||
\(727\) | 39.8861 | 1.47929 | 0.739647 | − | 0.672995i | \(-0.234993\pi\) | ||||
0.739647 | + | 0.672995i | \(0.234993\pi\) | |||||||
\(728\) | −18.0612 | −0.669391 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 21.6683 | 0.801979 | ||||||||
\(731\) | 6.63207 | 0.245296 | ||||||||
\(732\) | 18.5996 | 0.687462 | ||||||||
\(733\) | −0.00413344 | −0.000152672 0 | −7.63360e−5 | − | 1.00000i | \(-0.500024\pi\) | ||||
−7.63360e−5 | 1.00000i | \(0.500024\pi\) | ||||||||
\(734\) | −41.0085 | −1.51365 | ||||||||
\(735\) | −58.7132 | −2.16567 | ||||||||
\(736\) | −18.7438 | −0.690904 | ||||||||
\(737\) | −25.6969 | −0.946558 | ||||||||
\(738\) | 9.90269 | 0.364523 | ||||||||
\(739\) | −38.5093 | −1.41659 | −0.708294 | − | 0.705917i | \(-0.750535\pi\) | ||||
−0.708294 | + | 0.705917i | \(0.750535\pi\) | |||||||
\(740\) | −25.1140 | −0.923210 | ||||||||
\(741\) | −1.40053 | −0.0514498 | ||||||||
\(742\) | −63.5740 | −2.33388 | ||||||||
\(743\) | 36.2308 | 1.32918 | 0.664590 | − | 0.747209i | \(-0.268606\pi\) | ||||
0.664590 | + | 0.747209i | \(0.268606\pi\) | |||||||
\(744\) | 4.92796 | 0.180668 | ||||||||
\(745\) | −66.1920 | −2.42509 | ||||||||
\(746\) | 4.51459 | 0.165291 | ||||||||
\(747\) | 4.67665 | 0.171110 | ||||||||
\(748\) | −5.71491 | −0.208958 | ||||||||
\(749\) | −78.7150 | −2.87618 | ||||||||
\(750\) | −77.0441 | −2.81325 | ||||||||
\(751\) | 6.15872 | 0.224735 | 0.112367 | − | 0.993667i | \(-0.464157\pi\) | ||||
0.112367 | + | 0.993667i | \(0.464157\pi\) | |||||||
\(752\) | 26.1619 | 0.954027 | ||||||||
\(753\) | −6.99084 | −0.254761 | ||||||||
\(754\) | −52.1655 | −1.89975 | ||||||||
\(755\) | 94.9907 | 3.45707 | ||||||||
\(756\) | 5.55499 | 0.202033 | ||||||||
\(757\) | −25.7039 | −0.934224 | −0.467112 | − | 0.884198i | \(-0.654706\pi\) | ||||
−0.467112 | + | 0.884198i | \(0.654706\pi\) | |||||||
\(758\) | −49.6216 | −1.80234 | ||||||||
\(759\) | 14.1280 | 0.512814 | ||||||||
\(760\) | 2.93064 | 0.106305 | ||||||||
\(761\) | −17.1978 | −0.623420 | −0.311710 | − | 0.950177i | \(-0.600902\pi\) | ||||
−0.311710 | + | 0.950177i | \(0.600902\pi\) | |||||||
\(762\) | −1.60677 | −0.0582070 | ||||||||
\(763\) | −43.2185 | −1.56461 | ||||||||
\(764\) | 23.2672 | 0.841778 | ||||||||
\(765\) | 4.43407 | 0.160314 | ||||||||
\(766\) | 48.1840 | 1.74096 | ||||||||
\(767\) | 33.5065 | 1.20985 | ||||||||
\(768\) | −20.6632 | −0.745619 | ||||||||
\(769\) | 11.3752 | 0.410199 | 0.205099 | − | 0.978741i | \(-0.434248\pi\) | ||||
0.205099 | + | 0.978741i | \(0.434248\pi\) | |||||||
