Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.495377 | −0.350284 | −0.175142 | − | 0.984543i | \(-0.556039\pi\) | ||||
−0.175142 | + | 0.984543i | \(0.556039\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.75460 | −0.877301 | ||||||||
\(5\) | −3.92669 | −1.75607 | −0.878035 | − | 0.478597i | \(-0.841146\pi\) | ||||
−0.878035 | + | 0.478597i | \(0.841146\pi\) | |||||||
\(6\) | 0.495377 | 0.202237 | ||||||||
\(7\) | 0.792012 | 0.299352 | 0.149676 | − | 0.988735i | \(-0.452177\pi\) | ||||
0.149676 | + | 0.988735i | \(0.452177\pi\) | |||||||
\(8\) | 1.85994 | 0.657589 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.94519 | 0.615124 | ||||||||
\(11\) | 3.60141 | 1.08587 | 0.542933 | − | 0.839776i | \(-0.317314\pi\) | ||||
0.542933 | + | 0.839776i | \(0.317314\pi\) | |||||||
\(12\) | 1.75460 | 0.506510 | ||||||||
\(13\) | −4.35807 | −1.20871 | −0.604356 | − | 0.796714i | \(-0.706570\pi\) | ||||
−0.604356 | + | 0.796714i | \(0.706570\pi\) | |||||||
\(14\) | −0.392345 | −0.104858 | ||||||||
\(15\) | 3.92669 | 1.01387 | ||||||||
\(16\) | 2.58783 | 0.646957 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −0.495377 | −0.116761 | ||||||||
\(19\) | 5.25644 | 1.20591 | 0.602955 | − | 0.797775i | \(-0.293990\pi\) | ||||
0.602955 | + | 0.797775i | \(0.293990\pi\) | |||||||
\(20\) | 6.88978 | 1.54060 | ||||||||
\(21\) | −0.792012 | −0.172831 | ||||||||
\(22\) | −1.78406 | −0.380362 | ||||||||
\(23\) | −4.05074 | −0.844638 | −0.422319 | − | 0.906447i | \(-0.638784\pi\) | ||||
−0.422319 | + | 0.906447i | \(0.638784\pi\) | |||||||
\(24\) | −1.85994 | −0.379659 | ||||||||
\(25\) | 10.4189 | 2.08378 | ||||||||
\(26\) | 2.15889 | 0.423393 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.38967 | −0.262622 | ||||||||
\(29\) | −2.38181 | −0.442291 | −0.221145 | − | 0.975241i | \(-0.570980\pi\) | ||||
−0.221145 | + | 0.975241i | \(0.570980\pi\) | |||||||
\(30\) | −1.94519 | −0.355142 | ||||||||
\(31\) | −3.27296 | −0.587841 | −0.293920 | − | 0.955830i | \(-0.594960\pi\) | ||||
−0.293920 | + | 0.955830i | \(0.594960\pi\) | |||||||
\(32\) | −5.00184 | −0.884209 | ||||||||
\(33\) | −3.60141 | −0.626925 | ||||||||
\(34\) | −0.495377 | −0.0849565 | ||||||||
\(35\) | −3.10999 | −0.525684 | ||||||||
\(36\) | −1.75460 | −0.292434 | ||||||||
\(37\) | −8.28956 | −1.36280 | −0.681398 | − | 0.731913i | \(-0.738628\pi\) | ||||
−0.681398 | + | 0.731913i | \(0.738628\pi\) | |||||||
\(38\) | −2.60392 | −0.422411 | ||||||||
\(39\) | 4.35807 | 0.697850 | ||||||||
\(40\) | −7.30342 | −1.15477 | ||||||||
\(41\) | 5.75442 | 0.898690 | 0.449345 | − | 0.893358i | \(-0.351657\pi\) | ||||
0.449345 | + | 0.893358i | \(0.351657\pi\) | |||||||
\(42\) | 0.392345 | 0.0605401 | ||||||||
\(43\) | 2.25024 | 0.343159 | 0.171580 | − | 0.985170i | \(-0.445113\pi\) | ||||
0.171580 | + | 0.985170i | \(0.445113\pi\) | |||||||
\(44\) | −6.31904 | −0.952631 | ||||||||
\(45\) | −3.92669 | −0.585357 | ||||||||
\(46\) | 2.00664 | 0.295864 | ||||||||
\(47\) | −12.5423 | −1.82948 | −0.914740 | − | 0.404043i | \(-0.867605\pi\) | ||||
−0.914740 | + | 0.404043i | \(0.867605\pi\) | |||||||
\(48\) | −2.58783 | −0.373521 | ||||||||
\(49\) | −6.37272 | −0.910388 | ||||||||
\(50\) | −5.16128 | −0.729916 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 7.64668 | 1.06040 | ||||||||
\(53\) | −9.15188 | −1.25711 | −0.628554 | − | 0.777766i | \(-0.716353\pi\) | ||||
−0.628554 | + | 0.777766i | \(0.716353\pi\) | |||||||
\(54\) | 0.495377 | 0.0674123 | ||||||||
\(55\) | −14.1416 | −1.90686 | ||||||||
\(56\) | 1.47310 | 0.196851 | ||||||||
\(57\) | −5.25644 | −0.696232 | ||||||||
\(58\) | 1.17989 | 0.154928 | ||||||||
\(59\) | −11.9524 | −1.55607 | −0.778033 | − | 0.628223i | \(-0.783782\pi\) | ||||
−0.778033 | + | 0.628223i | \(0.783782\pi\) | |||||||
\(60\) | −6.88978 | −0.889466 | ||||||||
\(61\) | 5.37127 | 0.687720 | 0.343860 | − | 0.939021i | \(-0.388265\pi\) | ||||
0.343860 | + | 0.939021i | \(0.388265\pi\) | |||||||
\(62\) | 1.62135 | 0.205911 | ||||||||
\(63\) | 0.792012 | 0.0997841 | ||||||||
\(64\) | −2.69786 | −0.337233 | ||||||||
\(65\) | 17.1128 | 2.12258 | ||||||||
\(66\) | 1.78406 | 0.219602 | ||||||||
\(67\) | 7.52829 | 0.919727 | 0.459863 | − | 0.887990i | \(-0.347898\pi\) | ||||
0.459863 | + | 0.887990i | \(0.347898\pi\) | |||||||
\(68\) | −1.75460 | −0.212777 | ||||||||
\(69\) | 4.05074 | 0.487652 | ||||||||
\(70\) | 1.54062 | 0.184139 | ||||||||
\(71\) | 8.83540 | 1.04857 | 0.524284 | − | 0.851543i | \(-0.324333\pi\) | ||||
0.524284 | + | 0.851543i | \(0.324333\pi\) | |||||||
\(72\) | 1.85994 | 0.219196 | ||||||||
\(73\) | −8.78515 | −1.02822 | −0.514112 | − | 0.857723i | \(-0.671879\pi\) | ||||
−0.514112 | + | 0.857723i | \(0.671879\pi\) | |||||||
\(74\) | 4.10646 | 0.477366 | ||||||||
\(75\) | −10.4189 | −1.20307 | ||||||||
\(76\) | −9.22295 | −1.05795 | ||||||||
\(77\) | 2.85236 | 0.325057 | ||||||||
\(78\) | −2.15889 | −0.244446 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | −10.1616 | −1.13610 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.85061 | −0.314797 | ||||||||
\(83\) | 8.41255 | 0.923398 | 0.461699 | − | 0.887037i | \(-0.347240\pi\) | ||||
0.461699 | + | 0.887037i | \(0.347240\pi\) | |||||||
\(84\) | 1.38967 | 0.151625 | ||||||||
\(85\) | −3.92669 | −0.425909 | ||||||||
\(86\) | −1.11472 | −0.120203 | ||||||||
\(87\) | 2.38181 | 0.255357 | ||||||||
\(88\) | 6.69842 | 0.714054 | ||||||||
\(89\) | 8.58421 | 0.909925 | 0.454962 | − | 0.890511i | \(-0.349653\pi\) | ||||
0.454962 | + | 0.890511i | \(0.349653\pi\) | |||||||
\(90\) | 1.94519 | 0.205041 | ||||||||
\(91\) | −3.45165 | −0.361831 | ||||||||
\(92\) | 7.10744 | 0.741001 | ||||||||
\(93\) | 3.27296 | 0.339390 | ||||||||
\(94\) | 6.21316 | 0.640838 | ||||||||
\(95\) | −20.6404 | −2.11766 | ||||||||
\(96\) | 5.00184 | 0.510498 | ||||||||
\(97\) | 5.86365 | 0.595363 | 0.297682 | − | 0.954665i | \(-0.403787\pi\) | ||||
0.297682 | + | 0.954665i | \(0.403787\pi\) | |||||||
\(98\) | 3.15690 | 0.318895 | ||||||||
\(99\) | 3.60141 | 0.361955 | ||||||||
\(100\) | −18.2810 | −1.82810 | ||||||||
\(101\) | 17.3359 | 1.72499 | 0.862495 | − | 0.506065i | \(-0.168900\pi\) | ||||
0.862495 | + | 0.506065i | \(0.168900\pi\) | |||||||
\(102\) | 0.495377 | 0.0490496 | ||||||||
\(103\) | −5.69401 | −0.561048 | −0.280524 | − | 0.959847i | \(-0.590508\pi\) | ||||
−0.280524 | + | 0.959847i | \(0.590508\pi\) | |||||||
\(104\) | −8.10577 | −0.794836 | ||||||||
\(105\) | 3.10999 | 0.303504 | ||||||||
\(106\) | 4.53363 | 0.440345 | ||||||||
\(107\) | 10.6660 | 1.03112 | 0.515561 | − | 0.856853i | \(-0.327584\pi\) | ||||
0.515561 | + | 0.856853i | \(0.327584\pi\) | |||||||
\(108\) | 1.75460 | 0.168837 | ||||||||
\(109\) | 12.5951 | 1.20639 | 0.603194 | − | 0.797594i | \(-0.293894\pi\) | ||||
0.603194 | + | 0.797594i | \(0.293894\pi\) | |||||||
\(110\) | 7.00544 | 0.667942 | ||||||||
