Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.503095 | −0.355742 | −0.177871 | − | 0.984054i | \(-0.556921\pi\) | ||||
−0.177871 | + | 0.984054i | \(0.556921\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.74690 | −0.873448 | ||||||||
\(5\) | −1.55796 | −0.696742 | −0.348371 | − | 0.937357i | \(-0.613265\pi\) | ||||
−0.348371 | + | 0.937357i | \(0.613265\pi\) | |||||||
\(6\) | −0.503095 | −0.205388 | ||||||||
\(7\) | 2.07714 | 0.785085 | 0.392543 | − | 0.919734i | \(-0.371596\pi\) | ||||
0.392543 | + | 0.919734i | \(0.371596\pi\) | |||||||
\(8\) | 1.88504 | 0.666463 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.783803 | 0.247860 | ||||||||
\(11\) | −2.88035 | −0.868458 | −0.434229 | − | 0.900803i | \(-0.642979\pi\) | ||||
−0.434229 | + | 0.900803i | \(0.642979\pi\) | |||||||
\(12\) | −1.74690 | −0.504285 | ||||||||
\(13\) | 2.62239 | 0.727321 | 0.363661 | − | 0.931532i | \(-0.381527\pi\) | ||||
0.363661 | + | 0.931532i | \(0.381527\pi\) | |||||||
\(14\) | −1.04500 | −0.279288 | ||||||||
\(15\) | −1.55796 | −0.402264 | ||||||||
\(16\) | 2.54544 | 0.636359 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.503095 | −0.118581 | ||||||||
\(19\) | 5.60081 | 1.28491 | 0.642457 | − | 0.766321i | \(-0.277915\pi\) | ||||
0.642457 | + | 0.766321i | \(0.277915\pi\) | |||||||
\(20\) | 2.72160 | 0.608568 | ||||||||
\(21\) | 2.07714 | 0.453269 | ||||||||
\(22\) | 1.44909 | 0.308947 | ||||||||
\(23\) | 0.593598 | 0.123774 | 0.0618868 | − | 0.998083i | \(-0.480288\pi\) | ||||
0.0618868 | + | 0.998083i | \(0.480288\pi\) | |||||||
\(24\) | 1.88504 | 0.384783 | ||||||||
\(25\) | −2.57275 | −0.514551 | ||||||||
\(26\) | −1.31931 | −0.258738 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.62855 | −0.685731 | ||||||||
\(29\) | −9.84663 | −1.82847 | −0.914236 | − | 0.405181i | \(-0.867208\pi\) | ||||
−0.914236 | + | 0.405181i | \(0.867208\pi\) | |||||||
\(30\) | 0.783803 | 0.143102 | ||||||||
\(31\) | 2.75385 | 0.494607 | 0.247303 | − | 0.968938i | \(-0.420456\pi\) | ||||
0.247303 | + | 0.968938i | \(0.420456\pi\) | |||||||
\(32\) | −5.05068 | −0.892843 | ||||||||
\(33\) | −2.88035 | −0.501404 | ||||||||
\(34\) | 0.503095 | 0.0862800 | ||||||||
\(35\) | −3.23611 | −0.547002 | ||||||||
\(36\) | −1.74690 | −0.291149 | ||||||||
\(37\) | −2.67091 | −0.439095 | −0.219548 | − | 0.975602i | \(-0.570458\pi\) | ||||
−0.219548 | + | 0.975602i | \(0.570458\pi\) | |||||||
\(38\) | −2.81774 | −0.457098 | ||||||||
\(39\) | 2.62239 | 0.419919 | ||||||||
\(40\) | −2.93683 | −0.464353 | ||||||||
\(41\) | −8.19250 | −1.27945 | −0.639727 | − | 0.768603i | \(-0.720952\pi\) | ||||
−0.639727 | + | 0.768603i | \(0.720952\pi\) | |||||||
\(42\) | −1.04500 | −0.161247 | ||||||||
\(43\) | −4.66949 | −0.712091 | −0.356045 | − | 0.934469i | \(-0.615875\pi\) | ||||
−0.356045 | + | 0.934469i | \(0.615875\pi\) | |||||||
\(44\) | 5.03167 | 0.758553 | ||||||||
\(45\) | −1.55796 | −0.232247 | ||||||||
\(46\) | −0.298636 | −0.0440315 | ||||||||
\(47\) | 11.4351 | 1.66799 | 0.833993 | − | 0.551775i | \(-0.186049\pi\) | ||||
0.833993 | + | 0.551775i | \(0.186049\pi\) | |||||||
\(48\) | 2.54544 | 0.367402 | ||||||||
\(49\) | −2.68549 | −0.383641 | ||||||||
\(50\) | 1.29434 | 0.183047 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −4.58105 | −0.635277 | ||||||||
\(53\) | −9.27271 | −1.27370 | −0.636852 | − | 0.770986i | \(-0.719764\pi\) | ||||
−0.636852 | + | 0.770986i | \(0.719764\pi\) | |||||||
\(54\) | −0.503095 | −0.0684625 | ||||||||
\(55\) | 4.48748 | 0.605091 | ||||||||
\(56\) | 3.91550 | 0.523231 | ||||||||
\(57\) | 5.60081 | 0.741846 | ||||||||
\(58\) | 4.95379 | 0.650464 | ||||||||
\(59\) | −7.63345 | −0.993791 | −0.496895 | − | 0.867810i | \(-0.665527\pi\) | ||||
−0.496895 | + | 0.867810i | \(0.665527\pi\) | |||||||
\(60\) | 2.72160 | 0.351357 | ||||||||
\(61\) | 3.42981 | 0.439142 | 0.219571 | − | 0.975597i | \(-0.429534\pi\) | ||||
0.219571 | + | 0.975597i | \(0.429534\pi\) | |||||||
\(62\) | −1.38545 | −0.175952 | ||||||||
\(63\) | 2.07714 | 0.261695 | ||||||||
\(64\) | −2.54990 | −0.318738 | ||||||||
\(65\) | −4.08559 | −0.506755 | ||||||||
\(66\) | 1.44909 | 0.178370 | ||||||||
\(67\) | 14.2127 | 1.73636 | 0.868182 | − | 0.496247i | \(-0.165289\pi\) | ||||
0.868182 | + | 0.496247i | \(0.165289\pi\) | |||||||
\(68\) | 1.74690 | 0.211842 | ||||||||
\(69\) | 0.593598 | 0.0714608 | ||||||||
\(70\) | 1.62807 | 0.194591 | ||||||||
\(71\) | −2.18257 | −0.259023 | −0.129512 | − | 0.991578i | \(-0.541341\pi\) | ||||
−0.129512 | + | 0.991578i | \(0.541341\pi\) | |||||||
\(72\) | 1.88504 | 0.222154 | ||||||||
\(73\) | 8.60069 | 1.00663 | 0.503317 | − | 0.864102i | \(-0.332113\pi\) | ||||
0.503317 | + | 0.864102i | \(0.332113\pi\) | |||||||
\(74\) | 1.34372 | 0.156205 | ||||||||
\(75\) | −2.57275 | −0.297076 | ||||||||
\(76\) | −9.78404 | −1.12231 | ||||||||
\(77\) | −5.98289 | −0.681813 | ||||||||
\(78\) | −1.31931 | −0.149383 | ||||||||
\(79\) | −4.94394 | −0.556237 | −0.278119 | − | 0.960547i | \(-0.589711\pi\) | ||||
−0.278119 | + | 0.960547i | \(0.589711\pi\) | |||||||
\(80\) | −3.96569 | −0.443378 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.12160 | 0.455155 | ||||||||
\(83\) | −11.9546 | −1.31218 | −0.656091 | − | 0.754681i | \(-0.727791\pi\) | ||||
−0.656091 | + | 0.754681i | \(0.727791\pi\) | |||||||
\(84\) | −3.62855 | −0.395907 | ||||||||
\(85\) | 1.55796 | 0.168985 | ||||||||
\(86\) | 2.34920 | 0.253320 | ||||||||
\(87\) | −9.84663 | −1.05567 | ||||||||
\(88\) | −5.42958 | −0.578795 | ||||||||
\(89\) | 7.90847 | 0.838296 | 0.419148 | − | 0.907918i | \(-0.362329\pi\) | ||||
0.419148 | + | 0.907918i | \(0.362329\pi\) | |||||||
\(90\) | 0.783803 | 0.0826201 | ||||||||
\(91\) | 5.44708 | 0.571009 | ||||||||
\(92\) | −1.03695 | −0.108110 | ||||||||
\(93\) | 2.75385 | 0.285561 | ||||||||
\(94\) | −5.75296 | −0.593372 | ||||||||
\(95\) | −8.72586 | −0.895254 | ||||||||
\(96\) | −5.05068 | −0.515483 | ||||||||
\(97\) | 7.71587 | 0.783428 | 0.391714 | − | 0.920087i | \(-0.371882\pi\) | ||||
0.391714 | + | 0.920087i | \(0.371882\pi\) | |||||||
\(98\) | 1.35105 | 0.136477 | ||||||||
\(99\) | −2.88035 | −0.289486 | ||||||||
\(100\) | 4.49433 | 0.449433 | ||||||||
\(101\) | 3.17301 | 0.315726 | 0.157863 | − | 0.987461i | \(-0.449540\pi\) | ||||
0.157863 | + | 0.987461i | \(0.449540\pi\) | |||||||
\(102\) | 0.503095 | 0.0498138 | ||||||||
\(103\) | 4.99764 | 0.492432 | 0.246216 | − | 0.969215i | \(-0.420813\pi\) | ||||
0.246216 | + | 0.969215i | \(0.420813\pi\) | |||||||
\(104\) | 4.94333 | 0.484733 | ||||||||
\(105\) | −3.23611 | −0.315812 | ||||||||
\(106\) | 4.66505 | 0.453110 | ||||||||
\(107\) | 16.7318 | 1.61753 | 0.808763 | − | 0.588135i | \(-0.200138\pi\) | ||||
0.808763 | + | 0.588135i | \(0.200138\pi\) | |||||||
\(108\) | −1.74690 | −0.168095 | ||||||||
\(109\) | 10.9675 | 1.05049 | 0.525246 | − | 0.850950i | \(-0.323973\pi\) | ||||
0.525246 | + | 0.850950i | \(0.323973\pi\) | |||||||
\(110\) | −2.25763 | −0.215256 | ||||||||
\(111\) | −2.67091 | −0.253512 | ||||||||
\(112\) | 5.28723 | 0.499596 | ||||||||
\(113\) | 11.7341 | 1.10386 | 0.551928 | − | 0.833892i | \(-0.313892\pi\) | ||||