\(770\) | 166.068 | 5.98467 | ||||||||
\(771\) | −18.7213 | −0.674231 | ||||||||
\(772\) | −31.5031 | −1.13382 | ||||||||
\(773\) | −22.3853 | −0.805144 | −0.402572 | − | 0.915388i | \(-0.631884\pi\) | ||||
−0.402572 | + | 0.915388i | \(0.631884\pi\) | |||||||
\(774\) | 11.9280 | 0.428742 | ||||||||
\(775\) | 52.4908 | 1.88552 | ||||||||
\(776\) | −20.6002 | −0.739503 | ||||||||
\(777\) | −20.6382 | −0.740390 | ||||||||
\(778\) | 28.1830 | 1.01041 | ||||||||
\(779\) | −2.64393 | −0.0947285 | ||||||||
\(780\) | 15.9678 | 0.571738 | ||||||||
\(781\) | −36.9799 | −1.32324 | ||||||||
\(782\) | 5.48974 | 0.196313 | ||||||||
\(783\) | −9.94458 | −0.355390 | ||||||||
\(784\) | −65.4775 | −2.33848 | ||||||||
\(785\) | −4.43407 | −0.158259 | ||||||||
\(786\) | 14.2268 | 0.507453 | ||||||||
\(787\) | −18.0978 | −0.645118 | −0.322559 | − | 0.946549i | \(-0.604543\pi\) | ||||
−0.322559 | + | 0.946549i | \(0.604543\pi\) | |||||||
\(788\) | 7.24203 | 0.257987 | ||||||||
\(789\) | −12.9078 | −0.459529 | ||||||||
\(790\) | 108.452 | 3.85855 | ||||||||
\(791\) | −33.7229 | −1.19905 | ||||||||
\(792\) | 6.37078 | 0.226376 | ||||||||
\(793\) | 43.9360 | 1.56021 | ||||||||
\(794\) | −3.22354 | −0.114399 | ||||||||
\(795\) | −34.8373 | −1.23555 | ||||||||
\(796\) | −23.9537 | −0.849018 | ||||||||
\(797\) | 33.1451 | 1.17406 | 0.587030 | − | 0.809565i | \(-0.300297\pi\) | ||||
0.587030 | + | 0.809565i | \(0.300297\pi\) | |||||||
\(798\) | −3.88554 | −0.137546 | ||||||||
\(799\) | −5.29067 | −0.187171 | ||||||||
\(800\) | −90.0293 | −3.18302 | ||||||||
\(801\) | −9.95473 | −0.351733 | ||||||||
\(802\) | 41.3153 | 1.45889 | ||||||||
\(803\) | −12.5762 | −0.443806 | ||||||||
\(804\) | −6.85485 | −0.241752 | ||||||||
\(805\) | −60.8916 | −2.14615 | ||||||||
\(806\) | −18.7809 | −0.661530 | ||||||||
\(807\) | −4.68577 | −0.164947 | ||||||||
\(808\) | −13.7233 | −0.482784 | ||||||||
\(809\) | −15.2505 | −0.536180 | −0.268090 | − | 0.963394i | \(-0.586393\pi\) | ||||
−0.268090 | + | 0.963394i | \(0.586393\pi\) | |||||||
\(810\) | 7.97480 | 0.280206 | ||||||||
\(811\) | 10.8230 | 0.380046 | 0.190023 | − | 0.981780i | \(-0.439144\pi\) | ||||
0.190023 | + | 0.981780i | \(0.439144\pi\) | |||||||
\(812\) | −55.2421 | −1.93862 | ||||||||
\(813\) | 3.35006 | 0.117492 | ||||||||
\(814\) | 38.1869 | 1.33845 | ||||||||
\(815\) | −87.5080 | −3.06527 | ||||||||
\(816\) | 4.94491 | 0.173107 | ||||||||
\(817\) | −3.18466 | −0.111417 | ||||||||
\(818\) | −37.8025 | −1.32173 | ||||||||
\(819\) | 13.1220 | 0.458519 | ||||||||