\(111\) | 8.28956 | 0.786810 | ||||||||
\(112\) | 2.04959 | 0.193668 | ||||||||
\(113\) | −20.5979 | −1.93769 | −0.968845 | − | 0.247667i | \(-0.920336\pi\) | ||||
−0.968845 | + | 0.247667i | \(0.920336\pi\) | |||||||
\(114\) | 2.60392 | 0.243879 | ||||||||
\(115\) | 15.9060 | 1.48324 | ||||||||
\(116\) | 4.17913 | 0.388022 | ||||||||
\(117\) | −4.35807 | −0.402904 | ||||||||
\(118\) | 5.92093 | 0.545066 | ||||||||
\(119\) | 0.792012 | 0.0726036 | ||||||||
\(120\) | 7.30342 | 0.666708 | ||||||||
\(121\) | 1.97016 | 0.179105 | ||||||||
\(122\) | −2.66080 | −0.240898 | ||||||||
\(123\) | −5.75442 | −0.518859 | ||||||||
\(124\) | 5.74274 | 0.515713 | ||||||||
\(125\) | −21.2783 | −1.90319 | ||||||||
\(126\) | −0.392345 | −0.0349528 | ||||||||
\(127\) | 6.86580 | 0.609241 | 0.304621 | − | 0.952474i | \(-0.401470\pi\) | ||||
0.304621 | + | 0.952474i | \(0.401470\pi\) | |||||||
\(128\) | 11.3401 | 1.00234 | ||||||||
\(129\) | −2.25024 | −0.198123 | ||||||||
\(130\) | −8.47729 | −0.743508 | ||||||||
\(131\) | −8.05414 | −0.703693 | −0.351847 | − | 0.936058i | \(-0.614446\pi\) | ||||
−0.351847 | + | 0.936058i | \(0.614446\pi\) | |||||||
\(132\) | 6.31904 | 0.550002 | ||||||||
\(133\) | 4.16316 | 0.360992 | ||||||||
\(134\) | −3.72934 | −0.322166 | ||||||||
\(135\) | 3.92669 | 0.337956 | ||||||||
\(136\) | 1.85994 | 0.159489 | ||||||||
\(137\) | −19.6064 | −1.67509 | −0.837544 | − | 0.546371i | \(-0.816009\pi\) | ||||
−0.837544 | + | 0.546371i | \(0.816009\pi\) | |||||||
\(138\) | −2.00664 | −0.170817 | ||||||||
\(139\) | 16.2142 | 1.37527 | 0.687635 | − | 0.726056i | \(-0.258649\pi\) | ||||
0.687635 | + | 0.726056i | \(0.258649\pi\) | |||||||
\(140\) | 5.45679 | 0.461183 | ||||||||
\(141\) | 12.5423 | 1.05625 | ||||||||
\(142\) | −4.37685 | −0.367297 | ||||||||
\(143\) | −15.6952 | −1.31250 | ||||||||
\(144\) | 2.58783 | 0.215652 | ||||||||
\(145\) | 9.35263 | 0.776694 | ||||||||
\(146\) | 4.35196 | 0.360171 | ||||||||
\(147\) | 6.37272 | 0.525613 | ||||||||
\(148\) | 14.5449 | 1.19558 | ||||||||
\(149\) | −20.2760 | −1.66108 | −0.830538 | − | 0.556962i | \(-0.811967\pi\) | ||||
−0.830538 | + | 0.556962i | \(0.811967\pi\) | |||||||
\(150\) | 5.16128 | 0.421417 | ||||||||
\(151\) | −13.3506 | −1.08646 | −0.543228 | − | 0.839585i | \(-0.682798\pi\) | ||||
−0.543228 | + | 0.839585i | \(0.682798\pi\) | |||||||
\(152\) | 9.77668 | 0.792993 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −1.41299 | −0.113862 | ||||||||
\(155\) | 12.8519 | 1.03229 | ||||||||
\(156\) | −7.64668 | −0.612225 | ||||||||
\(157\) | 6.98952 | 0.557824 | 0.278912 | − | 0.960317i | \(-0.410026\pi\) | ||||
0.278912 | + | 0.960317i | \(0.410026\pi\) | |||||||
\(158\) | 0.495377 | 0.0394101 | ||||||||
\(159\) | 9.15188 | 0.725791 | ||||||||
\(160\) | 19.6407 | 1.55273 | ||||||||
\(161\) | −3.20824 | −0.252844 | ||||||||
\(162\) | −0.495377 | −0.0389205 | ||||||||
\(163\) | −14.4956 | −1.13538 | −0.567690 | − | 0.823242i | \(-0.692163\pi\) | ||||
−0.567690 | + | 0.823242i | \(0.692163\pi\) | |||||||
\(164\) | −10.0967 | −0.788422 | ||||||||
\(165\) | 14.1416 | 1.10092 | ||||||||
\(166\) | −4.16739 | −0.323452 | ||||||||
\(167\) | −5.23555 | −0.405139 | −0.202570 | − | 0.979268i | \(-0.564929\pi\) | ||||
−0.202570 | + | 0.979268i | \(0.564929\pi\) | |||||||
\(168\) | −1.47310 | −0.113652 | ||||||||
\(169\) | 5.99281 | 0.460986 | ||||||||
\(170\) | 1.94519 | 0.149189 | ||||||||
\(171\) | 5.25644 | 0.401970 | ||||||||
\(172\) | −3.94828 | −0.301054 | ||||||||
\(173\) | 13.6838 | 1.04036 | 0.520179 | − | 0.854058i | \(-0.325865\pi\) | ||||
0.520179 | + | 0.854058i | \(0.325865\pi\) | |||||||
\(174\) | −1.17989 | −0.0894475 | ||||||||
\(175\) | 8.25189 | 0.623785 | ||||||||
\(176\) | 9.31984 | 0.702509 | ||||||||
\(177\) | 11.9524 | 0.898395 | ||||||||
\(178\) | −4.25242 | −0.318732 | ||||||||
\(179\) | −14.9123 | −1.11460 | −0.557299 | − | 0.830312i | \(-0.688162\pi\) | ||||
−0.557299 | + | 0.830312i | \(0.688162\pi\) | |||||||
\(180\) | 6.88978 | 0.513534 | ||||||||
\(181\) | 19.2519 | 1.43098 | 0.715492 | − | 0.698621i | \(-0.246203\pi\) | ||||
0.715492 | + | 0.698621i | \(0.246203\pi\) | |||||||
\(182\) | 1.70987 | 0.126744 | ||||||||
\(183\) | −5.37127 | −0.397055 | ||||||||
\(184\) | −7.53415 | −0.555425 | ||||||||
\(185\) | 32.5505 | 2.39316 | ||||||||
\(186\) | −1.62135 | −0.118883 | ||||||||
\(187\) | 3.60141 | 0.263361 | ||||||||
\(188\) | 22.0067 | 1.60500 | ||||||||
\(189\) | −0.792012 | −0.0576104 | ||||||||
\(190\) | 10.2248 | 0.741784 | ||||||||
\(191\) | 0.704658 | 0.0509873 | 0.0254936 | − | 0.999675i | \(-0.491884\pi\) | ||||
0.0254936 | + | 0.999675i | \(0.491884\pi\) | |||||||
\(192\) | 2.69786 | 0.194702 | ||||||||
\(193\) | 8.38827 | 0.603801 | 0.301900 | − | 0.953339i | \(-0.402379\pi\) | ||||
0.301900 | + | 0.953339i | \(0.402379\pi\) | |||||||
\(194\) | −2.90472 | −0.208546 | ||||||||
\(195\) | −17.1128 | −1.22547 | ||||||||
\(196\) | 11.1816 | 0.798684 | ||||||||
\(197\) | −21.0730 | −1.50139 | −0.750696 | − | 0.660648i | \(-0.770282\pi\) | ||||
−0.750696 | + | 0.660648i | \(0.770282\pi\) | |||||||
\(198\) | −1.78406 | −0.126787 | ||||||||
\(199\) | 22.5529 | 1.59873 | 0.799365 | − | 0.600845i | \(-0.205169\pi\) | ||||
0.799365 | + | 0.600845i | \(0.205169\pi\) | |||||||
\(200\) | 19.3786 | 1.37027 | ||||||||
\(201\) | −7.52829 | −0.531004 | ||||||||
\(202\) | −8.58783 | −0.604238 | ||||||||
\(203\) | −1.88642 | −0.132401 | ||||||||
\(204\) | 1.75460 | 0.122847 | ||||||||
\(205\) | −22.5958 | −1.57816 | ||||||||
\(206\) | 2.82068 | 0.196526 | ||||||||
\(207\) | −4.05074 | −0.281546 | ||||||||
\(208\) | −11.2780 | −0.781985 | ||||||||
\(209\) | 18.9306 | 1.30946 | ||||||||
\(210\) | −1.54062 | −0.106313 | ||||||||
\(211\) | −3.98425 | −0.274287 | −0.137144 | − | 0.990551i | \(-0.543792\pi\) | ||||
−0.137144 | + | 0.990551i | \(0.543792\pi\) | |||||||
\(212\) | 16.0579 | 1.10286 | ||||||||
\(213\) | −8.83540 | −0.605391 | ||||||||
\(214\) | −5.28370 | −0.361186 | ||||||||
\(215\) | −8.83601 | −0.602611 | ||||||||
\(216\) | −1.85994 | −0.126553 | ||||||||
\(217\) | −2.59222 | −0.175972 | ||||||||
\(218\) | −6.23930 | −0.422579 | ||||||||
\(219\) | 8.78515 | 0.593646 | ||||||||
\(220\) | 24.8129 | 1.67289 | ||||||||
\(221\) | −4.35807 | −0.293156 | ||||||||
\(222\) | −4.10646 | −0.275607 | ||||||||
\(223\) | −29.6728 | −1.98704 | −0.993521 | − | 0.113653i | \(-0.963745\pi\) | ||||
−0.993521 | + | 0.113653i | \(0.963745\pi\) | |||||||
\(224\) | −3.96152 | −0.264690 | ||||||||
\(225\) | 10.4189 | 0.694593 | ||||||||
\(226\) | 10.2037 | 0.678743 | ||||||||
\(227\) | −26.6083 | −1.76605 | −0.883026 | − | 0.469323i | \(-0.844498\pi\) | ||||
−0.883026 | + | 0.469323i | \(0.844498\pi\) | |||||||
\(228\) | 9.22295 | 0.610805 | ||||||||
\(229\) | 20.9131 | 1.38198 | 0.690989 | − | 0.722865i | \(-0.257175\pi\) | ||||
0.690989 | + | 0.722865i | \(0.257175\pi\) | |||||||