0.551928 | + | 0.833892i | \(0.313892\pi\) | |||||||
\(114\) | −2.81774 | −0.263906 | ||||||||
\(115\) | −0.924803 | −0.0862383 | ||||||||
\(116\) | 17.2010 | 1.59708 | ||||||||
\(117\) | 2.62239 | 0.242440 | ||||||||
\(118\) | 3.84035 | 0.353533 | ||||||||
\(119\) | −2.07714 | −0.190411 | ||||||||
\(120\) | −2.93683 | −0.268094 | ||||||||
\(121\) | −2.70359 | −0.245781 | ||||||||
\(122\) | −1.72552 | −0.156221 | ||||||||
\(123\) | −8.19250 | −0.738693 | ||||||||
\(124\) | −4.81070 | −0.432013 | ||||||||
\(125\) | 11.7981 | 1.05525 | ||||||||
\(126\) | −1.04500 | −0.0930958 | ||||||||
\(127\) | −10.8830 | −0.965714 | −0.482857 | − | 0.875699i | \(-0.660401\pi\) | ||||
−0.482857 | + | 0.875699i | \(0.660401\pi\) | |||||||
\(128\) | 11.3842 | 1.00623 | ||||||||
\(129\) | −4.66949 | −0.411126 | ||||||||
\(130\) | 2.05544 | 0.180274 | ||||||||
\(131\) | −8.77004 | −0.766242 | −0.383121 | − | 0.923698i | \(-0.625151\pi\) | ||||
−0.383121 | + | 0.923698i | \(0.625151\pi\) | |||||||
\(132\) | 5.03167 | 0.437951 | ||||||||
\(133\) | 11.6337 | 1.00877 | ||||||||
\(134\) | −7.15036 | −0.617697 | ||||||||
\(135\) | −1.55796 | −0.134088 | ||||||||
\(136\) | −1.88504 | −0.161641 | ||||||||
\(137\) | −11.3931 | −0.973376 | −0.486688 | − | 0.873576i | \(-0.661795\pi\) | ||||
−0.486688 | + | 0.873576i | \(0.661795\pi\) | |||||||
\(138\) | −0.298636 | −0.0254216 | ||||||||
\(139\) | 3.70066 | 0.313886 | 0.156943 | − | 0.987608i | \(-0.449836\pi\) | ||||
0.156943 | + | 0.987608i | \(0.449836\pi\) | |||||||
\(140\) | 5.65314 | 0.477778 | ||||||||
\(141\) | 11.4351 | 0.963012 | ||||||||
\(142\) | 1.09804 | 0.0921454 | ||||||||
\(143\) | −7.55341 | −0.631648 | ||||||||
\(144\) | 2.54544 | 0.212120 | ||||||||
\(145\) | 15.3407 | 1.27397 | ||||||||
\(146\) | −4.32696 | −0.358102 | ||||||||
\(147\) | −2.68549 | −0.221495 | ||||||||
\(148\) | 4.66581 | 0.383527 | ||||||||
\(149\) | 21.4973 | 1.76112 | 0.880562 | − | 0.473930i | \(-0.157165\pi\) | ||||
0.880562 | + | 0.473930i | \(0.157165\pi\) | |||||||
\(150\) | 1.29434 | 0.105682 | ||||||||
\(151\) | −14.5312 | −1.18253 | −0.591264 | − | 0.806478i | \(-0.701371\pi\) | ||||
−0.591264 | + | 0.806478i | \(0.701371\pi\) | |||||||
\(152\) | 10.5578 | 0.856349 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 3.00996 | 0.242549 | ||||||||
\(155\) | −4.29040 | −0.344613 | ||||||||
\(156\) | −4.58105 | −0.366777 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 2.48727 | 0.197877 | ||||||||
\(159\) | −9.27271 | −0.735374 | ||||||||
\(160\) | 7.86877 | 0.622081 | ||||||||
\(161\) | 1.23299 | 0.0971729 | ||||||||
\(162\) | −0.503095 | −0.0395269 | ||||||||
\(163\) | −11.2459 | −0.880844 | −0.440422 | − | 0.897791i | \(-0.645171\pi\) | ||||
−0.440422 | + | 0.897791i | \(0.645171\pi\) | |||||||
\(164\) | 14.3114 | 1.11754 | ||||||||
\(165\) | 4.48748 | 0.349350 | ||||||||
\(166\) | 6.01427 | 0.466798 | ||||||||
\(167\) | −11.9886 | −0.927704 | −0.463852 | − | 0.885913i | \(-0.653533\pi\) | ||||
−0.463852 | + | 0.885913i | \(0.653533\pi\) | |||||||
\(168\) | 3.91550 | 0.302087 | ||||||||
\(169\) | −6.12305 | −0.471004 | ||||||||
\(170\) | −0.783803 | −0.0601149 | ||||||||
\(171\) | 5.60081 | 0.428305 | ||||||||
\(172\) | 8.15712 | 0.621974 | ||||||||
\(173\) | −21.0540 | −1.60071 | −0.800353 | − | 0.599529i | \(-0.795355\pi\) | ||||
−0.800353 | + | 0.599529i | \(0.795355\pi\) | |||||||
\(174\) | 4.95379 | 0.375546 | ||||||||
\(175\) | −5.34397 | −0.403966 | ||||||||
\(176\) | −7.33174 | −0.552651 | ||||||||
\(177\) | −7.63345 | −0.573765 | ||||||||
\(178\) | −3.97871 | −0.298217 | ||||||||
\(179\) | −23.0346 | −1.72169 | −0.860844 | − | 0.508869i | \(-0.830064\pi\) | ||||
−0.860844 | + | 0.508869i | \(0.830064\pi\) | |||||||
\(180\) | 2.72160 | 0.202856 | ||||||||
\(181\) | −12.5707 | −0.934372 | −0.467186 | − | 0.884159i | \(-0.654732\pi\) | ||||
−0.467186 | + | 0.884159i | \(0.654732\pi\) | |||||||
\(182\) | −2.74040 | −0.203132 | ||||||||
\(183\) | 3.42981 | 0.253539 | ||||||||
\(184\) | 1.11896 | 0.0824906 | ||||||||
\(185\) | 4.16118 | 0.305936 | ||||||||
\(186\) | −1.38545 | −0.101586 | ||||||||
\(187\) | 2.88035 | 0.210632 | ||||||||
\(188\) | −19.9760 | −1.45690 | ||||||||
\(189\) | 2.07714 | 0.151090 | ||||||||
\(190\) | 4.38993 | 0.318479 | ||||||||
\(191\) | −19.0475 | −1.37823 | −0.689113 | − | 0.724654i | \(-0.742000\pi\) | ||||
−0.689113 | + | 0.724654i | \(0.742000\pi\) | |||||||
\(192\) | −2.54990 | −0.184023 | ||||||||
\(193\) | 2.65031 | 0.190774 | 0.0953868 | − | 0.995440i | \(-0.469591\pi\) | ||||
0.0953868 | + | 0.995440i | \(0.469591\pi\) | |||||||
\(194\) | −3.88181 | −0.278698 | ||||||||
\(195\) | −4.08559 | −0.292575 | ||||||||
\(196\) | 4.69127 | 0.335091 | ||||||||
\(197\) | −21.2170 | −1.51165 | −0.755823 | − | 0.654775i | \(-0.772763\pi\) | ||||
−0.755823 | + | 0.654775i | \(0.772763\pi\) | |||||||
\(198\) | 1.44909 | 0.102982 | ||||||||
\(199\) | −9.57360 | −0.678654 | −0.339327 | − | 0.940668i | \(-0.610199\pi\) | ||||
−0.339327 | + | 0.940668i | \(0.610199\pi\) | |||||||
\(200\) | −4.84975 | −0.342929 | ||||||||
\(201\) | 14.2127 | 1.00249 | ||||||||
\(202\) | −1.59632 | −0.112317 | ||||||||
\(203\) | −20.4528 | −1.43551 | ||||||||
\(204\) | 1.74690 | 0.122307 | ||||||||
\(205\) | 12.7636 | 0.891449 | ||||||||
\(206\) | −2.51429 | −0.175179 | ||||||||
\(207\) | 0.593598 | 0.0412579 | ||||||||
\(208\) | 6.67514 | 0.462837 | ||||||||
\(209\) | −16.1323 | −1.11589 | ||||||||
\(210\) | 1.62807 | 0.112347 | ||||||||
\(211\) | −6.62775 | −0.456273 | −0.228137 | − | 0.973629i | \(-0.573263\pi\) | ||||
−0.228137 | + | 0.973629i | \(0.573263\pi\) | |||||||
\(212\) | 16.1985 | 1.11251 | ||||||||
\(213\) | −2.18257 | −0.149547 | ||||||||
\(214\) | −8.41768 | −0.575421 | ||||||||
\(215\) | 7.27490 | 0.496144 | ||||||||
\(216\) | 1.88504 | 0.128261 | ||||||||
\(217\) | 5.72014 | 0.388309 | ||||||||
\(218\) | −5.51767 | −0.373704 | ||||||||
\(219\) | 8.60069 | 0.581181 | ||||||||
\(220\) | −7.83915 | −0.528516 | ||||||||
\(221\) | −2.62239 | −0.176401 | ||||||||
\(222\) | 1.34372 | 0.0901847 | ||||||||
\(223\) | −7.81608 | −0.523403 | −0.261702 | − | 0.965149i | \(-0.584284\pi\) | ||||
−0.261702 | + | 0.965149i | \(0.584284\pi\) | |||||||
\(224\) | −10.4910 | −0.700958 | ||||||||
\(225\) | −2.57275 | −0.171517 | ||||||||
\(226\) | −5.90339 | −0.392688 | ||||||||
\(227\) | −4.26210 | −0.282886 | −0.141443 | − | 0.989946i | \(-0.545174\pi\) | ||||
−0.141443 | + | 0.989946i | \(0.545174\pi\) | |||||||
\(228\) | −9.78404 | −0.647964 | ||||||||
\(229\) | −2.65238 | −0.175274 | −0.0876370 | − | 0.996152i | \(-0.527932\pi\) | ||||
−0.0876370 | + | 0.996152i | \(0.527932\pi\) | |||||||
\(230\) | 0.465263 | 0.0306786 | ||||||||
\(231\) | −5.98289 | −0.393645 | ||||||||
\(232\) | −18.5613 | −1.21861 | ||||||||
\(233\) | 24.7740 | 1.62300 | 0.811500 | − | 0.584352i | \(-0.198651\pi\) | ||||
0.811500 | + | 0.584352i | \(0.198651\pi\) | |||||||
\(234\) | −1.31931 | −0.0862461 | ||||||||
\(235\) | −17.8155 | −1.16216 | ||||||||
\(236\) | 13.3348 | 0.868025 | ||||||||
\(237\) | −4.94394 | −0.321144 | ||||||||
\(238\) | 1.04500 | 0.0677372 | ||||||||