\(820\) | 30.1440 | 1.05267 | ||||||||
\(821\) | −3.73030 | −0.130188 | −0.0650942 | − | 0.997879i | \(-0.520735\pi\) | ||||
−0.0650942 | + | 0.997879i | \(0.520735\pi\) | |||||||
\(822\) | −13.4772 | −0.470072 | ||||||||
\(823\) | 34.3619 | 1.19778 | 0.598890 | − | 0.800832i | \(-0.295609\pi\) | ||||
0.598890 | + | 0.800832i | \(0.295609\pi\) | |||||||
\(824\) | −6.49221 | −0.226167 | ||||||||
\(825\) | 67.8591 | 2.36255 | ||||||||
\(826\) | 92.9581 | 3.23442 | ||||||||
\(827\) | 9.47172 | 0.329364 | 0.164682 | − | 0.986347i | \(-0.447340\pi\) | ||||
0.164682 | + | 0.986347i | \(0.447340\pi\) | |||||||
\(828\) | 3.76875 | 0.130973 | ||||||||
\(829\) | 46.5525 | 1.61684 | 0.808418 | − | 0.588609i | \(-0.200324\pi\) | ||||
0.808418 | + | 0.588609i | \(0.200324\pi\) | |||||||
\(830\) | 37.2953 | 1.29454 | ||||||||
\(831\) | −28.3758 | −0.984346 | ||||||||
\(832\) | 3.36722 | 0.116737 | ||||||||
\(833\) | 13.2414 | 0.458787 | ||||||||
\(834\) | 26.0561 | 0.902248 | ||||||||
\(835\) | 24.4683 | 0.846760 | ||||||||
\(836\) | 2.74424 | 0.0949116 | ||||||||
\(837\) | −3.58031 | −0.123754 | ||||||||
\(838\) | −20.6777 | −0.714301 | ||||||||
\(839\) | −24.3179 | −0.839546 | −0.419773 | − | 0.907629i | \(-0.637890\pi\) | ||||
−0.419773 | + | 0.907629i | \(0.637890\pi\) | |||||||
\(840\) | −27.4580 | −0.947391 | ||||||||
\(841\) | 69.8948 | 2.41016 | ||||||||
\(842\) | −13.1232 | −0.452255 | ||||||||
\(843\) | 16.2369 | 0.559229 | ||||||||
\(844\) | 15.5340 | 0.534702 | ||||||||
\(845\) | −19.9239 | −0.685402 | ||||||||
\(846\) | −9.51543 | −0.327147 | ||||||||
\(847\) | −46.8962 | −1.61137 | ||||||||
\(848\) | −38.8509 | −1.33415 | ||||||||
\(849\) | 10.7145 | 0.367720 | ||||||||
\(850\) | 26.3681 | 0.904420 | ||||||||
\(851\) | −14.0019 | −0.479978 | ||||||||
\(852\) | −9.86467 | −0.337958 | ||||||||
\(853\) | −48.6664 | −1.66631 | −0.833153 | − | 0.553043i | \(-0.813467\pi\) | ||||
−0.833153 | + | 0.553043i | \(0.813467\pi\) | |||||||
\(854\) | 121.893 | 4.17109 | ||||||||
\(855\) | −2.12920 | −0.0728170 | ||||||||
\(856\) | −24.0815 | −0.823090 | ||||||||
\(857\) | 44.9890 | 1.53679 | 0.768397 | − | 0.639973i | \(-0.221055\pi\) | ||||
0.768397 | + | 0.639973i | \(0.221055\pi\) | |||||||
\(858\) | −24.2797 | −0.828894 | ||||||||
\(859\) | −9.22248 | −0.314667 | −0.157333 | − | 0.987546i | \(-0.550290\pi\) | ||||
−0.157333 | + | 0.987546i | \(0.550290\pi\) | |||||||
\(860\) | 36.3090 | 1.23813 | ||||||||
\(861\) | 24.7717 | 0.844218 | ||||||||
\(862\) | 32.6802 | 1.11309 | ||||||||