\(230\) | −7.87947 | −0.519557 | ||||||||
\(231\) | −2.85236 | −0.187672 | ||||||||
\(232\) | −4.43003 | −0.290846 | ||||||||
\(233\) | 3.11401 | 0.204006 | 0.102003 | − | 0.994784i | \(-0.467475\pi\) | ||||
0.102003 | + | 0.994784i | \(0.467475\pi\) | |||||||
\(234\) | 2.15889 | 0.141131 | ||||||||
\(235\) | 49.2497 | 3.21269 | ||||||||
\(236\) | 20.9717 | 1.36514 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | −0.392345 | −0.0254319 | ||||||||
\(239\) | 1.29460 | 0.0837408 | 0.0418704 | − | 0.999123i | \(-0.486668\pi\) | ||||
0.0418704 | + | 0.999123i | \(0.486668\pi\) | |||||||
\(240\) | 10.1616 | 0.655929 | ||||||||
\(241\) | 24.4731 | 1.57645 | 0.788224 | − | 0.615388i | \(-0.211001\pi\) | ||||
0.788224 | + | 0.615388i | \(0.211001\pi\) | |||||||
\(242\) | −0.975970 | −0.0627377 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −9.42443 | −0.603337 | ||||||||
\(245\) | 25.0237 | 1.59870 | ||||||||
\(246\) | 2.85061 | 0.181748 | ||||||||
\(247\) | −22.9079 | −1.45760 | ||||||||
\(248\) | −6.08752 | −0.386558 | ||||||||
\(249\) | −8.41255 | −0.533124 | ||||||||
\(250\) | 10.5408 | 0.666659 | ||||||||
\(251\) | −4.52016 | −0.285310 | −0.142655 | − | 0.989772i | \(-0.545564\pi\) | ||||
−0.142655 | + | 0.989772i | \(0.545564\pi\) | |||||||
\(252\) | −1.38967 | −0.0875407 | ||||||||
\(253\) | −14.5884 | −0.917164 | ||||||||
\(254\) | −3.40116 | −0.213408 | ||||||||
\(255\) | 3.92669 | 0.245899 | ||||||||
\(256\) | −0.221918 | −0.0138698 | ||||||||
\(257\) | 27.0863 | 1.68959 | 0.844797 | − | 0.535087i | \(-0.179721\pi\) | ||||
0.844797 | + | 0.535087i | \(0.179721\pi\) | |||||||
\(258\) | 1.11472 | 0.0693994 | ||||||||
\(259\) | −6.56543 | −0.407956 | ||||||||
\(260\) | −30.0262 | −1.86214 | ||||||||
\(261\) | −2.38181 | −0.147430 | ||||||||
\(262\) | 3.98984 | 0.246493 | ||||||||
\(263\) | −16.7569 | −1.03327 | −0.516637 | − | 0.856205i | \(-0.672816\pi\) | ||||
−0.516637 | + | 0.856205i | \(0.672816\pi\) | |||||||
\(264\) | −6.69842 | −0.412259 | ||||||||
\(265\) | 35.9366 | 2.20757 | ||||||||
\(266\) | −2.06233 | −0.126450 | ||||||||
\(267\) | −8.58421 | −0.525345 | ||||||||
\(268\) | −13.2091 | −0.806877 | ||||||||
\(269\) | 13.3950 | 0.816710 | 0.408355 | − | 0.912823i | \(-0.366103\pi\) | ||||
0.408355 | + | 0.912823i | \(0.366103\pi\) | |||||||
\(270\) | −1.94519 | −0.118381 | ||||||||
\(271\) | 20.6607 | 1.25505 | 0.627523 | − | 0.778598i | \(-0.284069\pi\) | ||||
0.627523 | + | 0.778598i | \(0.284069\pi\) | |||||||
\(272\) | 2.58783 | 0.156910 | ||||||||
\(273\) | 3.45165 | 0.208903 | ||||||||
\(274\) | 9.71256 | 0.586757 | ||||||||
\(275\) | 37.5227 | 2.26271 | ||||||||
\(276\) | −7.10744 | −0.427817 | ||||||||
\(277\) | 15.5579 | 0.934784 | 0.467392 | − | 0.884050i | \(-0.345194\pi\) | ||||
0.467392 | + | 0.884050i | \(0.345194\pi\) | |||||||
\(278\) | −8.03214 | −0.481736 | ||||||||
\(279\) | −3.27296 | −0.195947 | ||||||||
\(280\) | −5.78440 | −0.345684 | ||||||||
\(281\) | 3.42774 | 0.204482 | 0.102241 | − | 0.994760i | \(-0.467399\pi\) | ||||
0.102241 | + | 0.994760i | \(0.467399\pi\) | |||||||
\(282\) | −6.21316 | −0.369988 | ||||||||
\(283\) | 4.99808 | 0.297105 | 0.148553 | − | 0.988905i | \(-0.452539\pi\) | ||||
0.148553 | + | 0.988905i | \(0.452539\pi\) | |||||||
\(284\) | −15.5026 | −0.919910 | ||||||||
\(285\) | 20.6404 | 1.22263 | ||||||||
\(286\) | 7.77505 | 0.459748 | ||||||||
\(287\) | 4.55757 | 0.269025 | ||||||||
\(288\) | −5.00184 | −0.294736 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −4.63308 | −0.272064 | ||||||||
\(291\) | −5.86365 | −0.343733 | ||||||||
\(292\) | 15.4144 | 0.902062 | ||||||||
\(293\) | 29.0788 | 1.69880 | 0.849401 | − | 0.527748i | \(-0.176963\pi\) | ||||
0.849401 | + | 0.527748i | \(0.176963\pi\) | |||||||
\(294\) | −3.15690 | −0.184114 | ||||||||
\(295\) | 46.9333 | 2.73256 | ||||||||
\(296\) | −15.4181 | −0.896160 | ||||||||
\(297\) | −3.60141 | −0.208975 | ||||||||
\(298\) | 10.0443 | 0.581849 | ||||||||
\(299\) | 17.6534 | 1.02092 | ||||||||
\(300\) | 18.2810 | 1.05546 | ||||||||
\(301\) | 1.78222 | 0.102725 | ||||||||
\(302\) | 6.61358 | 0.380569 | ||||||||
\(303\) | −17.3359 | −0.995924 | ||||||||
\(304\) | 13.6028 | 0.780172 | ||||||||
\(305\) | −21.0913 | −1.20768 | ||||||||
\(306\) | −0.495377 | −0.0283188 | ||||||||
\(307\) | 23.6235 | 1.34826 | 0.674131 | − | 0.738612i | \(-0.264518\pi\) | ||||
0.674131 | + | 0.738612i | \(0.264518\pi\) | |||||||
\(308\) | −5.00476 | −0.285172 | ||||||||
\(309\) | 5.69401 | 0.323921 | ||||||||
\(310\) | −6.36653 | −0.361595 | ||||||||
\(311\) | 13.4375 | 0.761972 | 0.380986 | − | 0.924581i | \(-0.375585\pi\) | ||||
0.380986 | + | 0.924581i | \(0.375585\pi\) | |||||||
\(312\) | 8.10577 | 0.458899 | ||||||||
\(313\) | 23.5037 | 1.32851 | 0.664254 | − | 0.747507i | \(-0.268749\pi\) | ||||
0.664254 | + | 0.747507i | \(0.268749\pi\) | |||||||
\(314\) | −3.46245 | −0.195397 | ||||||||
\(315\) | −3.10999 | −0.175228 | ||||||||
\(316\) | 1.75460 | 0.0987040 | ||||||||
\(317\) | 12.7005 | 0.713329 | 0.356664 | − | 0.934233i | \(-0.383914\pi\) | ||||
0.356664 | + | 0.934233i | \(0.383914\pi\) | |||||||
\(318\) | −4.53363 | −0.254233 | ||||||||
\(319\) | −8.57787 | −0.480269 | ||||||||
\(320\) | 10.5937 | 0.592204 | ||||||||
\(321\) | −10.6660 | −0.595318 | ||||||||
\(322\) | 1.58929 | 0.0885675 | ||||||||
\(323\) | 5.25644 | 0.292476 | ||||||||
\(324\) | −1.75460 | −0.0974779 | ||||||||
\(325\) | −45.4063 | −2.51869 | ||||||||
\(326\) | 7.18078 | 0.397706 | ||||||||
\(327\) | −12.5951 | −0.696508 | ||||||||
\(328\) | 10.7029 | 0.590969 | ||||||||
\(329\) | −9.93364 | −0.547659 | ||||||||
\(330\) | −7.00544 | −0.385637 | ||||||||
\(331\) | −3.69932 | −0.203333 | −0.101666 | − | 0.994819i | \(-0.532417\pi\) | ||||
−0.101666 | + | 0.994819i | \(0.532417\pi\) | |||||||
\(332\) | −14.7607 | −0.810098 | ||||||||
\(333\) | −8.28956 | −0.454265 | ||||||||
\(334\) | 2.59357 | 0.141914 | ||||||||
\(335\) | −29.5613 | −1.61510 | ||||||||
\(336\) | −2.04959 | −0.111814 | ||||||||
\(337\) | 3.58777 | 0.195438 | 0.0977191 | − | 0.995214i | \(-0.468845\pi\) | ||||
0.0977191 | + | 0.995214i | \(0.468845\pi\) | |||||||
\(338\) | −2.96870 | −0.161476 | ||||||||
\(339\) | 20.5979 | 1.11873 | ||||||||
\(340\) | 6.88978 | 0.373651 | ||||||||
\(341\) | −11.7873 | −0.638316 | ||||||||
\(342\) | −2.60392 | −0.140804 | ||||||||
\(343\) | −10.5914 | −0.571879 | ||||||||
\(344\) | 4.18533 | 0.225658 | ||||||||
\(345\) | −15.9060 | −0.856351 | ||||||||
\(346\) | −6.77862 | −0.364421 | ||||||||
\(347\) | 1.39029 | 0.0746349 | 0.0373174 | − | 0.999303i | \(-0.488119\pi\) | ||||
0.0373174 | + | 0.999303i | \(0.488119\pi\) | |||||||
\(348\) | −4.17913 | −0.224025 | ||||||||
\(349\) | 17.8730 | 0.956722 | 0.478361 | − | 0.878163i | \(-0.341231\pi\) | ||||
0.478361 | + | 0.878163i | \(0.341231\pi\) | |||||||
\(350\) | −4.08780 | −0.218502 | ||||||||