\(239\) | −26.1059 | −1.68865 | −0.844324 | − | 0.535833i | \(-0.819998\pi\) | ||||
−0.844324 | + | 0.535833i | \(0.819998\pi\) | |||||||
\(240\) | −3.96569 | −0.255984 | ||||||||
\(241\) | −28.0678 | −1.80801 | −0.904003 | − | 0.427525i | \(-0.859386\pi\) | ||||
−0.904003 | + | 0.427525i | \(0.859386\pi\) | |||||||
\(242\) | 1.36016 | 0.0874345 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.99152 | −0.383568 | ||||||||
\(245\) | 4.18389 | 0.267299 | ||||||||
\(246\) | 4.12160 | 0.262784 | ||||||||
\(247\) | 14.6875 | 0.934546 | ||||||||
\(248\) | 5.19113 | 0.329637 | ||||||||
\(249\) | −11.9546 | −0.757589 | ||||||||
\(250\) | −5.93554 | −0.375397 | ||||||||
\(251\) | 7.18179 | 0.453311 | 0.226655 | − | 0.973975i | \(-0.427221\pi\) | ||||
0.226655 | + | 0.973975i | \(0.427221\pi\) | |||||||
\(252\) | −3.62855 | −0.228577 | ||||||||
\(253\) | −1.70977 | −0.107492 | ||||||||
\(254\) | 5.47520 | 0.343545 | ||||||||
\(255\) | 1.55796 | 0.0975634 | ||||||||
\(256\) | −0.627532 | −0.0392208 | ||||||||
\(257\) | −0.0993936 | −0.00620000 | −0.00310000 | − | 0.999995i | \(-0.500987\pi\) | ||||
−0.00310000 | + | 0.999995i | \(0.500987\pi\) | |||||||
\(258\) | 2.34920 | 0.146255 | ||||||||
\(259\) | −5.54786 | −0.344727 | ||||||||
\(260\) | 7.13710 | 0.442624 | ||||||||
\(261\) | −9.84663 | −0.609491 | ||||||||
\(262\) | 4.41216 | 0.272584 | ||||||||
\(263\) | 16.9410 | 1.04463 | 0.522315 | − | 0.852753i | \(-0.325069\pi\) | ||||
0.522315 | + | 0.852753i | \(0.325069\pi\) | |||||||
\(264\) | −5.42958 | −0.334168 | ||||||||
\(265\) | 14.4465 | 0.887444 | ||||||||
\(266\) | −5.85284 | −0.358861 | ||||||||
\(267\) | 7.90847 | 0.483991 | ||||||||
\(268\) | −24.8282 | −1.51662 | ||||||||
\(269\) | 20.4855 | 1.24902 | 0.624512 | − | 0.781015i | \(-0.285298\pi\) | ||||
0.624512 | + | 0.781015i | \(0.285298\pi\) | |||||||
\(270\) | 0.783803 | 0.0477007 | ||||||||
\(271\) | −9.61120 | −0.583839 | −0.291919 | − | 0.956443i | \(-0.594294\pi\) | ||||
−0.291919 | + | 0.956443i | \(0.594294\pi\) | |||||||
\(272\) | −2.54544 | −0.154340 | ||||||||
\(273\) | 5.44708 | 0.329672 | ||||||||
\(274\) | 5.73179 | 0.346270 | ||||||||
\(275\) | 7.41043 | 0.446865 | ||||||||
\(276\) | −1.03695 | −0.0624173 | ||||||||
\(277\) | 11.6939 | 0.702619 | 0.351309 | − | 0.936259i | \(-0.385737\pi\) | ||||
0.351309 | + | 0.936259i | \(0.385737\pi\) | |||||||
\(278\) | −1.86178 | −0.111662 | ||||||||
\(279\) | 2.75385 | 0.164869 | ||||||||
\(280\) | −6.10020 | −0.364557 | ||||||||
\(281\) | 12.4451 | 0.742415 | 0.371207 | − | 0.928550i | \(-0.378944\pi\) | ||||
0.371207 | + | 0.928550i | \(0.378944\pi\) | |||||||
\(282\) | −5.75296 | −0.342584 | ||||||||
\(283\) | 8.85469 | 0.526357 | 0.263178 | − | 0.964747i | \(-0.415229\pi\) | ||||
0.263178 | + | 0.964747i | \(0.415229\pi\) | |||||||
\(284\) | 3.81272 | 0.226243 | ||||||||
\(285\) | −8.72586 | −0.516875 | ||||||||
\(286\) | 3.80008 | 0.224703 | ||||||||
\(287\) | −17.0170 | −1.00448 | ||||||||
\(288\) | −5.05068 | −0.297614 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −7.71781 | −0.453206 | ||||||||
\(291\) | 7.71587 | 0.452312 | ||||||||
\(292\) | −15.0245 | −0.879243 | ||||||||
\(293\) | 23.2694 | 1.35941 | 0.679705 | − | 0.733486i | \(-0.262108\pi\) | ||||
0.679705 | + | 0.733486i | \(0.262108\pi\) | |||||||
\(294\) | 1.35105 | 0.0787951 | ||||||||
\(295\) | 11.8926 | 0.692416 | ||||||||
\(296\) | −5.03479 | −0.292641 | ||||||||
\(297\) | −2.88035 | −0.167135 | ||||||||
\(298\) | −10.8152 | −0.626505 | ||||||||
\(299\) | 1.55665 | 0.0900232 | ||||||||
\(300\) | 4.49433 | 0.259480 | ||||||||
\(301\) | −9.69919 | −0.559052 | ||||||||
\(302\) | 7.31055 | 0.420675 | ||||||||
\(303\) | 3.17301 | 0.182285 | ||||||||
\(304\) | 14.2565 | 0.817667 | ||||||||
\(305\) | −5.34351 | −0.305969 | ||||||||
\(306\) | 0.503095 | 0.0287600 | ||||||||
\(307\) | −22.8169 | −1.30223 | −0.651116 | − | 0.758978i | \(-0.725699\pi\) | ||||
−0.651116 | + | 0.758978i | \(0.725699\pi\) | |||||||
\(308\) | 10.4515 | 0.595529 | ||||||||
\(309\) | 4.99764 | 0.284306 | ||||||||
\(310\) | 2.15848 | 0.122593 | ||||||||
\(311\) | 11.1896 | 0.634504 | 0.317252 | − | 0.948341i | \(-0.397240\pi\) | ||||
0.317252 | + | 0.948341i | \(0.397240\pi\) | |||||||
\(312\) | 4.94333 | 0.279861 | ||||||||
\(313\) | −10.9958 | −0.621519 | −0.310760 | − | 0.950489i | \(-0.600583\pi\) | ||||
−0.310760 | + | 0.950489i | \(0.600583\pi\) | |||||||
\(314\) | −0.503095 | −0.0283913 | ||||||||
\(315\) | −3.23611 | −0.182334 | ||||||||
\(316\) | 8.63655 | 0.485844 | ||||||||
\(317\) | −0.0439860 | −0.00247050 | −0.00123525 | − | 0.999999i | \(-0.500393\pi\) | ||||
−0.00123525 | + | 0.999999i | \(0.500393\pi\) | |||||||
\(318\) | 4.66505 | 0.261603 | ||||||||
\(319\) | 28.3617 | 1.58795 | ||||||||
\(320\) | 3.97265 | 0.222078 | ||||||||
\(321\) | 16.7318 | 0.933878 | ||||||||
\(322\) | −0.620309 | −0.0345684 | ||||||||
\(323\) | −5.60081 | −0.311638 | ||||||||
\(324\) | −1.74690 | −0.0970498 | ||||||||
\(325\) | −6.74677 | −0.374243 | ||||||||
\(326\) | 5.65773 | 0.313353 | ||||||||
\(327\) | 10.9675 | 0.606502 | ||||||||
\(328\) | −15.4432 | −0.852709 | ||||||||
\(329\) | 23.7524 | 1.30951 | ||||||||
\(330\) | −2.25763 | −0.124278 | ||||||||
\(331\) | −13.4548 | −0.739541 | −0.369770 | − | 0.929123i | \(-0.620564\pi\) | ||||
−0.369770 | + | 0.929123i | \(0.620564\pi\) | |||||||
\(332\) | 20.8834 | 1.14612 | ||||||||
\(333\) | −2.67091 | −0.146365 | ||||||||
\(334\) | 6.03139 | 0.330023 | ||||||||
\(335\) | −22.1429 | −1.20980 | ||||||||
\(336\) | 5.28723 | 0.288442 | ||||||||
\(337\) | 0.544072 | 0.0296375 | 0.0148188 | − | 0.999890i | \(-0.495283\pi\) | ||||
0.0148188 | + | 0.999890i | \(0.495283\pi\) | |||||||
\(338\) | 3.08047 | 0.167556 | ||||||||
\(339\) | 11.7341 | 0.637312 | ||||||||
\(340\) | −2.72160 | −0.147599 | ||||||||
\(341\) | −7.93206 | −0.429545 | ||||||||
\(342\) | −2.81774 | −0.152366 | ||||||||
\(343\) | −20.1181 | −1.08628 | ||||||||
\(344\) | −8.80220 | −0.474583 | ||||||||
\(345\) | −0.924803 | −0.0497897 | ||||||||
\(346\) | 10.5922 | 0.569438 | ||||||||
\(347\) | −20.2952 | −1.08950 | −0.544752 | − | 0.838597i | \(-0.683376\pi\) | ||||
−0.544752 | + | 0.838597i | \(0.683376\pi\) | |||||||
\(348\) | 17.2010 | 0.922072 | ||||||||
\(349\) | −5.88048 | −0.314775 | −0.157387 | − | 0.987537i | \(-0.550307\pi\) | ||||
−0.157387 | + | 0.987537i | \(0.550307\pi\) | |||||||
\(350\) | 2.68852 | 0.143708 | ||||||||
\(351\) | 2.62239 | 0.139973 | ||||||||
\(352\) | 14.5477 | 0.775396 | ||||||||
\(353\) | −20.8745 | −1.11104 | −0.555520 | − | 0.831503i | \(-0.687481\pi\) | ||||
−0.555520 | + | 0.831503i | \(0.687481\pi\) | |||||||
\(354\) | 3.84035 | 0.204112 | ||||||||
\(355\) | 3.40036 | 0.180472 | ||||||||
\(356\) | −13.8153 | −0.732208 | ||||||||
\(357\) | −2.07714 | −0.109934 | ||||||||
\(358\) | 11.5886 | 0.612476 | ||||||||
\(359\) | −7.61532 | −0.401921 | −0.200961 | − | 0.979599i | \(-0.564406\pi\) | ||||
−0.200961 | + | 0.979599i | \(0.564406\pi\) | |||||||
\(360\) | −2.93683 | −0.154784 | ||||||||
\(361\) | 12.3691 | 0.651006 | ||||||||
\(362\) | 6.32425 | 0.332395 | ||||||||