\(863\) | −4.34652 | −0.147957 | −0.0739786 | − | 0.997260i | \(-0.523570\pi\) | ||||
−0.0739786 | + | 0.997260i | \(0.523570\pi\) | |||||||
\(864\) | 6.14076 | 0.208913 | ||||||||
\(865\) | −85.5267 | −2.90800 | ||||||||
\(866\) | 73.3496 | 2.49252 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −19.8886 | −0.675063 | ||||||||
\(869\) | −62.9455 | −2.13528 | ||||||||
\(870\) | −79.3060 | −2.68873 | ||||||||
\(871\) | −16.1925 | −0.548662 | ||||||||
\(872\) | −13.2220 | −0.447752 | ||||||||
\(873\) | 14.9666 | 0.506544 | ||||||||
\(874\) | −2.63612 | −0.0891682 | ||||||||
\(875\) | −192.727 | −6.51536 | ||||||||
\(876\) | −3.35481 | −0.113348 | ||||||||
\(877\) | −13.2669 | −0.447991 | −0.223995 | − | 0.974590i | \(-0.571910\pi\) | ||||
−0.223995 | + | 0.974590i | \(0.571910\pi\) | |||||||
\(878\) | 9.90505 | 0.334279 | ||||||||
\(879\) | 26.3958 | 0.890307 | ||||||||
\(880\) | 101.486 | 3.42110 | ||||||||
\(881\) | −24.6111 | −0.829168 | −0.414584 | − | 0.910011i | \(-0.636073\pi\) | ||||
−0.414584 | + | 0.910011i | \(0.636073\pi\) | |||||||
\(882\) | 23.8150 | 0.801893 | ||||||||
\(883\) | 32.7570 | 1.10236 | 0.551180 | − | 0.834386i | \(-0.314178\pi\) | ||||
0.551180 | + | 0.834386i | \(0.314178\pi\) | |||||||
\(884\) | −3.60116 | −0.121120 | ||||||||
\(885\) | 50.9392 | 1.71230 | ||||||||
\(886\) | 10.6560 | 0.357995 | ||||||||
\(887\) | 26.9699 | 0.905560 | 0.452780 | − | 0.891622i | \(-0.350432\pi\) | ||||
0.452780 | + | 0.891622i | \(0.350432\pi\) | |||||||
\(888\) | −6.31390 | −0.211881 | ||||||||
\(889\) | −4.01935 | −0.134805 | ||||||||
\(890\) | −79.3869 | −2.66106 | ||||||||
\(891\) | −4.62856 | −0.155063 | ||||||||
\(892\) | −26.5831 | −0.890068 | ||||||||
\(893\) | 2.54053 | 0.0850156 | ||||||||
\(894\) | 26.8485 | 0.897949 | ||||||||
\(895\) | 48.8824 | 1.63396 | ||||||||
\(896\) | −45.9133 | −1.53385 | ||||||||
\(897\) | 8.90254 | 0.297247 | ||||||||
\(898\) | 51.5728 | 1.72101 | ||||||||
\(899\) | 35.6047 | 1.18748 | ||||||||
\(900\) | 18.1019 | 0.603398 | ||||||||
\(901\) | 7.85674 | 0.261746 | ||||||||
\(902\) | −45.8352 | −1.52615 | ||||||||
\(903\) | 29.8380 | 0.992945 | ||||||||
\(904\) | −10.3170 | −0.343137 | ||||||||
\(905\) | −54.2094 | −1.80198 | ||||||||
\(906\) | −38.5297 | −1.28007 | ||||||||
\(907\) | 30.1573 | 1.00136 | 0.500678 | − | 0.865634i | \(-0.333084\pi\) | ||||
0.500678 | + | 0.865634i | \(0.333084\pi\) | |||||||
\(908\) | −15.9536 | −0.529438 | ||||||||
\(909\) | 9.97039 | 0.330697 | ||||||||
\(910\) | 104.645 | 3.46895 | ||||||||