\(351\) | 4.35807 | 0.232617 | ||||||||
\(352\) | −18.0137 | −0.960132 | ||||||||
\(353\) | 14.8977 | 0.792925 | 0.396462 | − | 0.918051i | \(-0.370238\pi\) | ||||
0.396462 | + | 0.918051i | \(0.370238\pi\) | |||||||
\(354\) | −5.92093 | −0.314694 | ||||||||
\(355\) | −34.6939 | −1.84136 | ||||||||
\(356\) | −15.0619 | −0.798278 | ||||||||
\(357\) | −0.792012 | −0.0419177 | ||||||||
\(358\) | 7.38721 | 0.390426 | ||||||||
\(359\) | −33.1403 | −1.74908 | −0.874540 | − | 0.484953i | \(-0.838837\pi\) | ||||
−0.874540 | + | 0.484953i | \(0.838837\pi\) | |||||||
\(360\) | −7.30342 | −0.384924 | ||||||||
\(361\) | 8.63014 | 0.454218 | ||||||||
\(362\) | −9.53696 | −0.501251 | ||||||||
\(363\) | −1.97016 | −0.103406 | ||||||||
\(364\) | 6.05627 | 0.317435 | ||||||||
\(365\) | 34.4966 | 1.80563 | ||||||||
\(366\) | 2.66080 | 0.139082 | ||||||||
\(367\) | −16.2431 | −0.847881 | −0.423940 | − | 0.905690i | \(-0.639353\pi\) | ||||
−0.423940 | + | 0.905690i | \(0.639353\pi\) | |||||||
\(368\) | −10.4826 | −0.546445 | ||||||||
\(369\) | 5.75442 | 0.299563 | ||||||||
\(370\) | −16.1248 | −0.838288 | ||||||||
\(371\) | −7.24840 | −0.376318 | ||||||||
\(372\) | −5.74274 | −0.297747 | ||||||||
\(373\) | 16.1495 | 0.836189 | 0.418094 | − | 0.908404i | \(-0.362698\pi\) | ||||
0.418094 | + | 0.908404i | \(0.362698\pi\) | |||||||
\(374\) | −1.78406 | −0.0922513 | ||||||||
\(375\) | 21.2783 | 1.09881 | ||||||||
\(376\) | −23.3279 | −1.20305 | ||||||||
\(377\) | 10.3801 | 0.534602 | ||||||||
\(378\) | 0.392345 | 0.0201800 | ||||||||
\(379\) | 1.44922 | 0.0744414 | 0.0372207 | − | 0.999307i | \(-0.488150\pi\) | ||||
0.0372207 | + | 0.999307i | \(0.488150\pi\) | |||||||
\(380\) | 36.2157 | 1.85783 | ||||||||
\(381\) | −6.86580 | −0.351746 | ||||||||
\(382\) | −0.349071 | −0.0178601 | ||||||||
\(383\) | −15.3908 | −0.786432 | −0.393216 | − | 0.919446i | \(-0.628638\pi\) | ||||
−0.393216 | + | 0.919446i | \(0.628638\pi\) | |||||||
\(384\) | −11.3401 | −0.578699 | ||||||||
\(385\) | −11.2003 | −0.570822 | ||||||||
\(386\) | −4.15536 | −0.211502 | ||||||||
\(387\) | 2.25024 | 0.114386 | ||||||||
\(388\) | −10.2884 | −0.522312 | ||||||||
\(389\) | −28.3777 | −1.43881 | −0.719404 | − | 0.694592i | \(-0.755585\pi\) | ||||
−0.719404 | + | 0.694592i | \(0.755585\pi\) | |||||||
\(390\) | 8.47729 | 0.429264 | ||||||||
\(391\) | −4.05074 | −0.204855 | ||||||||
\(392\) | −11.8529 | −0.598662 | ||||||||
\(393\) | 8.05414 | 0.406278 | ||||||||
\(394\) | 10.4391 | 0.525914 | ||||||||
\(395\) | 3.92669 | 0.197573 | ||||||||
\(396\) | −6.31904 | −0.317544 | ||||||||
\(397\) | −9.06834 | −0.455127 | −0.227564 | − | 0.973763i | \(-0.573076\pi\) | ||||
−0.227564 | + | 0.973763i | \(0.573076\pi\) | |||||||
\(398\) | −11.1722 | −0.560011 | ||||||||
\(399\) | −4.16316 | −0.208419 | ||||||||
\(400\) | 26.9623 | 1.34812 | ||||||||
\(401\) | −23.3030 | −1.16369 | −0.581847 | − | 0.813298i | \(-0.697670\pi\) | ||||
−0.581847 | + | 0.813298i | \(0.697670\pi\) | |||||||
\(402\) | 3.72934 | 0.186003 | ||||||||
\(403\) | 14.2638 | 0.710530 | ||||||||
\(404\) | −30.4177 | −1.51334 | ||||||||
\(405\) | −3.92669 | −0.195119 | ||||||||
\(406\) | 0.934490 | 0.0463780 | ||||||||
\(407\) | −29.8541 | −1.47981 | ||||||||
\(408\) | −1.85994 | −0.0920809 | ||||||||
\(409\) | −32.5065 | −1.60734 | −0.803671 | − | 0.595074i | \(-0.797123\pi\) | ||||
−0.803671 | + | 0.595074i | \(0.797123\pi\) | |||||||
\(410\) | 11.1935 | 0.552806 | ||||||||
\(411\) | 19.6064 | 0.967112 | ||||||||
\(412\) | 9.99072 | 0.492208 | ||||||||
\(413\) | −9.46642 | −0.465812 | ||||||||
\(414\) | 2.00664 | 0.0986212 | ||||||||
\(415\) | −33.0335 | −1.62155 | ||||||||
\(416\) | 21.7984 | 1.06875 | ||||||||
\(417\) | −16.2142 | −0.794013 | ||||||||
\(418\) | −9.37778 | −0.458682 | ||||||||
\(419\) | −1.02269 | −0.0499618 | −0.0249809 | − | 0.999688i | \(-0.507953\pi\) | ||||
−0.0249809 | + | 0.999688i | \(0.507953\pi\) | |||||||
\(420\) | −5.45679 | −0.266264 | ||||||||
\(421\) | 15.8912 | 0.774491 | 0.387246 | − | 0.921977i | \(-0.373427\pi\) | ||||
0.387246 | + | 0.921977i | \(0.373427\pi\) | |||||||
\(422\) | 1.97371 | 0.0960786 | ||||||||
\(423\) | −12.5423 | −0.609827 | ||||||||
\(424\) | −17.0220 | −0.826660 | ||||||||
\(425\) | 10.4189 | 0.505391 | ||||||||
\(426\) | 4.37685 | 0.212059 | ||||||||
\(427\) | 4.25411 | 0.205871 | ||||||||
\(428\) | −18.7146 | −0.904604 | ||||||||
\(429\) | 15.6952 | 0.757772 | ||||||||
\(430\) | 4.37716 | 0.211085 | ||||||||
\(431\) | 26.7563 | 1.28880 | 0.644402 | − | 0.764687i | \(-0.277107\pi\) | ||||
0.644402 | + | 0.764687i | \(0.277107\pi\) | |||||||
\(432\) | −2.58783 | −0.124507 | ||||||||
\(433\) | −8.32382 | −0.400017 | −0.200009 | − | 0.979794i | \(-0.564097\pi\) | ||||
−0.200009 | + | 0.979794i | \(0.564097\pi\) | |||||||
\(434\) | 1.28413 | 0.0616401 | ||||||||
\(435\) | −9.35263 | −0.448424 | ||||||||
\(436\) | −22.0993 | −1.05837 | ||||||||
\(437\) | −21.2925 | −1.01856 | ||||||||
\(438\) | −4.35196 | −0.207945 | ||||||||
\(439\) | −30.2260 | −1.44261 | −0.721303 | − | 0.692619i | \(-0.756457\pi\) | ||||
−0.721303 | + | 0.692619i | \(0.756457\pi\) | |||||||
\(440\) | −26.3026 | −1.25393 | ||||||||
\(441\) | −6.37272 | −0.303463 | ||||||||
\(442\) | 2.15889 | 0.102688 | ||||||||
\(443\) | 18.7955 | 0.893001 | 0.446500 | − | 0.894783i | \(-0.352670\pi\) | ||||
0.446500 | + | 0.894783i | \(0.352670\pi\) | |||||||
\(444\) | −14.5449 | −0.690269 | ||||||||
\(445\) | −33.7075 | −1.59789 | ||||||||
\(446\) | 14.6992 | 0.696030 | ||||||||
\(447\) | 20.2760 | 0.959023 | ||||||||
\(448\) | −2.13674 | −0.100951 | ||||||||
\(449\) | 35.1265 | 1.65772 | 0.828861 | − | 0.559455i | \(-0.188990\pi\) | ||||
0.828861 | + | 0.559455i | \(0.188990\pi\) | |||||||
\(450\) | −5.16128 | −0.243305 | ||||||||
\(451\) | 20.7240 | 0.975857 | ||||||||
\(452\) | 36.1412 | 1.69994 | ||||||||
\(453\) | 13.3506 | 0.627266 | ||||||||
\(454\) | 13.1811 | 0.618621 | ||||||||
\(455\) | 13.5536 | 0.635400 | ||||||||
\(456\) | −9.77668 | −0.457835 | ||||||||
\(457\) | 11.7903 | 0.551526 | 0.275763 | − | 0.961226i | \(-0.411069\pi\) | ||||
0.275763 | + | 0.961226i | \(0.411069\pi\) | |||||||
\(458\) | −10.3599 | −0.484086 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −27.9087 | −1.30125 | ||||||||
\(461\) | −7.13431 | −0.332278 | −0.166139 | − | 0.986102i | \(-0.553130\pi\) | ||||
−0.166139 | + | 0.986102i | \(0.553130\pi\) | |||||||
\(462\) | 1.41299 | 0.0657384 | ||||||||
\(463\) | 36.5804 | 1.70003 | 0.850017 | − | 0.526755i | \(-0.176591\pi\) | ||||
0.850017 | + | 0.526755i | \(0.176591\pi\) | |||||||
\(464\) | −6.16372 | −0.286143 | ||||||||
\(465\) | −12.8519 | −0.595992 | ||||||||
\(466\) | −1.54261 | −0.0714600 | ||||||||
\(467\) | 26.5379 | 1.22803 | 0.614014 | − | 0.789295i | \(-0.289554\pi\) | ||||
0.614014 | + | 0.789295i | \(0.289554\pi\) | |||||||
\(468\) | 7.64668 | 0.353468 | ||||||||