\(363\) | −2.70359 | −0.141902 | ||||||||
\(364\) | −9.51548 | −0.498747 | ||||||||
\(365\) | −13.3996 | −0.701365 | ||||||||
\(366\) | −1.72552 | −0.0901943 | ||||||||
\(367\) | −14.3904 | −0.751173 | −0.375586 | − | 0.926787i | \(-0.622559\pi\) | ||||
−0.375586 | + | 0.926787i | \(0.622559\pi\) | |||||||
\(368\) | 1.51096 | 0.0787645 | ||||||||
\(369\) | −8.19250 | −0.426484 | ||||||||
\(370\) | −2.09347 | −0.108834 | ||||||||
\(371\) | −19.2607 | −0.999967 | ||||||||
\(372\) | −4.81070 | −0.249423 | ||||||||
\(373\) | 1.66468 | 0.0861940 | 0.0430970 | − | 0.999071i | \(-0.486278\pi\) | ||||
0.0430970 | + | 0.999071i | \(0.486278\pi\) | |||||||
\(374\) | −1.44909 | −0.0749306 | ||||||||
\(375\) | 11.7981 | 0.609249 | ||||||||
\(376\) | 21.5557 | 1.11165 | ||||||||
\(377\) | −25.8217 | −1.32989 | ||||||||
\(378\) | −1.04500 | −0.0537489 | ||||||||
\(379\) | −25.3244 | −1.30082 | −0.650412 | − | 0.759581i | \(-0.725404\pi\) | ||||
−0.650412 | + | 0.759581i | \(0.725404\pi\) | |||||||
\(380\) | 15.2432 | 0.781958 | ||||||||
\(381\) | −10.8830 | −0.557555 | ||||||||
\(382\) | 9.58268 | 0.490292 | ||||||||
\(383\) | −32.2795 | −1.64940 | −0.824702 | − | 0.565567i | \(-0.808657\pi\) | ||||
−0.824702 | + | 0.565567i | \(0.808657\pi\) | |||||||
\(384\) | 11.3842 | 0.580948 | ||||||||
\(385\) | 9.32112 | 0.475048 | ||||||||
\(386\) | −1.33336 | −0.0678661 | ||||||||
\(387\) | −4.66949 | −0.237364 | ||||||||
\(388\) | −13.4788 | −0.684283 | ||||||||
\(389\) | 26.1678 | 1.32676 | 0.663379 | − | 0.748283i | \(-0.269122\pi\) | ||||
0.663379 | + | 0.748283i | \(0.269122\pi\) | |||||||
\(390\) | 2.05544 | 0.104081 | ||||||||
\(391\) | −0.593598 | −0.0300195 | ||||||||
\(392\) | −5.06226 | −0.255683 | ||||||||
\(393\) | −8.77004 | −0.442390 | ||||||||
\(394\) | 10.6741 | 0.537756 | ||||||||
\(395\) | 7.70248 | 0.387554 | ||||||||
\(396\) | 5.03167 | 0.252851 | ||||||||
\(397\) | −26.3583 | −1.32289 | −0.661443 | − | 0.749995i | \(-0.730056\pi\) | ||||
−0.661443 | + | 0.749995i | \(0.730056\pi\) | |||||||
\(398\) | 4.81643 | 0.241426 | ||||||||
\(399\) | 11.6337 | 0.582412 | ||||||||
\(400\) | −6.54878 | −0.327439 | ||||||||
\(401\) | −12.4311 | −0.620779 | −0.310389 | − | 0.950609i | \(-0.600459\pi\) | ||||
−0.310389 | + | 0.950609i | \(0.600459\pi\) | |||||||
\(402\) | −7.15036 | −0.356627 | ||||||||
\(403\) | 7.22169 | 0.359738 | ||||||||
\(404\) | −5.54292 | −0.275770 | ||||||||
\(405\) | −1.55796 | −0.0774158 | ||||||||
\(406\) | 10.2897 | 0.510670 | ||||||||
\(407\) | 7.69316 | 0.381336 | ||||||||
\(408\) | −1.88504 | −0.0933236 | ||||||||
\(409\) | −15.7451 | −0.778547 | −0.389274 | − | 0.921122i | \(-0.627274\pi\) | ||||
−0.389274 | + | 0.921122i | \(0.627274\pi\) | |||||||
\(410\) | −6.42130 | −0.317126 | ||||||||
\(411\) | −11.3931 | −0.561979 | ||||||||
\(412\) | −8.73036 | −0.430114 | ||||||||
\(413\) | −15.8558 | −0.780211 | ||||||||
\(414\) | −0.298636 | −0.0146772 | ||||||||
\(415\) | 18.6247 | 0.914253 | ||||||||
\(416\) | −13.2449 | −0.649384 | ||||||||
\(417\) | 3.70066 | 0.181222 | ||||||||
\(418\) | 8.11607 | 0.396970 | ||||||||
\(419\) | 1.31712 | 0.0643457 | 0.0321729 | − | 0.999482i | \(-0.489757\pi\) | ||||
0.0321729 | + | 0.999482i | \(0.489757\pi\) | |||||||
\(420\) | 5.65314 | 0.275845 | ||||||||
\(421\) | 7.68705 | 0.374644 | 0.187322 | − | 0.982299i | \(-0.440019\pi\) | ||||
0.187322 | + | 0.982299i | \(0.440019\pi\) | |||||||
\(422\) | 3.33439 | 0.162315 | ||||||||
\(423\) | 11.4351 | 0.555995 | ||||||||
\(424\) | −17.4795 | −0.848878 | ||||||||
\(425\) | 2.57275 | 0.124797 | ||||||||
\(426\) | 1.09804 | 0.0532002 | ||||||||
\(427\) | 7.12420 | 0.344764 | ||||||||
\(428\) | −29.2287 | −1.41282 | ||||||||
\(429\) | −7.55341 | −0.364682 | ||||||||
\(430\) | −3.65996 | −0.176499 | ||||||||
\(431\) | 10.9619 | 0.528018 | 0.264009 | − | 0.964520i | \(-0.414955\pi\) | ||||
0.264009 | + | 0.964520i | \(0.414955\pi\) | |||||||
\(432\) | 2.54544 | 0.122467 | ||||||||
\(433\) | 24.0589 | 1.15620 | 0.578098 | − | 0.815967i | \(-0.303795\pi\) | ||||
0.578098 | + | 0.815967i | \(0.303795\pi\) | |||||||
\(434\) | −2.87777 | −0.138138 | ||||||||
\(435\) | 15.3407 | 0.735529 | ||||||||
\(436\) | −19.1590 | −0.917550 | ||||||||
\(437\) | 3.32463 | 0.159039 | ||||||||
\(438\) | −4.32696 | −0.206750 | ||||||||
\(439\) | −15.8395 | −0.755979 | −0.377989 | − | 0.925810i | \(-0.623384\pi\) | ||||
−0.377989 | + | 0.925810i | \(0.623384\pi\) | |||||||
\(440\) | 8.45909 | 0.403271 | ||||||||
\(441\) | −2.68549 | −0.127880 | ||||||||
\(442\) | 1.31931 | 0.0627533 | ||||||||
\(443\) | 17.3210 | 0.822945 | 0.411473 | − | 0.911422i | \(-0.365015\pi\) | ||||
0.411473 | + | 0.911422i | \(0.365015\pi\) | |||||||
\(444\) | 4.66581 | 0.221429 | ||||||||
\(445\) | −12.3211 | −0.584076 | ||||||||
\(446\) | 3.93223 | 0.186196 | ||||||||
\(447\) | 21.4973 | 1.01679 | ||||||||
\(448\) | −5.29650 | −0.250236 | ||||||||
\(449\) | −25.2040 | −1.18945 | −0.594725 | − | 0.803929i | \(-0.702739\pi\) | ||||
−0.594725 | + | 0.803929i | \(0.702739\pi\) | |||||||
\(450\) | 1.29434 | 0.0610157 | ||||||||
\(451\) | 23.5973 | 1.11115 | ||||||||
\(452\) | −20.4983 | −0.964161 | ||||||||
\(453\) | −14.5312 | −0.682733 | ||||||||
\(454\) | 2.14424 | 0.100634 | ||||||||
\(455\) | −8.48635 | −0.397846 | ||||||||
\(456\) | 10.5578 | 0.494413 | ||||||||
\(457\) | −1.74607 | −0.0816778 | −0.0408389 | − | 0.999166i | \(-0.513003\pi\) | ||||
−0.0408389 | + | 0.999166i | \(0.513003\pi\) | |||||||
\(458\) | 1.33440 | 0.0623523 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 1.61553 | 0.0753247 | ||||||||
\(461\) | 30.9165 | 1.43993 | 0.719963 | − | 0.694012i | \(-0.244159\pi\) | ||||
0.719963 | + | 0.694012i | \(0.244159\pi\) | |||||||
\(462\) | 3.00996 | 0.140036 | ||||||||
\(463\) | 31.2806 | 1.45373 | 0.726865 | − | 0.686780i | \(-0.240976\pi\) | ||||
0.726865 | + | 0.686780i | \(0.240976\pi\) | |||||||
\(464\) | −25.0640 | −1.16357 | ||||||||
\(465\) | −4.29040 | −0.198963 | ||||||||
\(466\) | −12.4637 | −0.577369 | ||||||||
\(467\) | 30.3699 | 1.40535 | 0.702675 | − | 0.711511i | \(-0.251989\pi\) | ||||
0.702675 | + | 0.711511i | \(0.251989\pi\) | |||||||
\(468\) | −4.58105 | −0.211759 | ||||||||
\(469\) | 29.5219 | 1.36319 | ||||||||
\(470\) | 8.96289 | 0.413427 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −14.3894 | −0.662325 | ||||||||
\(473\) | 13.4498 | 0.618421 | ||||||||
\(474\) | 2.48727 | 0.114244 | ||||||||
\(475\) | −14.4095 | −0.661154 | ||||||||
\(476\) | 3.62855 | 0.166314 | ||||||||
\(477\) | −9.27271 | −0.424568 | ||||||||
\(478\) | 13.1337 | 0.600722 | ||||||||
\(479\) | −6.92807 | −0.316552 | −0.158276 | − | 0.987395i | \(-0.550594\pi\) | ||||
−0.158276 | + | 0.987395i | \(0.550594\pi\) | |||||||
\(480\) | 7.86877 | 0.359159 | ||||||||
\(481\) | −7.00418 | −0.319363 | ||||||||
\(482\) | 14.1208 | 0.643183 | ||||||||
\(483\) | 1.23299 | 0.0561028 | ||||||||
\(484\) | 4.72289 | 0.214677 | ||||||||
\(485\) | −12.0210 | −0.545847 | ||||||||
\(486\) | −0.503095 | −0.0228208 | ||||||||
\(487\) | −3.49344 | −0.158303 | −0.0791515 | − | 0.996863i | \(-0.525221\pi\) | ||||