\(911\) | −34.8651 | −1.15513 | −0.577566 | − | 0.816344i | \(-0.695998\pi\) | ||||
−0.577566 | + | 0.816344i | \(0.695998\pi\) | |||||||
\(912\) | −2.37450 | −0.0786276 | ||||||||
\(913\) | −21.6462 | −0.716384 | ||||||||
\(914\) | −15.1780 | −0.502045 | ||||||||
\(915\) | 66.7949 | 2.20817 | ||||||||
\(916\) | 23.4940 | 0.776263 | ||||||||
\(917\) | 35.5885 | 1.17524 | ||||||||
\(918\) | −1.79853 | −0.0593603 | ||||||||
\(919\) | −30.9380 | −1.02055 | −0.510274 | − | 0.860012i | \(-0.670456\pi\) | ||||
−0.510274 | + | 0.860012i | \(0.670456\pi\) | |||||||
\(920\) | −18.6287 | −0.614172 | ||||||||
\(921\) | 19.1507 | 0.631036 | ||||||||
\(922\) | −40.4885 | −1.33342 | ||||||||
\(923\) | −23.3023 | −0.767004 | ||||||||
\(924\) | −25.7116 | −0.845850 | ||||||||
\(925\) | −67.2532 | −2.21127 | ||||||||
\(926\) | 5.10115 | 0.167634 | ||||||||
\(927\) | 4.71678 | 0.154919 | ||||||||
\(928\) | −61.0673 | −2.00463 | ||||||||
\(929\) | −41.1794 | −1.35105 | −0.675526 | − | 0.737336i | \(-0.736083\pi\) | ||||
−0.675526 | + | 0.737336i | \(0.736083\pi\) | |||||||
\(930\) | −28.5522 | −0.936265 | ||||||||
\(931\) | −6.35839 | −0.208388 | ||||||||
\(932\) | 23.3137 | 0.763666 | ||||||||
\(933\) | −1.52003 | −0.0497635 | ||||||||
\(934\) | −15.3545 | −0.502414 | ||||||||
\(935\) | −20.5234 | −0.671186 | ||||||||
\(936\) | 4.01445 | 0.131216 | ||||||||
\(937\) | −5.48833 | −0.179296 | −0.0896480 | − | 0.995974i | \(-0.528574\pi\) | ||||
−0.0896480 | + | 0.995974i | \(0.528574\pi\) | |||||||
\(938\) | −44.9234 | −1.46680 | ||||||||
\(939\) | −8.83884 | −0.288445 | ||||||||
\(940\) | −28.9652 | −0.944740 | ||||||||
\(941\) | −28.5263 | −0.929930 | −0.464965 | − | 0.885329i | \(-0.653933\pi\) | ||||
−0.464965 | + | 0.885329i | \(0.653933\pi\) | |||||||
\(942\) | 1.79853 | 0.0585992 | ||||||||
\(943\) | 16.8063 | 0.547287 | ||||||||
\(944\) | 56.8078 | 1.84894 | ||||||||
\(945\) | 19.9491 | 0.648943 | ||||||||
\(946\) | −55.2093 | −1.79501 | ||||||||
\(947\) | 50.0379 | 1.62601 | 0.813007 | − | 0.582254i | \(-0.197829\pi\) | ||||
0.813007 | + | 0.582254i | \(0.197829\pi\) | |||||||
\(948\) | −16.7912 | −0.545352 | ||||||||
\(949\) | −7.92472 | −0.257247 | ||||||||
\(950\) | −12.6617 | −0.410801 | ||||||||
\(951\) | 0.200835 | 0.00651251 | ||||||||
\(952\) | 6.19251 | 0.200700 | ||||||||
\(953\) | 49.6915 | 1.60966 | 0.804832 | − | 0.593503i | \(-0.202255\pi\) | ||||
0.804832 | + | 0.593503i | \(0.202255\pi\) | |||||||
\(954\) | 14.1306 | 0.457494 | ||||||||
\(955\) | 83.5572 | 2.70385 | ||||||||