\(469\) | 5.96249 | 0.275322 | ||||||||
\(470\) | −24.3972 | −1.12536 | ||||||||
\(471\) | −6.98952 | −0.322060 | ||||||||
\(472\) | −22.2307 | −1.02325 | ||||||||
\(473\) | 8.10405 | 0.372625 | ||||||||
\(474\) | −0.495377 | −0.0227534 | ||||||||
\(475\) | 54.7663 | 2.51285 | ||||||||
\(476\) | −1.38967 | −0.0636952 | ||||||||
\(477\) | −9.15188 | −0.419036 | ||||||||
\(478\) | −0.641316 | −0.0293331 | ||||||||
\(479\) | 11.7997 | 0.539142 | 0.269571 | − | 0.962981i | \(-0.413118\pi\) | ||||
0.269571 | + | 0.962981i | \(0.413118\pi\) | |||||||
\(480\) | −19.6407 | −0.896470 | ||||||||
\(481\) | 36.1265 | 1.64723 | ||||||||
\(482\) | −12.1234 | −0.552206 | ||||||||
\(483\) | 3.20824 | 0.145980 | ||||||||
\(484\) | −3.45684 | −0.157129 | ||||||||
\(485\) | −23.0247 | −1.04550 | ||||||||
\(486\) | 0.495377 | 0.0224708 | ||||||||
\(487\) | −1.77231 | −0.0803109 | −0.0401554 | − | 0.999193i | \(-0.512785\pi\) | ||||
−0.0401554 | + | 0.999193i | \(0.512785\pi\) | |||||||
\(488\) | 9.99025 | 0.452237 | ||||||||
\(489\) | 14.4956 | 0.655513 | ||||||||
\(490\) | −12.3962 | −0.560002 | ||||||||
\(491\) | −18.3073 | −0.826198 | −0.413099 | − | 0.910686i | \(-0.635554\pi\) | ||||
−0.413099 | + | 0.910686i | \(0.635554\pi\) | |||||||
\(492\) | 10.0967 | 0.455195 | ||||||||
\(493\) | −2.38181 | −0.107271 | ||||||||
\(494\) | 11.3481 | 0.510574 | ||||||||
\(495\) | −14.1416 | −0.635619 | ||||||||
\(496\) | −8.46986 | −0.380308 | ||||||||
\(497\) | 6.99774 | 0.313892 | ||||||||
\(498\) | 4.16739 | 0.186745 | ||||||||
\(499\) | −13.6566 | −0.611356 | −0.305678 | − | 0.952135i | \(-0.598883\pi\) | ||||
−0.305678 | + | 0.952135i | \(0.598883\pi\) | |||||||
\(500\) | 37.3350 | 1.66967 | ||||||||
\(501\) | 5.23555 | 0.233907 | ||||||||
\(502\) | 2.23918 | 0.0999396 | ||||||||
\(503\) | 26.0719 | 1.16249 | 0.581244 | − | 0.813729i | \(-0.302566\pi\) | ||||
0.581244 | + | 0.813729i | \(0.302566\pi\) | |||||||
\(504\) | 1.47310 | 0.0656170 | ||||||||
\(505\) | −68.0729 | −3.02920 | ||||||||
\(506\) | 7.22675 | 0.321268 | ||||||||
\(507\) | −5.99281 | −0.266150 | ||||||||
\(508\) | −12.0467 | −0.534488 | ||||||||
\(509\) | 12.5753 | 0.557392 | 0.278696 | − | 0.960379i | \(-0.410098\pi\) | ||||
0.278696 | + | 0.960379i | \(0.410098\pi\) | |||||||
\(510\) | −1.94519 | −0.0861346 | ||||||||
\(511\) | −6.95795 | −0.307801 | ||||||||
\(512\) | −22.5703 | −0.997478 | ||||||||
\(513\) | −5.25644 | −0.232077 | ||||||||
\(514\) | −13.4179 | −0.591839 | ||||||||
\(515\) | 22.3586 | 0.985239 | ||||||||
\(516\) | 3.94828 | 0.173813 | ||||||||
\(517\) | −45.1699 | −1.98657 | ||||||||
\(518\) | 3.25236 | 0.142901 | ||||||||
\(519\) | −13.6838 | −0.600650 | ||||||||
\(520\) | 31.8289 | 1.39579 | ||||||||
\(521\) | −18.1821 | −0.796571 | −0.398286 | − | 0.917261i | \(-0.630395\pi\) | ||||
−0.398286 | + | 0.917261i | \(0.630395\pi\) | |||||||
\(522\) | 1.17989 | 0.0516425 | ||||||||
\(523\) | −14.8318 | −0.648547 | −0.324274 | − | 0.945963i | \(-0.605120\pi\) | ||||
−0.324274 | + | 0.945963i | \(0.605120\pi\) | |||||||
\(524\) | 14.1318 | 0.617351 | ||||||||
\(525\) | −8.25189 | −0.360142 | ||||||||
\(526\) | 8.30097 | 0.361940 | ||||||||
\(527\) | −3.27296 | −0.142572 | ||||||||
\(528\) | −9.31984 | −0.405594 | ||||||||
\(529\) | −6.59150 | −0.286587 | ||||||||
\(530\) | −17.8022 | −0.773277 | ||||||||
\(531\) | −11.9524 | −0.518689 | ||||||||
\(532\) | −7.30469 | −0.316698 | ||||||||
\(533\) | −25.0782 | −1.08626 | ||||||||
\(534\) | 4.25242 | 0.184020 | ||||||||
\(535\) | −41.8821 | −1.81072 | ||||||||
\(536\) | 14.0022 | 0.604802 | ||||||||
\(537\) | 14.9123 | 0.643513 | ||||||||
\(538\) | −6.63560 | −0.286081 | ||||||||
\(539\) | −22.9508 | −0.988560 | ||||||||
\(540\) | −6.88978 | −0.296489 | ||||||||
\(541\) | 26.4803 | 1.13848 | 0.569238 | − | 0.822173i | \(-0.307238\pi\) | ||||
0.569238 | + | 0.822173i | \(0.307238\pi\) | |||||||
\(542\) | −10.2348 | −0.439623 | ||||||||
\(543\) | −19.2519 | −0.826179 | ||||||||
\(544\) | −5.00184 | −0.214452 | ||||||||
\(545\) | −49.4569 | −2.11850 | ||||||||
\(546\) | −1.70987 | −0.0731755 | ||||||||
\(547\) | 26.7236 | 1.14262 | 0.571310 | − | 0.820734i | \(-0.306435\pi\) | ||||
0.571310 | + | 0.820734i | \(0.306435\pi\) | |||||||
\(548\) | 34.4014 | 1.46956 | ||||||||
\(549\) | 5.37127 | 0.229240 | ||||||||
\(550\) | −18.5879 | −0.792591 | ||||||||
\(551\) | −12.5198 | −0.533363 | ||||||||
\(552\) | 7.53415 | 0.320675 | ||||||||
\(553\) | −0.792012 | −0.0336798 | ||||||||
\(554\) | −7.70703 | −0.327440 | ||||||||
\(555\) | −32.5505 | −1.38169 | ||||||||
\(556\) | −28.4495 | −1.20653 | ||||||||
\(557\) | −22.9463 | −0.972267 | −0.486133 | − | 0.873885i | \(-0.661593\pi\) | ||||
−0.486133 | + | 0.873885i | \(0.661593\pi\) | |||||||
\(558\) | 1.62135 | 0.0686372 | ||||||||
\(559\) | −9.80673 | −0.414781 | ||||||||
\(560\) | −8.04811 | −0.340095 | ||||||||
\(561\) | −3.60141 | −0.152052 | ||||||||
\(562\) | −1.69802 | −0.0716268 | ||||||||
\(563\) | 40.0035 | 1.68595 | 0.842973 | − | 0.537956i | \(-0.180803\pi\) | ||||
0.842973 | + | 0.537956i | \(0.180803\pi\) | |||||||
\(564\) | −22.0067 | −0.926650 | ||||||||
\(565\) | 80.8817 | 3.40272 | ||||||||
\(566\) | −2.47593 | −0.104071 | ||||||||
\(567\) | 0.792012 | 0.0332614 | ||||||||
\(568\) | 16.4333 | 0.689528 | ||||||||
\(569\) | −19.0081 | −0.796863 | −0.398431 | − | 0.917198i | \(-0.630445\pi\) | ||||
−0.398431 | + | 0.917198i | \(0.630445\pi\) | |||||||
\(570\) | −10.2248 | −0.428269 | ||||||||
\(571\) | 23.6266 | 0.988742 | 0.494371 | − | 0.869251i | \(-0.335398\pi\) | ||||
0.494371 | + | 0.869251i | \(0.335398\pi\) | |||||||
\(572\) | 27.5388 | 1.15146 | ||||||||
\(573\) | −0.704658 | −0.0294375 | ||||||||
\(574\) | −2.25772 | −0.0942353 | ||||||||
\(575\) | −42.2043 | −1.76004 | ||||||||
\(576\) | −2.69786 | −0.112411 | ||||||||
\(577\) | 19.3914 | 0.807273 | 0.403637 | − | 0.914919i | \(-0.367746\pi\) | ||||
0.403637 | + | 0.914919i | \(0.367746\pi\) | |||||||
\(578\) | −0.495377 | −0.0206050 | ||||||||
\(579\) | −8.38827 | −0.348604 | ||||||||
\(580\) | −16.4101 | −0.681394 | ||||||||
\(581\) | 6.66284 | 0.276421 | ||||||||
\(582\) | 2.90472 | 0.120404 | ||||||||
\(583\) | −32.9597 | −1.36505 | ||||||||
\(584\) | −16.3399 | −0.676149 | ||||||||
\(585\) | 17.1128 | 0.707528 | ||||||||
\(586\) | −14.4050 | −0.595064 | ||||||||
\(587\) | 19.2357 | 0.793942 | 0.396971 | − | 0.917831i | \(-0.370061\pi\) | ||||
0.396971 | + | 0.917831i | \(0.370061\pi\) | |||||||
\(588\) | −11.1816 | −0.461121 | ||||||||
\(589\) | −17.2041 | −0.708883 | ||||||||
\(590\) | −23.2497 | −0.957174 | ||||||||
\(591\) | 21.0730 | 0.866829 | ||||||||
\(592\) | −21.4520 | −0.881671 | ||||||||
\(593\) | 3.61238 | 0.148343 | 0.0741714 | − | 0.997246i | \(-0.476369\pi\) | ||||
0.0741714 | + | 0.997246i | \(0.476369\pi\) | |||||||
\(594\) | 1.78406 | 0.0732007 | ||||||||