−0.0791515 | + | 0.996863i | \(0.525221\pi\) | |||||||
\(488\) | 6.46534 | 0.292672 | ||||||||
\(489\) | −11.2459 | −0.508555 | ||||||||
\(490\) | −2.10489 | −0.0950894 | ||||||||
\(491\) | −13.7945 | −0.622537 | −0.311268 | − | 0.950322i | \(-0.600754\pi\) | ||||
−0.311268 | + | 0.950322i | \(0.600754\pi\) | |||||||
\(492\) | 14.3114 | 0.645210 | ||||||||
\(493\) | 9.84663 | 0.443470 | ||||||||
\(494\) | −7.38922 | −0.332457 | ||||||||
\(495\) | 4.48748 | 0.201697 | ||||||||
\(496\) | 7.00976 | 0.314748 | ||||||||
\(497\) | −4.53350 | −0.203355 | ||||||||
\(498\) | 6.01427 | 0.269506 | ||||||||
\(499\) | −19.0073 | −0.850881 | −0.425441 | − | 0.904986i | \(-0.639881\pi\) | ||||
−0.425441 | + | 0.904986i | \(0.639881\pi\) | |||||||
\(500\) | −20.6100 | −0.921707 | ||||||||
\(501\) | −11.9886 | −0.535610 | ||||||||
\(502\) | −3.61312 | −0.161262 | ||||||||
\(503\) | −30.7080 | −1.36920 | −0.684600 | − | 0.728919i | \(-0.740023\pi\) | ||||
−0.684600 | + | 0.728919i | \(0.740023\pi\) | |||||||
\(504\) | 3.91550 | 0.174410 | ||||||||
\(505\) | −4.94343 | −0.219980 | ||||||||
\(506\) | 0.860175 | 0.0382395 | ||||||||
\(507\) | −6.12305 | −0.271934 | ||||||||
\(508\) | 19.0115 | 0.843501 | ||||||||
\(509\) | −0.426399 | −0.0188998 | −0.00944991 | − | 0.999955i | \(-0.503008\pi\) | ||||
−0.00944991 | + | 0.999955i | \(0.503008\pi\) | |||||||
\(510\) | −0.783803 | −0.0347074 | ||||||||
\(511\) | 17.8648 | 0.790294 | ||||||||
\(512\) | −22.4527 | −0.992279 | ||||||||
\(513\) | 5.60081 | 0.247282 | ||||||||
\(514\) | 0.0500044 | 0.00220560 | ||||||||
\(515\) | −7.78614 | −0.343098 | ||||||||
\(516\) | 8.15712 | 0.359097 | ||||||||
\(517\) | −32.9372 | −1.44858 | ||||||||
\(518\) | 2.79110 | 0.122634 | ||||||||
\(519\) | −21.0540 | −0.924168 | ||||||||
\(520\) | −7.70152 | −0.337734 | ||||||||
\(521\) | −34.9731 | −1.53220 | −0.766099 | − | 0.642722i | \(-0.777805\pi\) | ||||
−0.766099 | + | 0.642722i | \(0.777805\pi\) | |||||||
\(522\) | 4.95379 | 0.216821 | ||||||||
\(523\) | 19.9792 | 0.873629 | 0.436815 | − | 0.899552i | \(-0.356107\pi\) | ||||
0.436815 | + | 0.899552i | \(0.356107\pi\) | |||||||
\(524\) | 15.3203 | 0.669272 | ||||||||
\(525\) | −5.34397 | −0.233230 | ||||||||
\(526\) | −8.52295 | −0.371618 | ||||||||
\(527\) | −2.75385 | −0.119960 | ||||||||
\(528\) | −7.33174 | −0.319073 | ||||||||
\(529\) | −22.6476 | −0.984680 | ||||||||
\(530\) | −7.26798 | −0.315701 | ||||||||
\(531\) | −7.63345 | −0.331264 | ||||||||
\(532\) | −20.3228 | −0.881106 | ||||||||
\(533\) | −21.4840 | −0.930573 | ||||||||
\(534\) | −3.97871 | −0.172176 | ||||||||
\(535\) | −26.0675 | −1.12700 | ||||||||
\(536\) | 26.7916 | 1.15722 | ||||||||
\(537\) | −23.0346 | −0.994017 | ||||||||
\(538\) | −10.3062 | −0.444330 | ||||||||
\(539\) | 7.73514 | 0.333176 | ||||||||
\(540\) | 2.72160 | 0.117119 | ||||||||
\(541\) | −21.3330 | −0.917176 | −0.458588 | − | 0.888649i | \(-0.651645\pi\) | ||||
−0.458588 | + | 0.888649i | \(0.651645\pi\) | |||||||
\(542\) | 4.83534 | 0.207696 | ||||||||
\(543\) | −12.5707 | −0.539460 | ||||||||
\(544\) | 5.05068 | 0.216546 | ||||||||
\(545\) | −17.0869 | −0.731922 | ||||||||
\(546\) | −2.74040 | −0.117278 | ||||||||
\(547\) | 28.3364 | 1.21158 | 0.605789 | − | 0.795625i | \(-0.292858\pi\) | ||||
0.605789 | + | 0.795625i | \(0.292858\pi\) | |||||||
\(548\) | 19.9025 | 0.850193 | ||||||||
\(549\) | 3.42981 | 0.146381 | ||||||||
\(550\) | −3.72815 | −0.158969 | ||||||||
\(551\) | −55.1491 | −2.34943 | ||||||||
\(552\) | 1.11896 | 0.0476260 | ||||||||
\(553\) | −10.2693 | −0.436693 | ||||||||
\(554\) | −5.88314 | −0.249951 | ||||||||
\(555\) | 4.16118 | 0.176632 | ||||||||
\(556\) | −6.46467 | −0.274163 | ||||||||
\(557\) | −30.0196 | −1.27197 | −0.635985 | − | 0.771701i | \(-0.719406\pi\) | ||||
−0.635985 | + | 0.771701i | \(0.719406\pi\) | |||||||
\(558\) | −1.38545 | −0.0586508 | ||||||||
\(559\) | −12.2452 | −0.517919 | ||||||||
\(560\) | −8.23730 | −0.348090 | ||||||||
\(561\) | 2.88035 | 0.121608 | ||||||||
\(562\) | −6.26108 | −0.264108 | ||||||||
\(563\) | 29.7665 | 1.25451 | 0.627254 | − | 0.778815i | \(-0.284179\pi\) | ||||
0.627254 | + | 0.778815i | \(0.284179\pi\) | |||||||
\(564\) | −19.9760 | −0.841141 | ||||||||
\(565\) | −18.2814 | −0.769103 | ||||||||
\(566\) | −4.45475 | −0.187247 | ||||||||
\(567\) | 2.07714 | 0.0872317 | ||||||||
\(568\) | −4.11424 | −0.172630 | ||||||||
\(569\) | −33.3902 | −1.39979 | −0.699895 | − | 0.714245i | \(-0.746770\pi\) | ||||
−0.699895 | + | 0.714245i | \(0.746770\pi\) | |||||||
\(570\) | 4.38993 | 0.183874 | ||||||||
\(571\) | 2.44786 | 0.102440 | 0.0512198 | − | 0.998687i | \(-0.483689\pi\) | ||||
0.0512198 | + | 0.998687i | \(0.483689\pi\) | |||||||
\(572\) | 13.1950 | 0.551711 | ||||||||
\(573\) | −19.0475 | −0.795719 | ||||||||
\(574\) | 8.56115 | 0.357335 | ||||||||
\(575\) | −1.52718 | −0.0636878 | ||||||||
\(576\) | −2.54990 | −0.106246 | ||||||||
\(577\) | 1.37179 | 0.0571085 | 0.0285543 | − | 0.999592i | \(-0.490910\pi\) | ||||
0.0285543 | + | 0.999592i | \(0.490910\pi\) | |||||||
\(578\) | −0.503095 | −0.0209260 | ||||||||
\(579\) | 2.65031 | 0.110143 | ||||||||
\(580\) | −26.7986 | −1.11275 | ||||||||
\(581\) | −24.8313 | −1.03018 | ||||||||
\(582\) | −3.88181 | −0.160906 | ||||||||
\(583\) | 26.7086 | 1.10616 | ||||||||
\(584\) | 16.2127 | 0.670885 | ||||||||
\(585\) | −4.08559 | −0.168918 | ||||||||
\(586\) | −11.7067 | −0.483599 | ||||||||
\(587\) | −15.2560 | −0.629681 | −0.314841 | − | 0.949145i | \(-0.601951\pi\) | ||||
−0.314841 | + | 0.949145i | \(0.601951\pi\) | |||||||
\(588\) | 4.69127 | 0.193465 | ||||||||
\(589\) | 15.4238 | 0.635528 | ||||||||
\(590\) | −5.98312 | −0.246321 | ||||||||
\(591\) | −21.2170 | −0.872750 | ||||||||
\(592\) | −6.79864 | −0.279422 | ||||||||
\(593\) | −7.63775 | −0.313645 | −0.156822 | − | 0.987627i | \(-0.550125\pi\) | ||||
−0.156822 | + | 0.987627i | \(0.550125\pi\) | |||||||
\(594\) | 1.44909 | 0.0594568 | ||||||||
\(595\) | 3.23611 | 0.132667 | ||||||||
\(596\) | −37.5535 | −1.53825 | ||||||||
\(597\) | −9.57360 | −0.391821 | ||||||||
\(598\) | −0.783141 | −0.0320250 | ||||||||
\(599\) | 5.05547 | 0.206561 | 0.103280 | − | 0.994652i | \(-0.467066\pi\) | ||||
0.103280 | + | 0.994652i | \(0.467066\pi\) | |||||||
\(600\) | −4.84975 | −0.197990 | ||||||||
\(601\) | 31.3523 | 1.27889 | 0.639444 | − | 0.768838i | \(-0.279165\pi\) | ||||
0.639444 | + | 0.768838i | \(0.279165\pi\) | |||||||
\(602\) | 4.87961 | 0.198878 | ||||||||
\(603\) | 14.2127 | 0.578788 | ||||||||
\(604\) | 25.3844 | 1.03288 | ||||||||
\(605\) | 4.21209 | 0.171246 | ||||||||
\(606\) | −1.59632 | −0.0648463 | ||||||||
\(607\) | 22.5778 | 0.916405 | 0.458203 | − | 0.888848i | \(-0.348493\pi\) | ||||
0.458203 | + | 0.888848i | \(0.348493\pi\) | |||||||
\(608\) | −28.2879 | −1.14723 | ||||||||
\(609\) | −20.4528 | −0.828790 | ||||||||
\(610\) | 2.68829 | 0.108846 | ||||||||
\(611\) | 29.9874 | 1.21316 | ||||||||
\(612\) | 1.74690 | 0.0706141 | ||||||||
\(613\) | 21.2044 | 0.856438 | 0.428219 | − | 0.903675i | \(-0.359141\pi\) | ||||
0.428219 | + | 0.903675i | \(0.359141\pi\) | |||||||
\(614\) | 11.4791 | 0.463258 | ||||||||