\(956\) | −20.0854 | −0.649610 | ||||||||
\(957\) | 46.0291 | 1.48791 | ||||||||
\(958\) | 18.8008 | 0.607427 | ||||||||
\(959\) | −33.7134 | −1.08866 | ||||||||
\(960\) | 5.11912 | 0.165219 | ||||||||
\(961\) | −18.1814 | −0.586496 | ||||||||
\(962\) | 24.0629 | 0.775818 | ||||||||
\(963\) | 17.4959 | 0.563799 | ||||||||
\(964\) | 5.35307 | 0.172411 | ||||||||
\(965\) | −113.134 | −3.64191 | ||||||||
\(966\) | 24.6986 | 0.794664 | ||||||||
\(967\) | 11.9168 | 0.383218 | 0.191609 | − | 0.981471i | \(-0.438629\pi\) | ||||
0.191609 | + | 0.981471i | \(0.438629\pi\) | |||||||
\(968\) | −14.3471 | −0.461133 | ||||||||
\(969\) | 0.480190 | 0.0154259 | ||||||||
\(970\) | 119.356 | 3.83229 | ||||||||
\(971\) | −41.4905 | −1.33149 | −0.665747 | − | 0.746178i | \(-0.731887\pi\) | ||||
−0.665747 | + | 0.746178i | \(0.731887\pi\) | |||||||
\(972\) | −1.23470 | −0.0396032 | ||||||||
\(973\) | 65.1796 | 2.08956 | ||||||||
\(974\) | −33.6298 | −1.07757 | ||||||||
\(975\) | 42.7603 | 1.36943 | ||||||||
\(976\) | 74.4903 | 2.38438 | ||||||||
\(977\) | −20.5042 | −0.655987 | −0.327993 | − | 0.944680i | \(-0.606372\pi\) | ||||
−0.327993 | + | 0.944680i | \(0.606372\pi\) | |||||||
\(978\) | 35.4947 | 1.13499 | ||||||||
\(979\) | 46.0761 | 1.47260 | ||||||||
\(980\) | 72.4934 | 2.31572 | ||||||||
\(981\) | 9.60614 | 0.306701 | ||||||||
\(982\) | −31.7321 | −1.01261 | ||||||||
\(983\) | 20.1667 | 0.643219 | 0.321610 | − | 0.946872i | \(-0.395776\pi\) | ||||
0.321610 | + | 0.946872i | \(0.395776\pi\) | |||||||
\(984\) | 7.57849 | 0.241593 | ||||||||
\(985\) | 26.0076 | 0.828670 | ||||||||
\(986\) | 17.8856 | 0.569594 | ||||||||
\(987\) | −23.8030 | −0.757657 | ||||||||
\(988\) | 1.72924 | 0.0550145 | ||||||||
\(989\) | 20.2434 | 0.643703 | ||||||||
\(990\) | −36.9118 | −1.17314 | ||||||||
\(991\) | 49.8803 | 1.58450 | 0.792250 | − | 0.610197i | \(-0.208910\pi\) | ||||
0.792250 | + | 0.610197i | \(0.208910\pi\) | |||||||
\(992\) | −21.9858 | −0.698050 | ||||||||
\(993\) | −17.9318 | −0.569048 | ||||||||
\(994\) | −64.6483 | −2.05052 | ||||||||
\(995\) | −86.0226 | −2.72710 | ||||||||
\(996\) | −5.77428 | −0.182965 | ||||||||
\(997\) | −12.2513 | −0.388001 | −0.194001 | − | 0.981001i | \(-0.562146\pi\) | ||||
−0.194001 | + | 0.981001i | \(0.562146\pi\) | |||||||
\(998\) | −39.3417 | −1.24534 | ||||||||
\(999\) | 4.58724 | 0.145134 |
(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.j.1.48 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.j.1.48 | ✓ | 64 | 1.1 | even | 1 | trivial |