\(595\) | −3.10999 | −0.127497 | ||||||||
\(596\) | 35.5763 | 1.45726 | ||||||||
\(597\) | −22.5529 | −0.923028 | ||||||||
\(598\) | −8.74511 | −0.357614 | ||||||||
\(599\) | 17.9370 | 0.732886 | 0.366443 | − | 0.930441i | \(-0.380576\pi\) | ||||
0.366443 | + | 0.930441i | \(0.380576\pi\) | |||||||
\(600\) | −19.3786 | −0.791127 | ||||||||
\(601\) | −1.01370 | −0.0413498 | −0.0206749 | − | 0.999786i | \(-0.506581\pi\) | ||||
−0.0206749 | + | 0.999786i | \(0.506581\pi\) | |||||||
\(602\) | −0.882871 | −0.0359831 | ||||||||
\(603\) | 7.52829 | 0.306576 | ||||||||
\(604\) | 23.4250 | 0.953149 | ||||||||
\(605\) | −7.73619 | −0.314521 | ||||||||
\(606\) | 8.58783 | 0.348857 | ||||||||
\(607\) | −17.8098 | −0.722877 | −0.361438 | − | 0.932396i | \(-0.617714\pi\) | ||||
−0.361438 | + | 0.932396i | \(0.617714\pi\) | |||||||
\(608\) | −26.2919 | −1.06628 | ||||||||
\(609\) | 1.88642 | 0.0764416 | ||||||||
\(610\) | 10.4481 | 0.423033 | ||||||||
\(611\) | 54.6602 | 2.21132 | ||||||||
\(612\) | −1.75460 | −0.0709256 | ||||||||
\(613\) | 43.1244 | 1.74178 | 0.870890 | − | 0.491479i | \(-0.163543\pi\) | ||||
0.870890 | + | 0.491479i | \(0.163543\pi\) | |||||||
\(614\) | −11.7025 | −0.472275 | ||||||||
\(615\) | 22.5958 | 0.911153 | ||||||||
\(616\) | 5.30523 | 0.213754 | ||||||||
\(617\) | 41.9429 | 1.68856 | 0.844279 | − | 0.535904i | \(-0.180029\pi\) | ||||
0.844279 | + | 0.535904i | \(0.180029\pi\) | |||||||
\(618\) | −2.82068 | −0.113465 | ||||||||
\(619\) | 12.8511 | 0.516531 | 0.258265 | − | 0.966074i | \(-0.416849\pi\) | ||||
0.258265 | + | 0.966074i | \(0.416849\pi\) | |||||||
\(620\) | −22.5500 | −0.905628 | ||||||||
\(621\) | 4.05074 | 0.162551 | ||||||||
\(622\) | −6.65664 | −0.266907 | ||||||||
\(623\) | 6.79880 | 0.272388 | ||||||||
\(624\) | 11.2780 | 0.451480 | ||||||||
\(625\) | 31.4590 | 1.25836 | ||||||||
\(626\) | −11.6432 | −0.465356 | ||||||||
\(627\) | −18.9306 | −0.756015 | ||||||||
\(628\) | −12.2638 | −0.489380 | ||||||||
\(629\) | −8.28956 | −0.330526 | ||||||||
\(630\) | 1.54062 | 0.0613796 | ||||||||
\(631\) | −9.62468 | −0.383152 | −0.191576 | − | 0.981478i | \(-0.561360\pi\) | ||||
−0.191576 | + | 0.981478i | \(0.561360\pi\) | |||||||
\(632\) | −1.85994 | −0.0739846 | ||||||||
\(633\) | 3.98425 | 0.158360 | ||||||||
\(634\) | −6.29152 | −0.249868 | ||||||||
\(635\) | −26.9599 | −1.06987 | ||||||||
\(636\) | −16.0579 | −0.636737 | ||||||||
\(637\) | 27.7728 | 1.10040 | ||||||||
\(638\) | 4.24928 | 0.168231 | ||||||||
\(639\) | 8.83540 | 0.349523 | ||||||||
\(640\) | −44.5292 | −1.76017 | ||||||||
\(641\) | 17.7457 | 0.700912 | 0.350456 | − | 0.936579i | \(-0.386027\pi\) | ||||
0.350456 | + | 0.936579i | \(0.386027\pi\) | |||||||
\(642\) | 5.28370 | 0.208531 | ||||||||
\(643\) | 39.9832 | 1.57678 | 0.788391 | − | 0.615175i | \(-0.210915\pi\) | ||||
0.788391 | + | 0.615175i | \(0.210915\pi\) | |||||||
\(644\) | 5.62917 | 0.221821 | ||||||||
\(645\) | 8.83601 | 0.347918 | ||||||||
\(646\) | −2.60392 | −0.102450 | ||||||||
\(647\) | 25.2225 | 0.991598 | 0.495799 | − | 0.868437i | \(-0.334875\pi\) | ||||
0.495799 | + | 0.868437i | \(0.334875\pi\) | |||||||
\(648\) | 1.85994 | 0.0730655 | ||||||||
\(649\) | −43.0454 | −1.68968 | ||||||||
\(650\) | 22.4933 | 0.882258 | ||||||||
\(651\) | 2.59222 | 0.101597 | ||||||||
\(652\) | 25.4340 | 0.996071 | ||||||||
\(653\) | −42.7676 | −1.67363 | −0.836814 | − | 0.547488i | \(-0.815584\pi\) | ||||
−0.836814 | + | 0.547488i | \(0.815584\pi\) | |||||||
\(654\) | 6.23930 | 0.243976 | ||||||||
\(655\) | 31.6261 | 1.23573 | ||||||||
\(656\) | 14.8915 | 0.581414 | ||||||||
\(657\) | −8.78515 | −0.342741 | ||||||||
\(658\) | 4.92090 | 0.191837 | ||||||||
\(659\) | 17.1039 | 0.666274 | 0.333137 | − | 0.942878i | \(-0.391893\pi\) | ||||
0.333137 | + | 0.942878i | \(0.391893\pi\) | |||||||
\(660\) | −24.8129 | −0.965841 | ||||||||
\(661\) | −11.1344 | −0.433079 | −0.216540 | − | 0.976274i | \(-0.569477\pi\) | ||||
−0.216540 | + | 0.976274i | \(0.569477\pi\) | |||||||
\(662\) | 1.83256 | 0.0712244 | ||||||||
\(663\) | 4.35807 | 0.169254 | ||||||||
\(664\) | 15.6469 | 0.607217 | ||||||||
\(665\) | −16.3474 | −0.633927 | ||||||||
\(666\) | 4.10646 | 0.159122 | ||||||||
\(667\) | 9.64809 | 0.373576 | ||||||||
\(668\) | 9.18630 | 0.355429 | ||||||||
\(669\) | 29.6728 | 1.14722 | ||||||||
\(670\) | 14.6440 | 0.565746 | ||||||||
\(671\) | 19.3441 | 0.746772 | ||||||||
\(672\) | 3.96152 | 0.152819 | ||||||||
\(673\) | 18.1149 | 0.698280 | 0.349140 | − | 0.937071i | \(-0.386474\pi\) | ||||
0.349140 | + | 0.937071i | \(0.386474\pi\) | |||||||
\(674\) | −1.77730 | −0.0684590 | ||||||||
\(675\) | −10.4189 | −0.401024 | ||||||||
\(676\) | −10.5150 | −0.404423 | ||||||||
\(677\) | −24.6404 | −0.947007 | −0.473503 | − | 0.880792i | \(-0.657011\pi\) | ||||
−0.473503 | + | 0.880792i | \(0.657011\pi\) | |||||||
\(678\) | −10.2037 | −0.391872 | ||||||||
\(679\) | 4.64408 | 0.178223 | ||||||||
\(680\) | −7.30342 | −0.280073 | ||||||||
\(681\) | 26.6083 | 1.01963 | ||||||||
\(682\) | 5.83914 | 0.223592 | ||||||||
\(683\) | −36.0127 | −1.37799 | −0.688994 | − | 0.724767i | \(-0.741947\pi\) | ||||
−0.688994 | + | 0.724767i | \(0.741947\pi\) | |||||||
\(684\) | −9.22295 | −0.352648 | ||||||||
\(685\) | 76.9882 | 2.94157 | ||||||||
\(686\) | 5.24671 | 0.200320 | ||||||||
\(687\) | −20.9131 | −0.797886 | ||||||||
\(688\) | 5.82325 | 0.222009 | ||||||||
\(689\) | 39.8846 | 1.51948 | ||||||||
\(690\) | 7.87947 | 0.299966 | ||||||||
\(691\) | 32.6885 | 1.24353 | 0.621764 | − | 0.783205i | \(-0.286416\pi\) | ||||
0.621764 | + | 0.783205i | \(0.286416\pi\) | |||||||
\(692\) | −24.0095 | −0.912706 | ||||||||
\(693\) | 2.85236 | 0.108352 | ||||||||
\(694\) | −0.688719 | −0.0261434 | ||||||||
\(695\) | −63.6681 | −2.41507 | ||||||||
\(696\) | 4.43003 | 0.167920 | ||||||||
\(697\) | 5.75442 | 0.217964 | ||||||||
\(698\) | −8.85390 | −0.335125 | ||||||||
\(699\) | −3.11401 | −0.117783 | ||||||||
\(700\) | −14.4788 | −0.547247 | ||||||||
\(701\) | −30.8554 | −1.16539 | −0.582696 | − | 0.812690i | \(-0.698002\pi\) | ||||
−0.582696 | + | 0.812690i | \(0.698002\pi\) | |||||||
\(702\) | −2.15889 | −0.0814821 | ||||||||
\(703\) | −43.5736 | −1.64341 | ||||||||
\(704\) | −9.71611 | −0.366190 | ||||||||
\(705\) | −49.2497 | −1.85485 | ||||||||
\(706\) | −7.37998 | −0.277749 | ||||||||
\(707\) | 13.7303 | 0.516380 | ||||||||
\(708\) | −20.9717 | −0.788163 | ||||||||
\(709\) | 0.552903 | 0.0207647 | 0.0103823 | − | 0.999946i | \(-0.496695\pi\) | ||||
0.0103823 | + | 0.999946i | \(0.496695\pi\) | |||||||
\(710\) | 17.1865 | 0.645000 | ||||||||
\(711\) | −1.00000 | −0.0375029 | ||||||||
\(712\) | 15.9661 | 0.598357 | ||||||||
\(713\) | 13.2579 | 0.496513 | ||||||||
\(714\) | 0.392345 | 0.0146831 | ||||||||
\(715\) | 61.6303 | 2.30484 | ||||||||
\(716\) | 26.1651 | 0.977837 | ||||||||
\(717\) | −1.29460 | −0.0483478 | ||||||||