\(615\) | 12.7636 | 0.514678 | ||||||||
\(616\) | −11.2780 | −0.454404 | ||||||||
\(617\) | 19.8455 | 0.798950 | 0.399475 | − | 0.916744i | \(-0.369193\pi\) | ||||
0.399475 | + | 0.916744i | \(0.369193\pi\) | |||||||
\(618\) | −2.51429 | −0.101139 | ||||||||
\(619\) | 10.7616 | 0.432547 | 0.216273 | − | 0.976333i | \(-0.430610\pi\) | ||||
0.216273 | + | 0.976333i | \(0.430610\pi\) | |||||||
\(620\) | 7.49488 | 0.301002 | ||||||||
\(621\) | 0.593598 | 0.0238203 | ||||||||
\(622\) | −5.62943 | −0.225720 | ||||||||
\(623\) | 16.4270 | 0.658134 | ||||||||
\(624\) | 6.67514 | 0.267219 | ||||||||
\(625\) | −5.51718 | −0.220687 | ||||||||
\(626\) | 5.53193 | 0.221100 | ||||||||
\(627\) | −16.1323 | −0.644262 | ||||||||
\(628\) | −1.74690 | −0.0697087 | ||||||||
\(629\) | 2.67091 | 0.106496 | ||||||||
\(630\) | 1.62807 | 0.0648638 | ||||||||
\(631\) | −19.4830 | −0.775604 | −0.387802 | − | 0.921743i | \(-0.626766\pi\) | ||||
−0.387802 | + | 0.921743i | \(0.626766\pi\) | |||||||
\(632\) | −9.31955 | −0.370712 | ||||||||
\(633\) | −6.62775 | −0.263429 | ||||||||
\(634\) | 0.0221291 | 0.000878859 0 | ||||||||
\(635\) | 16.9554 | 0.672853 | ||||||||
\(636\) | 16.1985 | 0.642311 | ||||||||
\(637\) | −7.04241 | −0.279030 | ||||||||
\(638\) | −14.2686 | −0.564901 | ||||||||
\(639\) | −2.18257 | −0.0863411 | ||||||||
\(640\) | −17.7362 | −0.701084 | ||||||||
\(641\) | −11.4029 | −0.450387 | −0.225193 | − | 0.974314i | \(-0.572301\pi\) | ||||
−0.225193 | + | 0.974314i | \(0.572301\pi\) | |||||||
\(642\) | −8.41768 | −0.332220 | ||||||||
\(643\) | 23.0921 | 0.910665 | 0.455333 | − | 0.890321i | \(-0.349520\pi\) | ||||
0.455333 | + | 0.890321i | \(0.349520\pi\) | |||||||
\(644\) | −2.15390 | −0.0848754 | ||||||||
\(645\) | 7.27490 | 0.286449 | ||||||||
\(646\) | 2.81774 | 0.110862 | ||||||||
\(647\) | −14.1041 | −0.554489 | −0.277244 | − | 0.960799i | \(-0.589421\pi\) | ||||
−0.277244 | + | 0.960799i | \(0.589421\pi\) | |||||||
\(648\) | 1.88504 | 0.0740515 | ||||||||
\(649\) | 21.9870 | 0.863066 | ||||||||
\(650\) | 3.39426 | 0.133134 | ||||||||
\(651\) | 5.72014 | 0.224190 | ||||||||
\(652\) | 19.6453 | 0.769371 | ||||||||
\(653\) | 12.1568 | 0.475733 | 0.237866 | − | 0.971298i | \(-0.423552\pi\) | ||||
0.237866 | + | 0.971298i | \(0.423552\pi\) | |||||||
\(654\) | −5.51767 | −0.215758 | ||||||||
\(655\) | 13.6634 | 0.533873 | ||||||||
\(656\) | −20.8535 | −0.814192 | ||||||||
\(657\) | 8.60069 | 0.335545 | ||||||||
\(658\) | −11.9497 | −0.465848 | ||||||||
\(659\) | −4.63902 | −0.180711 | −0.0903553 | − | 0.995910i | \(-0.528800\pi\) | ||||
−0.0903553 | + | 0.995910i | \(0.528800\pi\) | |||||||
\(660\) | −7.83915 | −0.305139 | ||||||||
\(661\) | −16.4934 | −0.641520 | −0.320760 | − | 0.947161i | \(-0.603938\pi\) | ||||
−0.320760 | + | 0.947161i | \(0.603938\pi\) | |||||||
\(662\) | 6.76902 | 0.263085 | ||||||||
\(663\) | −2.62239 | −0.101845 | ||||||||
\(664\) | −22.5349 | −0.874522 | ||||||||
\(665\) | −18.1248 | −0.702851 | ||||||||
\(666\) | 1.34372 | 0.0520682 | ||||||||
\(667\) | −5.84493 | −0.226317 | ||||||||
\(668\) | 20.9428 | 0.810301 | ||||||||
\(669\) | −7.81608 | −0.302187 | ||||||||
\(670\) | 11.1400 | 0.430375 | ||||||||
\(671\) | −9.87905 | −0.381376 | ||||||||
\(672\) | −10.4910 | −0.404698 | ||||||||
\(673\) | −12.6348 | −0.487035 | −0.243518 | − | 0.969896i | \(-0.578301\pi\) | ||||
−0.243518 | + | 0.969896i | \(0.578301\pi\) | |||||||
\(674\) | −0.273720 | −0.0105433 | ||||||||
\(675\) | −2.57275 | −0.0990253 | ||||||||
\(676\) | 10.6963 | 0.411397 | ||||||||
\(677\) | 5.05087 | 0.194121 | 0.0970603 | − | 0.995279i | \(-0.469056\pi\) | ||||
0.0970603 | + | 0.995279i | \(0.469056\pi\) | |||||||
\(678\) | −5.90339 | −0.226718 | ||||||||
\(679\) | 16.0269 | 0.615057 | ||||||||
\(680\) | 2.93683 | 0.112622 | ||||||||
\(681\) | −4.26210 | −0.163324 | ||||||||
\(682\) | 3.99058 | 0.152807 | ||||||||
\(683\) | −8.38588 | −0.320877 | −0.160438 | − | 0.987046i | \(-0.551291\pi\) | ||||
−0.160438 | + | 0.987046i | \(0.551291\pi\) | |||||||
\(684\) | −9.78404 | −0.374102 | ||||||||
\(685\) | 17.7500 | 0.678192 | ||||||||
\(686\) | 10.1213 | 0.386434 | ||||||||
\(687\) | −2.65238 | −0.101194 | ||||||||
\(688\) | −11.8859 | −0.453146 | ||||||||
\(689\) | −24.3167 | −0.926392 | ||||||||
\(690\) | 0.465263 | 0.0177123 | ||||||||
\(691\) | −45.5839 | −1.73409 | −0.867046 | − | 0.498227i | \(-0.833984\pi\) | ||||
−0.867046 | + | 0.498227i | \(0.833984\pi\) | |||||||
\(692\) | 36.7792 | 1.39813 | ||||||||
\(693\) | −5.98289 | −0.227271 | ||||||||
\(694\) | 10.2104 | 0.387582 | ||||||||
\(695\) | −5.76549 | −0.218698 | ||||||||
\(696\) | −18.5613 | −0.703565 | ||||||||
\(697\) | 8.19250 | 0.310313 | ||||||||
\(698\) | 2.95844 | 0.111978 | ||||||||
\(699\) | 24.7740 | 0.937040 | ||||||||
\(700\) | 9.33536 | 0.352843 | ||||||||
\(701\) | 5.83362 | 0.220333 | 0.110166 | − | 0.993913i | \(-0.464862\pi\) | ||||
0.110166 | + | 0.993913i | \(0.464862\pi\) | |||||||
\(702\) | −1.31931 | −0.0497942 | ||||||||
\(703\) | −14.9593 | −0.564200 | ||||||||
\(704\) | 7.34460 | 0.276810 | ||||||||
\(705\) | −17.8155 | −0.670971 | ||||||||
\(706\) | 10.5019 | 0.395243 | ||||||||
\(707\) | 6.59079 | 0.247872 | ||||||||
\(708\) | 13.3348 | 0.501154 | ||||||||
\(709\) | 24.6438 | 0.925517 | 0.462758 | − | 0.886484i | \(-0.346860\pi\) | ||||
0.462758 | + | 0.886484i | \(0.346860\pi\) | |||||||
\(710\) | −1.71070 | −0.0642016 | ||||||||
\(711\) | −4.94394 | −0.185412 | ||||||||
\(712\) | 14.9078 | 0.558694 | ||||||||
\(713\) | 1.63468 | 0.0612193 | ||||||||
\(714\) | 1.04500 | 0.0391081 | ||||||||
\(715\) | 11.7679 | 0.440096 | ||||||||
\(716\) | 40.2391 | 1.50380 | ||||||||
\(717\) | −26.1059 | −0.974941 | ||||||||
\(718\) | 3.83123 | 0.142980 | ||||||||
\(719\) | 10.4581 | 0.390023 | 0.195012 | − | 0.980801i | \(-0.437526\pi\) | ||||
0.195012 | + | 0.980801i | \(0.437526\pi\) | |||||||
\(720\) | −3.96569 | −0.147793 | ||||||||
\(721\) | 10.3808 | 0.386601 | ||||||||
\(722\) | −6.22284 | −0.231590 | ||||||||
\(723\) | −28.0678 | −1.04385 | ||||||||
\(724\) | 21.9597 | 0.816125 | ||||||||
\(725\) | 25.3329 | 0.940842 | ||||||||
\(726\) | 1.36016 | 0.0504803 | ||||||||
\(727\) | −15.0902 | −0.559666 | −0.279833 | − | 0.960049i | \(-0.590279\pi\) | ||||
−0.279833 | + | 0.960049i | \(0.590279\pi\) | |||||||
\(728\) | 10.2680 | 0.380557 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.74124 | 0.249505 | ||||||||
\(731\) | 4.66949 | 0.172707 | ||||||||
\(732\) | −5.99152 | −0.221453 | ||||||||
\(733\) | −4.49988 | −0.166207 | −0.0831035 | − | 0.996541i | \(-0.526483\pi\) | ||||
−0.0831035 | + | 0.996541i | \(0.526483\pi\) | |||||||
\(734\) | 7.23973 | 0.267223 | ||||||||
\(735\) | 4.18389 | 0.154325 | ||||||||
\(736\) | −2.99807 | −0.110510 | ||||||||
\(737\) | −40.9377 | −1.50796 | ||||||||
\(738\) | 4.12160 | 0.151718 | ||||||||
\(739\) | 32.6044 | 1.19937 | 0.599686 | − | 0.800235i | \(-0.295292\pi\) | ||||
0.599686 | + | 0.800235i | \(0.295292\pi\) | |||||||
\(740\) | −7.26915 | −0.267219 | ||||||||
\(741\) | 14.6875 | 0.539560 | ||||||||
\(742\) | 9.68997 | 0.355730 | ||||||||
\(743\) | 23.8912 | 0.876483 | 0.438241 | − | 0.898857i | \(-0.355602\pi\) | ||||
0.438241 | + | 0.898857i | \(0.355602\pi\) | |||||||
\(744\) | 5.19113 | 0.190316 | ||||||||
\(745\) | −33.4919 | −1.22705 | ||||||||
\(746\) | −0.837493 | −0.0306628 | ||||||||
\(747\) | −11.9546 | −0.437394 | ||||||||
\(748\) | −5.03167 | −0.183976 | ||||||||
\(749\) | 34.7543 | 1.26989 | ||||||||
\(750\) | −5.93554 | −0.216735 | ||||||||
\(751\) | −36.7164 | −1.33980 | −0.669901 | − | 0.742450i | \(-0.733663\pi\) | ||||
−0.669901 | + | 0.742450i | \(0.733663\pi\) | |||||||
\(752\) | 29.1074 | 1.06144 | ||||||||
\(753\) | 7.18179 | 0.261719 | ||||||||
\(754\) | 12.9908 | 0.473096 | ||||||||
\(755\) | 22.6390 | 0.823917 | ||||||||
\(756\) | −3.62855 | −0.131969 | ||||||||
\(757\) | 11.4179 | 0.414989 | 0.207495 | − | 0.978236i | \(-0.433469\pi\) | ||||
0.207495 | + | 0.978236i | \(0.433469\pi\) | |||||||
\(758\) | 12.7405 | 0.462758 | ||||||||
\(759\) | −1.70977 | −0.0620607 | ||||||||
\(760\) | −16.4486 | −0.596654 | ||||||||
\(761\) | −3.18226 | −0.115357 | −0.0576784 | − | 0.998335i | \(-0.518370\pi\) | ||||
−0.0576784 | + | 0.998335i | \(0.518370\pi\) | |||||||
\(762\) | 5.47520 | 0.198346 | ||||||||
\(763\) | 22.7810 | 0.824726 | ||||||||
\(764\) | 33.2739 | 1.20381 | ||||||||
\(765\) | 1.55796 | 0.0563283 | ||||||||
\(766\) | 16.2396 | 0.586762 | ||||||||
\(767\) | −20.0179 | −0.722805 | ||||||||
\(768\) | −0.627532 | −0.0226441 | ||||||||
\(769\) | 4.91157 | 0.177116 | 0.0885578 | − | 0.996071i | \(-0.471774\pi\) | ||||
0.0885578 | + | 0.996071i | \(0.471774\pi\) | |||||||
\(770\) | −4.68940 | −0.168994 | ||||||||
\(771\) | −0.0993936 | −0.00357957 | ||||||||
\(772\) | −4.62982 | −0.166631 | ||||||||
\(773\) | −26.7153 | −0.960884 | −0.480442 | − | 0.877026i | \(-0.659524\pi\) | ||||
−0.480442 | + | 0.877026i | \(0.659524\pi\) | |||||||
\(774\) | 2.34920 | 0.0844401 | ||||||||
\(775\) | −7.08499 | −0.254500 | ||||||||
\(776\) | 14.5447 | 0.522126 | ||||||||
\(777\) | −5.54786 | −0.199028 | ||||||||
\(778\) | −13.1649 | −0.471983 | ||||||||
\(779\) | −45.8847 | −1.64399 | ||||||||
\(780\) | 7.13710 | 0.255549 | ||||||||
\(781\) | 6.28656 | 0.224951 | ||||||||
\(782\) | 0.298636 | 0.0106792 | ||||||||
\(783\) | −9.84663 | −0.351890 | ||||||||
\(784\) | −6.83574 | −0.244134 | ||||||||
\(785\) | −1.55796 | −0.0556061 | ||||||||
\(786\) | 4.41216 | 0.157377 | ||||||||
\(787\) | −48.5491 | −1.73059 | −0.865294 | − | 0.501265i | \(-0.832868\pi\) | ||||
−0.865294 | + | 0.501265i | \(0.832868\pi\) | |||||||
\(788\) | 37.0638 | 1.32034 | ||||||||
\(789\) | 16.9410 | 0.603117 | ||||||||
\(790\) | −3.87508 | −0.137869 | ||||||||
\(791\) | 24.3735 | 0.866621 | ||||||||
\(792\) | −5.42958 | −0.192932 | ||||||||
\(793\) | 8.99431 | 0.319397 | ||||||||
\(794\) | 13.2607 | 0.470606 | ||||||||
\(795\) | 14.4465 | 0.512366 | ||||||||
\(796\) | 16.7241 | 0.592769 | ||||||||
\(797\) | 26.6633 | 0.944463 | 0.472232 | − | 0.881475i | \(-0.343449\pi\) | ||||
0.472232 | + | 0.881475i | \(0.343449\pi\) | |||||||
\(798\) | −5.85284 | −0.207188 | ||||||||
\(799\) | −11.4351 | −0.404546 | ||||||||
\(800\) | 12.9942 | 0.459413 | ||||||||
\(801\) | 7.90847 | 0.279432 | ||||||||
\(802\) | 6.25401 | 0.220837 | ||||||||
\(803\) | −24.7730 | −0.874220 | ||||||||
\(804\) | −24.8282 | −0.875622 | ||||||||
\(805\) | −1.92095 | −0.0677044 | ||||||||
\(806\) | −3.63319 | −0.127974 | ||||||||
\(807\) | 20.4855 | 0.721125 | ||||||||
\(808\) | 5.98126 | 0.210420 | ||||||||
\(809\) | −13.1255 | −0.461466 | −0.230733 | − | 0.973017i | \(-0.574112\pi\) | ||||
−0.230733 | + | 0.973017i | \(0.574112\pi\) | |||||||
\(810\) | 0.783803 | 0.0275400 | ||||||||
\(811\) | 43.5021 | 1.52756 | 0.763782 | − | 0.645475i | \(-0.223340\pi\) | ||||
0.763782 | + | 0.645475i | \(0.223340\pi\) | |||||||
\(812\) | 35.7290 | 1.25384 | ||||||||
\(813\) | −9.61120 | −0.337079 | ||||||||
\(814\) | −3.87039 | −0.135657 | ||||||||
\(815\) | 17.5206 | 0.613721 | ||||||||
\(816\) | −2.54544 | −0.0891081 | ||||||||
\(817\) | −26.1530 | −0.914976 | ||||||||
\(818\) | 7.92130 | 0.276962 | ||||||||
\(819\) | 5.44708 | 0.190336 | ||||||||
\(820\) | −22.2967 | −0.778634 | ||||||||
\(821\) | −36.6761 | −1.28001 | −0.640003 | − | 0.768372i | \(-0.721067\pi\) | ||||
−0.640003 | + | 0.768372i | \(0.721067\pi\) | |||||||
\(822\) | 5.73179 | 0.199919 | ||||||||
\(823\) | 7.32603 | 0.255369 | 0.127685 | − | 0.991815i | \(-0.459245\pi\) | ||||
0.127685 | + | 0.991815i | \(0.459245\pi\) | |||||||
\(824\) | 9.42077 | 0.328188 | ||||||||
\(825\) | 7.41043 | 0.257998 | ||||||||
\(826\) | 7.97695 | 0.277553 | ||||||||
\(827\) | 1.72713 | 0.0600581 | 0.0300290 | − | 0.999549i | \(-0.490440\pi\) | ||||
0.0300290 | + | 0.999549i | \(0.490440\pi\) | |||||||
\(828\) | −1.03695 | −0.0360366 | ||||||||
\(829\) | −16.3117 | −0.566527 | −0.283264 | − | 0.959042i | \(-0.591417\pi\) | ||||
−0.283264 | + | 0.959042i | \(0.591417\pi\) | |||||||
\(830\) | −9.37001 | −0.325238 | ||||||||
\(831\) | 11.6939 | 0.405657 | ||||||||
\(832\) | −6.68684 | −0.231825 | ||||||||
\(833\) | 2.68549 | 0.0930467 | ||||||||
\(834\) | −1.86178 | −0.0644683 | ||||||||
\(835\) | 18.6778 | 0.646371 | ||||||||
\(836\) | 28.1814 | 0.974676 | ||||||||
\(837\) | 2.75385 | 0.0951871 | ||||||||
\(838\) | −0.662638 | −0.0228905 | ||||||||
\(839\) | −37.1343 | −1.28202 | −0.641009 | − | 0.767533i | \(-0.721484\pi\) | ||||
−0.641009 | + | 0.767533i | \(0.721484\pi\) | |||||||
\(840\) | −6.10020 | −0.210477 | ||||||||
\(841\) | 67.9561 | 2.34331 | ||||||||
\(842\) | −3.86731 | −0.133276 | ||||||||
\(843\) | 12.4451 | 0.428633 | ||||||||
\(844\) | 11.5780 | 0.398531 | ||||||||
\(845\) | 9.53948 | 0.328168 | ||||||||
\(846\) | −5.75296 | −0.197791 | ||||||||
\(847\) | −5.61574 | −0.192959 | ||||||||
\(848\) | −23.6031 | −0.810534 | ||||||||
\(849\) | 8.85469 | 0.303892 | ||||||||
\(850\) | −1.29434 | −0.0443954 | ||||||||
\(851\) | −1.58545 | −0.0543484 | ||||||||
\(852\) | 3.81272 | 0.130622 | ||||||||
\(853\) | −11.1651 | −0.382284 | −0.191142 | − | 0.981562i | \(-0.561219\pi\) | ||||
−0.191142 | + | 0.981562i | \(0.561219\pi\) | |||||||
\(854\) | −3.58414 | −0.122647 | ||||||||
\(855\) | −8.72586 | −0.298418 | ||||||||
\(856\) | 31.5402 | 1.07802 | ||||||||
\(857\) | −43.7997 | −1.49617 | −0.748085 | − | 0.663603i | \(-0.769027\pi\) | ||||
−0.748085 | + | 0.663603i | \(0.769027\pi\) | |||||||
\(858\) | 3.80008 | 0.129733 | ||||||||
\(859\) | 14.6278 | 0.499095 | 0.249547 | − | 0.968363i | \(-0.419718\pi\) | ||||
0.249547 | + | 0.968363i | \(0.419718\pi\) | |||||||
\(860\) | −12.7085 | −0.433356 | ||||||||
\(861\) | −17.0170 | −0.579937 | ||||||||
\(862\) | −5.51489 | −0.187838 | ||||||||
\(863\) | −14.5636 | −0.495750 | −0.247875 | − | 0.968792i | \(-0.579732\pi\) | ||||
−0.247875 | + | 0.968792i | \(0.579732\pi\) | |||||||
\(864\) | −5.05068 | −0.171828 | ||||||||
\(865\) | 32.8014 | 1.11528 | ||||||||
\(866\) | −12.1039 | −0.411307 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −9.99249 | −0.339167 | ||||||||
\(869\) | 14.2403 | 0.483068 | ||||||||
\(870\) | −7.71781 | −0.261658 | ||||||||
\(871\) | 37.2714 | 1.26289 | ||||||||
\(872\) | 20.6741 | 0.700115 | ||||||||