\(718\) | 16.4170 | 0.612676 | ||||||||
\(719\) | −21.2962 | −0.794214 | −0.397107 | − | 0.917772i | \(-0.629986\pi\) | ||||
−0.397107 | + | 0.917772i | \(0.629986\pi\) | |||||||
\(720\) | −10.1616 | −0.378701 | ||||||||
\(721\) | −4.50973 | −0.167951 | ||||||||
\(722\) | −4.27517 | −0.159105 | ||||||||
\(723\) | −24.4731 | −0.910163 | ||||||||
\(724\) | −33.7794 | −1.25540 | ||||||||
\(725\) | −24.8158 | −0.921637 | ||||||||
\(726\) | 0.975970 | 0.0362216 | ||||||||
\(727\) | −35.5209 | −1.31740 | −0.658698 | − | 0.752408i | \(-0.728892\pi\) | ||||
−0.658698 | + | 0.752408i | \(0.728892\pi\) | |||||||
\(728\) | −6.41987 | −0.237936 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −17.0888 | −0.632485 | ||||||||
\(731\) | 2.25024 | 0.0832283 | ||||||||
\(732\) | 9.42443 | 0.348337 | ||||||||
\(733\) | 17.5317 | 0.647550 | 0.323775 | − | 0.946134i | \(-0.395048\pi\) | ||||
0.323775 | + | 0.946134i | \(0.395048\pi\) | |||||||
\(734\) | 8.04644 | 0.296999 | ||||||||
\(735\) | −25.0237 | −0.923013 | ||||||||
\(736\) | 20.2612 | 0.746836 | ||||||||
\(737\) | 27.1124 | 0.998700 | ||||||||
\(738\) | −2.85061 | −0.104932 | ||||||||
\(739\) | 28.7687 | 1.05827 | 0.529137 | − | 0.848536i | \(-0.322516\pi\) | ||||
0.529137 | + | 0.848536i | \(0.322516\pi\) | |||||||
\(740\) | −57.1132 | −2.09952 | ||||||||
\(741\) | 22.9079 | 0.841544 | ||||||||
\(742\) | 3.59069 | 0.131818 | ||||||||
\(743\) | −38.6159 | −1.41668 | −0.708340 | − | 0.705871i | \(-0.750556\pi\) | ||||
−0.708340 | + | 0.705871i | \(0.750556\pi\) | |||||||
\(744\) | 6.08752 | 0.223179 | ||||||||
\(745\) | 79.6177 | 2.91697 | ||||||||
\(746\) | −8.00009 | −0.292904 | ||||||||
\(747\) | 8.41255 | 0.307799 | ||||||||
\(748\) | −6.31904 | −0.231047 | ||||||||
\(749\) | 8.44761 | 0.308669 | ||||||||
\(750\) | −10.5408 | −0.384896 | ||||||||
\(751\) | −5.76962 | −0.210537 | −0.105268 | − | 0.994444i | \(-0.533570\pi\) | ||||
−0.105268 | + | 0.994444i | \(0.533570\pi\) | |||||||
\(752\) | −32.4573 | −1.18360 | ||||||||
\(753\) | 4.52016 | 0.164724 | ||||||||
\(754\) | −5.14206 | −0.187263 | ||||||||
\(755\) | 52.4237 | 1.90789 | ||||||||
\(756\) | 1.38967 | 0.0505416 | ||||||||
\(757\) | 13.4890 | 0.490267 | 0.245133 | − | 0.969489i | \(-0.421168\pi\) | ||||
0.245133 | + | 0.969489i | \(0.421168\pi\) | |||||||
\(758\) | −0.717910 | −0.0260757 | ||||||||
\(759\) | 14.5884 | 0.529525 | ||||||||
\(760\) | −38.3900 | −1.39255 | ||||||||
\(761\) | −18.3884 | −0.666577 | −0.333289 | − | 0.942825i | \(-0.608158\pi\) | ||||
−0.333289 | + | 0.942825i | \(0.608158\pi\) | |||||||
\(762\) | 3.40116 | 0.123211 | ||||||||
\(763\) | 9.97544 | 0.361135 | ||||||||
\(764\) | −1.23639 | −0.0447312 | ||||||||
\(765\) | −3.92669 | −0.141970 | ||||||||
\(766\) | 7.62424 | 0.275475 | ||||||||
\(767\) | 52.0893 | 1.88084 | ||||||||
\(768\) | 0.221918 | 0.00800776 | ||||||||
\(769\) | −29.2070 | −1.05323 | −0.526615 | − | 0.850104i | \(-0.676539\pi\) | ||||
−0.526615 | + | 0.850104i | \(0.676539\pi\) | |||||||
\(770\) | 5.54839 | 0.199950 | ||||||||
\(771\) | −27.0863 | −0.975487 | ||||||||
\(772\) | −14.7181 | −0.529715 | ||||||||
\(773\) | 13.4818 | 0.484907 | 0.242454 | − | 0.970163i | \(-0.422048\pi\) | ||||
0.242454 | + | 0.970163i | \(0.422048\pi\) | |||||||
\(774\) | −1.11472 | −0.0400678 | ||||||||
\(775\) | −34.1006 | −1.22493 | ||||||||
\(776\) | 10.9061 | 0.391504 | ||||||||
\(777\) | 6.56543 | 0.235534 | ||||||||
\(778\) | 14.0577 | 0.503992 | ||||||||
\(779\) | 30.2478 | 1.08374 | ||||||||
\(780\) | 30.0262 | 1.07511 | ||||||||
\(781\) | 31.8199 | 1.13861 | ||||||||
\(782\) | 2.00664 | 0.0717575 | ||||||||
\(783\) | 2.38181 | 0.0851189 | ||||||||
\(784\) | −16.4915 | −0.588982 | ||||||||
\(785\) | −27.4457 | −0.979578 | ||||||||
\(786\) | −3.98984 | −0.142313 | ||||||||
\(787\) | 29.1255 | 1.03821 | 0.519107 | − | 0.854709i | \(-0.326265\pi\) | ||||
0.519107 | + | 0.854709i | \(0.326265\pi\) | |||||||
\(788\) | 36.9748 | 1.31717 | ||||||||
\(789\) | 16.7569 | 0.596561 | ||||||||
\(790\) | −1.94519 | −0.0692068 | ||||||||
\(791\) | −16.3138 | −0.580052 | ||||||||
\(792\) | 6.69842 | 0.238018 | ||||||||
\(793\) | −23.4084 | −0.831256 | ||||||||
\(794\) | 4.49225 | 0.159424 | ||||||||
\(795\) | −35.9366 | −1.27454 | ||||||||
\(796\) | −39.5713 | −1.40257 | ||||||||
\(797\) | 50.5438 | 1.79035 | 0.895176 | − | 0.445713i | \(-0.147050\pi\) | ||||
0.895176 | + | 0.445713i | \(0.147050\pi\) | |||||||
\(798\) | 2.06233 | 0.0730059 | ||||||||
\(799\) | −12.5423 | −0.443714 | ||||||||
\(800\) | −52.1137 | −1.84250 | ||||||||
\(801\) | 8.58421 | 0.303308 | ||||||||
\(802\) | 11.5438 | 0.407624 | ||||||||
\(803\) | −31.6389 | −1.11651 | ||||||||
\(804\) | 13.2091 | 0.465851 | ||||||||
\(805\) | 12.5977 | 0.444012 | ||||||||
\(806\) | −7.06596 | −0.248888 | ||||||||
\(807\) | −13.3950 | −0.471528 | ||||||||
\(808\) | 32.2439 | 1.13434 | ||||||||
\(809\) | −26.5517 | −0.933509 | −0.466755 | − | 0.884387i | \(-0.654577\pi\) | ||||
−0.466755 | + | 0.884387i | \(0.654577\pi\) | |||||||
\(810\) | 1.94519 | 0.0683471 | ||||||||
\(811\) | 5.23369 | 0.183780 | 0.0918898 | − | 0.995769i | \(-0.470709\pi\) | ||||
0.0918898 | + | 0.995769i | \(0.470709\pi\) | |||||||
\(812\) | 3.30992 | 0.116155 | ||||||||
\(813\) | −20.6607 | −0.724601 | ||||||||
\(814\) | 14.7890 | 0.518356 | ||||||||
\(815\) | 56.9196 | 1.99381 | ||||||||
\(816\) | −2.58783 | −0.0905922 | ||||||||
\(817\) | 11.8283 | 0.413819 | ||||||||
\(818\) | 16.1030 | 0.563027 | ||||||||
\(819\) | −3.45165 | −0.120610 | ||||||||
\(820\) | 39.6467 | 1.38452 | ||||||||
\(821\) | 5.58871 | 0.195047 | 0.0975237 | − | 0.995233i | \(-0.468908\pi\) | ||||
0.0975237 | + | 0.995233i | \(0.468908\pi\) | |||||||
\(822\) | −9.71256 | −0.338764 | ||||||||
\(823\) | 17.8202 | 0.621171 | 0.310586 | − | 0.950545i | \(-0.399475\pi\) | ||||
0.310586 | + | 0.950545i | \(0.399475\pi\) | |||||||
\(824\) | −10.5905 | −0.368939 | ||||||||
\(825\) | −37.5227 | −1.30637 | ||||||||
\(826\) | 4.68945 | 0.163167 | ||||||||
\(827\) | 41.1804 | 1.43198 | 0.715991 | − | 0.698110i | \(-0.245975\pi\) | ||||
0.715991 | + | 0.698110i | \(0.245975\pi\) | |||||||
\(828\) | 7.10744 | 0.247000 | ||||||||
\(829\) | −44.2796 | −1.53789 | −0.768947 | − | 0.639312i | \(-0.779219\pi\) | ||||
−0.768947 | + | 0.639312i | \(0.779219\pi\) | |||||||
\(830\) | 16.3640 | 0.568004 | ||||||||
\(831\) | −15.5579 | −0.539698 | ||||||||
\(832\) | 11.7575 | 0.407618 | ||||||||
\(833\) | −6.37272 | −0.220802 | ||||||||
\(834\) | 8.03214 | 0.278130 | ||||||||
\(835\) | 20.5584 | 0.711452 | ||||||||
\(836\) | −33.2156 | −1.14879 | ||||||||
\(837\) | 3.27296 | 0.113130 | ||||||||
\(838\) | 0.506619 | 0.0175009 | ||||||||
\(839\) | −8.39870 | −0.289955 | −0.144978 | − | 0.989435i | \(-0.546311\pi\) | ||||
−0.144978 | + | 0.989435i | \(0.546311\pi\) | |||||||
\(840\) | 5.78440 | 0.199581 | ||||||||