\(873\) | 7.71587 | 0.261143 | ||||||||
\(874\) | −1.67260 | −0.0565767 | ||||||||
\(875\) | 24.5062 | 0.828462 | ||||||||
\(876\) | −15.0245 | −0.507631 | ||||||||
\(877\) | −46.8453 | −1.58185 | −0.790926 | − | 0.611912i | \(-0.790401\pi\) | ||||
−0.790926 | + | 0.611912i | \(0.790401\pi\) | |||||||
\(878\) | 7.96878 | 0.268933 | ||||||||
\(879\) | 23.2694 | 0.784856 | ||||||||
\(880\) | 11.4226 | 0.385055 | ||||||||
\(881\) | −31.3706 | −1.05690 | −0.528452 | − | 0.848963i | \(-0.677227\pi\) | ||||
−0.528452 | + | 0.848963i | \(0.677227\pi\) | |||||||
\(882\) | 1.35105 | 0.0454924 | ||||||||
\(883\) | 17.0836 | 0.574909 | 0.287454 | − | 0.957794i | \(-0.407191\pi\) | ||||
0.287454 | + | 0.957794i | \(0.407191\pi\) | |||||||
\(884\) | 4.58105 | 0.154077 | ||||||||
\(885\) | 11.8926 | 0.399767 | ||||||||
\(886\) | −8.71410 | −0.292756 | ||||||||
\(887\) | −0.155587 | −0.00522409 | −0.00261205 | − | 0.999997i | \(-0.500831\pi\) | ||||
−0.00261205 | + | 0.999997i | \(0.500831\pi\) | |||||||
\(888\) | −5.03479 | −0.168956 | ||||||||
\(889\) | −22.6056 | −0.758168 | ||||||||
\(890\) | 6.19868 | 0.207780 | ||||||||
\(891\) | −2.88035 | −0.0964953 | ||||||||
\(892\) | 13.6539 | 0.457165 | ||||||||
\(893\) | 64.0461 | 2.14322 | ||||||||
\(894\) | −10.8152 | −0.361713 | ||||||||
\(895\) | 35.8871 | 1.19957 | ||||||||
\(896\) | 23.6466 | 0.789977 | ||||||||
\(897\) | 1.55665 | 0.0519749 | ||||||||
\(898\) | 12.6800 | 0.423137 | ||||||||
\(899\) | −27.1162 | −0.904375 | ||||||||
\(900\) | 4.49433 | 0.149811 | ||||||||
\(901\) | 9.27271 | 0.308919 | ||||||||
\(902\) | −11.8717 | −0.395283 | ||||||||
\(903\) | −9.69919 | −0.322769 | ||||||||
\(904\) | 22.1194 | 0.735680 | ||||||||
\(905\) | 19.5847 | 0.651016 | ||||||||
\(906\) | 7.31055 | 0.242877 | ||||||||
\(907\) | 28.2458 | 0.937887 | 0.468943 | − | 0.883228i | \(-0.344635\pi\) | ||||
0.468943 | + | 0.883228i | \(0.344635\pi\) | |||||||
\(908\) | 7.44545 | 0.247086 | ||||||||
\(909\) | 3.17301 | 0.105242 | ||||||||
\(910\) | 4.26944 | 0.141530 | ||||||||
\(911\) | −14.0118 | −0.464231 | −0.232116 | − | 0.972688i | \(-0.574565\pi\) | ||||
−0.232116 | + | 0.972688i | \(0.574565\pi\) | |||||||
\(912\) | 14.2565 | 0.472080 | ||||||||
\(913\) | 34.4333 | 1.13958 | ||||||||
\(914\) | 0.878440 | 0.0290562 | ||||||||
\(915\) | −5.34351 | −0.176651 | ||||||||
\(916\) | 4.63343 | 0.153093 | ||||||||
\(917\) | −18.2166 | −0.601565 | ||||||||
\(918\) | 0.503095 | 0.0166046 | ||||||||
\(919\) | 38.2987 | 1.26336 | 0.631679 | − | 0.775230i | \(-0.282366\pi\) | ||||
0.631679 | + | 0.775230i | \(0.282366\pi\) | |||||||
\(920\) | −1.74329 | −0.0574747 | ||||||||
\(921\) | −22.8169 | −0.751844 | ||||||||
\(922\) | −15.5539 | −0.512242 | ||||||||
\(923\) | −5.72356 | −0.188393 | ||||||||
\(924\) | 10.4515 | 0.343829 | ||||||||
\(925\) | 6.87160 | 0.225937 | ||||||||
\(926\) | −15.7371 | −0.517153 | ||||||||
\(927\) | 4.99764 | 0.164144 | ||||||||
\(928\) | 49.7322 | 1.63254 | ||||||||
\(929\) | −35.9691 | −1.18011 | −0.590054 | − | 0.807364i | \(-0.700894\pi\) | ||||
−0.590054 | + | 0.807364i | \(0.700894\pi\) | |||||||
\(930\) | 2.15848 | 0.0707793 | ||||||||
\(931\) | −15.0409 | −0.492946 | ||||||||
\(932\) | −43.2776 | −1.41761 | ||||||||
\(933\) | 11.1896 | 0.366331 | ||||||||
\(934\) | −15.2789 | −0.499942 | ||||||||
\(935\) | −4.48748 | −0.146756 | ||||||||
\(936\) | 4.94333 | 0.161578 | ||||||||
\(937\) | −10.0553 | −0.328493 | −0.164247 | − | 0.986419i | \(-0.552519\pi\) | ||||
−0.164247 | + | 0.986419i | \(0.552519\pi\) | |||||||
\(938\) | −14.8523 | −0.484945 | ||||||||
\(939\) | −10.9958 | −0.358834 | ||||||||
\(940\) | 31.1219 | 1.01508 | ||||||||
\(941\) | −19.1212 | −0.623332 | −0.311666 | − | 0.950192i | \(-0.600887\pi\) | ||||
−0.311666 | + | 0.950192i | \(0.600887\pi\) | |||||||
\(942\) | −0.503095 | −0.0163917 | ||||||||
\(943\) | −4.86305 | −0.158363 | ||||||||
\(944\) | −19.4305 | −0.632408 | ||||||||
\(945\) | −3.23611 | −0.105271 | ||||||||
\(946\) | −6.76651 | −0.219998 | ||||||||
\(947\) | 42.2977 | 1.37449 | 0.687245 | − | 0.726426i | \(-0.258820\pi\) | ||||
0.687245 | + | 0.726426i | \(0.258820\pi\) | |||||||
\(948\) | 8.63655 | 0.280502 | ||||||||
\(949\) | 22.5544 | 0.732147 | ||||||||
\(950\) | 7.24935 | 0.235200 | ||||||||
\(951\) | −0.0439860 | −0.00142634 | ||||||||
\(952\) | −3.91550 | −0.126902 | ||||||||
\(953\) | 16.4739 | 0.533643 | 0.266822 | − | 0.963746i | \(-0.414027\pi\) | ||||
0.266822 | + | 0.963746i | \(0.414027\pi\) | |||||||
\(954\) | 4.66505 | 0.151037 | ||||||||
\(955\) | 29.6752 | 0.960268 | ||||||||
\(956\) | 45.6042 | 1.47495 | ||||||||
\(957\) | 28.3617 | 0.916804 | ||||||||
\(958\) | 3.48548 | 0.112611 | ||||||||
\(959\) | −23.6650 | −0.764183 | ||||||||
\(960\) | 3.97265 | 0.128217 | ||||||||
\(961\) | −23.4163 | −0.755364 | ||||||||
\(962\) | 3.52377 | 0.113611 | ||||||||
\(963\) | 16.7318 | 0.539175 | ||||||||
\(964\) | 49.0315 | 1.57920 | ||||||||
\(965\) | −4.12908 | −0.132920 | ||||||||
\(966\) | −0.620309 | −0.0199581 | ||||||||
\(967\) | −21.3418 | −0.686305 | −0.343152 | − | 0.939280i | \(-0.611495\pi\) | ||||
−0.343152 | + | 0.939280i | \(0.611495\pi\) | |||||||
\(968\) | −5.09638 | −0.163804 | ||||||||
\(969\) | −5.60081 | −0.179924 | ||||||||
\(970\) | 6.04772 | 0.194181 | ||||||||
\(971\) | −6.77170 | −0.217314 | −0.108657 | − | 0.994079i | \(-0.534655\pi\) | ||||
−0.108657 | + | 0.994079i | \(0.534655\pi\) | |||||||
\(972\) | −1.74690 | −0.0560317 | ||||||||
\(973\) | 7.68679 | 0.246427 | ||||||||
\(974\) | 1.75753 | 0.0563150 | ||||||||
\(975\) | −6.74677 | −0.216070 | ||||||||
\(976\) | 8.73036 | 0.279452 | ||||||||
\(977\) | 54.5680 | 1.74578 | 0.872892 | − | 0.487913i | \(-0.162242\pi\) | ||||
0.872892 | + | 0.487913i | \(0.162242\pi\) | |||||||
\(978\) | 5.65773 | 0.180914 | ||||||||
\(979\) | −22.7792 | −0.728025 | ||||||||
\(980\) | −7.30882 | −0.233472 | ||||||||
\(981\) | 10.9675 | 0.350164 | ||||||||
\(982\) | 6.93994 | 0.221462 | ||||||||
\(983\) | −58.4317 | −1.86368 | −0.931841 | − | 0.362868i | \(-0.881798\pi\) | ||||
−0.931841 | + | 0.362868i | \(0.881798\pi\) | |||||||
\(984\) | −15.4432 | −0.492312 | ||||||||
\(985\) | 33.0553 | 1.05323 | ||||||||
\(986\) | −4.95379 | −0.157761 | ||||||||
\(987\) | 23.7524 | 0.756047 | ||||||||
\(988\) | −25.6576 | −0.816277 | ||||||||
\(989\) | −2.77180 | −0.0881381 | ||||||||
\(990\) | −2.25763 | −0.0717520 | ||||||||
\(991\) | −41.1223 | −1.30629 | −0.653146 | − | 0.757232i | \(-0.726551\pi\) | ||||
−0.653146 | + | 0.757232i | \(0.726551\pi\) | |||||||
\(992\) | −13.9088 | −0.441606 | ||||||||
\(993\) | −13.4548 | −0.426974 | ||||||||
\(994\) | 2.28078 | 0.0723420 | ||||||||
\(995\) | 14.9153 | 0.472847 | ||||||||
\(996\) | 20.8834 | 0.661715 | ||||||||
\(997\) | −39.1177 | −1.23887 | −0.619435 | − | 0.785048i | \(-0.712638\pi\) | ||||
−0.619435 | + | 0.785048i | \(0.712638\pi\) | |||||||
\(998\) | 9.56245 | 0.302694 | ||||||||
\(999\) | −2.67091 | −0.0845039 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8007.2.a.e.1.21 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.e.1.21 | ✓ | 46 | 1.1 | even | 1 | trivial |