\(841\) | −23.3270 | −0.804379 | ||||||||
\(842\) | −7.87215 | −0.271292 | ||||||||
\(843\) | −3.42774 | −0.118058 | ||||||||
\(844\) | 6.99078 | 0.240633 | ||||||||
\(845\) | −23.5319 | −0.809523 | ||||||||
\(846\) | 6.21316 | 0.213613 | ||||||||
\(847\) | 1.56039 | 0.0536155 | ||||||||
\(848\) | −23.6835 | −0.813295 | ||||||||
\(849\) | −4.99808 | −0.171534 | ||||||||
\(850\) | −5.16128 | −0.177031 | ||||||||
\(851\) | 33.5789 | 1.15107 | ||||||||
\(852\) | 15.5026 | 0.531110 | ||||||||
\(853\) | 40.8685 | 1.39931 | 0.699656 | − | 0.714480i | \(-0.253337\pi\) | ||||
0.699656 | + | 0.714480i | \(0.253337\pi\) | |||||||
\(854\) | −2.10739 | −0.0721133 | ||||||||
\(855\) | −20.6404 | −0.705887 | ||||||||
\(856\) | 19.8382 | 0.678055 | ||||||||
\(857\) | −47.8137 | −1.63329 | −0.816643 | − | 0.577143i | \(-0.804167\pi\) | ||||
−0.816643 | + | 0.577143i | \(0.804167\pi\) | |||||||
\(858\) | −7.77505 | −0.265436 | ||||||||
\(859\) | −25.9929 | −0.886867 | −0.443433 | − | 0.896307i | \(-0.646240\pi\) | ||||
−0.443433 | + | 0.896307i | \(0.646240\pi\) | |||||||
\(860\) | 15.5037 | 0.528671 | ||||||||
\(861\) | −4.55757 | −0.155322 | ||||||||
\(862\) | −13.2544 | −0.451448 | ||||||||
\(863\) | −16.0387 | −0.545965 | −0.272982 | − | 0.962019i | \(-0.588010\pi\) | ||||
−0.272982 | + | 0.962019i | \(0.588010\pi\) | |||||||
\(864\) | 5.00184 | 0.170166 | ||||||||
\(865\) | −53.7319 | −1.82694 | ||||||||
\(866\) | 4.12343 | 0.140120 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 4.54832 | 0.154380 | ||||||||
\(869\) | −3.60141 | −0.122169 | ||||||||
\(870\) | 4.63308 | 0.157076 | ||||||||
\(871\) | −32.8088 | −1.11168 | ||||||||
\(872\) | 23.4261 | 0.793308 | ||||||||
\(873\) | 5.86365 | 0.198454 | ||||||||
\(874\) | 10.5478 | 0.356785 | ||||||||
\(875\) | −16.8527 | −0.569725 | ||||||||
\(876\) | −15.4144 | −0.520806 | ||||||||
\(877\) | 7.11057 | 0.240107 | 0.120054 | − | 0.992767i | \(-0.461693\pi\) | ||||
0.120054 | + | 0.992767i | \(0.461693\pi\) | |||||||
\(878\) | 14.9732 | 0.505323 | ||||||||
\(879\) | −29.0788 | −0.980804 | ||||||||
\(880\) | −36.5961 | −1.23365 | ||||||||
\(881\) | 40.6863 | 1.37076 | 0.685378 | − | 0.728188i | \(-0.259637\pi\) | ||||
0.685378 | + | 0.728188i | \(0.259637\pi\) | |||||||
\(882\) | 3.15690 | 0.106298 | ||||||||
\(883\) | −27.2209 | −0.916055 | −0.458027 | − | 0.888938i | \(-0.651444\pi\) | ||||
−0.458027 | + | 0.888938i | \(0.651444\pi\) | |||||||
\(884\) | 7.64668 | 0.257186 | ||||||||
\(885\) | −46.9333 | −1.57764 | ||||||||
\(886\) | −9.31086 | −0.312804 | ||||||||
\(887\) | 32.7743 | 1.10045 | 0.550227 | − | 0.835015i | \(-0.314541\pi\) | ||||
0.550227 | + | 0.835015i | \(0.314541\pi\) | |||||||
\(888\) | 15.4181 | 0.517398 | ||||||||
\(889\) | 5.43779 | 0.182378 | ||||||||
\(890\) | 16.6979 | 0.559716 | ||||||||
\(891\) | 3.60141 | 0.120652 | ||||||||
\(892\) | 52.0640 | 1.74323 | ||||||||
\(893\) | −65.9277 | −2.20619 | ||||||||
\(894\) | −10.0443 | −0.335931 | ||||||||
\(895\) | 58.5560 | 1.95731 | ||||||||
\(896\) | 8.98152 | 0.300052 | ||||||||
\(897\) | −17.6534 | −0.589431 | ||||||||
\(898\) | −17.4009 | −0.580674 | ||||||||
\(899\) | 7.79556 | 0.259997 | ||||||||
\(900\) | −18.2810 | −0.609367 | ||||||||
\(901\) | −9.15188 | −0.304893 | ||||||||
\(902\) | −10.2662 | −0.341828 | ||||||||
\(903\) | −1.78222 | −0.0593086 | ||||||||
\(904\) | −38.3110 | −1.27420 | ||||||||
\(905\) | −75.5963 | −2.51291 | ||||||||
\(906\) | −6.61358 | −0.219721 | ||||||||
\(907\) | −25.2980 | −0.840007 | −0.420003 | − | 0.907523i | \(-0.637971\pi\) | ||||
−0.420003 | + | 0.907523i | \(0.637971\pi\) | |||||||
\(908\) | 46.6869 | 1.54936 | ||||||||
\(909\) | 17.3359 | 0.574997 | ||||||||
\(910\) | −6.71412 | −0.222571 | ||||||||
\(911\) | 43.0898 | 1.42763 | 0.713814 | − | 0.700335i | \(-0.246966\pi\) | ||||
0.713814 | + | 0.700335i | \(0.246966\pi\) | |||||||
\(912\) | −13.6028 | −0.450433 | ||||||||
\(913\) | 30.2971 | 1.00269 | ||||||||
\(914\) | −5.84064 | −0.193191 | ||||||||
\(915\) | 21.0913 | 0.697257 | ||||||||
\(916\) | −36.6942 | −1.21241 | ||||||||
\(917\) | −6.37897 | −0.210652 | ||||||||
\(918\) | 0.495377 | 0.0163499 | ||||||||
\(919\) | 41.6507 | 1.37393 | 0.686965 | − | 0.726690i | \(-0.258942\pi\) | ||||
0.686965 | + | 0.726690i | \(0.258942\pi\) | |||||||
\(920\) | 29.5843 | 0.975365 | ||||||||
\(921\) | −23.6235 | −0.778420 | ||||||||
\(922\) | 3.53417 | 0.116392 | ||||||||
\(923\) | −38.5053 | −1.26742 | ||||||||
\(924\) | 5.00476 | 0.164644 | ||||||||
\(925\) | −86.3681 | −2.83977 | ||||||||
\(926\) | −18.1211 | −0.595496 | ||||||||
\(927\) | −5.69401 | −0.187016 | ||||||||
\(928\) | 11.9134 | 0.391077 | ||||||||
\(929\) | −24.1981 | −0.793912 | −0.396956 | − | 0.917838i | \(-0.629934\pi\) | ||||
−0.396956 | + | 0.917838i | \(0.629934\pi\) | |||||||
\(930\) | 6.36653 | 0.208767 | ||||||||
\(931\) | −33.4978 | −1.09785 | ||||||||
\(932\) | −5.46385 | −0.178974 | ||||||||
\(933\) | −13.4375 | −0.439925 | ||||||||
\(934\) | −13.1463 | −0.430159 | ||||||||
\(935\) | −14.1416 | −0.462481 | ||||||||
\(936\) | −8.10577 | −0.264945 | ||||||||
\(937\) | 41.5780 | 1.35829 | 0.679146 | − | 0.734003i | \(-0.262350\pi\) | ||||
0.679146 | + | 0.734003i | \(0.262350\pi\) | |||||||
\(938\) | −2.95368 | −0.0964411 | ||||||||
\(939\) | −23.5037 | −0.767015 | ||||||||
\(940\) | −86.4135 | −2.81850 | ||||||||
\(941\) | −34.4303 | −1.12240 | −0.561198 | − | 0.827681i | \(-0.689660\pi\) | ||||
−0.561198 | + | 0.827681i | \(0.689660\pi\) | |||||||
\(942\) | 3.46245 | 0.112813 | ||||||||
\(943\) | −23.3097 | −0.759068 | ||||||||
\(944\) | −30.9307 | −1.00671 | ||||||||
\(945\) | 3.10999 | 0.101168 | ||||||||
\(946\) | −4.01456 | −0.130525 | ||||||||
\(947\) | 41.0605 | 1.33429 | 0.667144 | − | 0.744929i | \(-0.267517\pi\) | ||||
0.667144 | + | 0.744929i | \(0.267517\pi\) | |||||||
\(948\) | −1.75460 | −0.0569868 | ||||||||
\(949\) | 38.2864 | 1.24283 | ||||||||
\(950\) | −27.1300 | −0.880213 | ||||||||
\(951\) | −12.7005 | −0.411841 | ||||||||
\(952\) | 1.47310 | 0.0477434 | ||||||||
\(953\) | −21.3535 | −0.691706 | −0.345853 | − | 0.938289i | \(-0.612410\pi\) | ||||
−0.345853 | + | 0.938289i | \(0.612410\pi\) | |||||||
\(954\) | 4.53363 | 0.146782 | ||||||||
\(955\) | −2.76697 | −0.0895372 | ||||||||
\(956\) | −2.27151 | −0.0734658 | ||||||||
\(957\) | 8.57787 | 0.277283 | ||||||||
\(958\) | −5.84530 | −0.188853 | ||||||||
\(959\) | −15.5285 | −0.501441 | ||||||||
\(960\) | −10.5937 | −0.341909 | ||||||||
\(961\) | −20.2877 | −0.654443 | ||||||||
\(962\) | −17.8962 | −0.576998 | ||||||||
\(963\) | 10.6660 | 0.343707 | ||||||||
\(964\) | −42.9405 | −1.38302 | ||||||||
\(965\) | −32.9381 | −1.06032 | ||||||||
\(966\) | −1.58929 | −0.0511344 | ||||||||
\(967\) | 2.54388 | 0.0818056 | 0.0409028 | − | 0.999163i | \(-0.486977\pi\) | ||||
0.0409028 | + | 0.999163i | \(0.486977\pi\) | |||||||
\(968\) | 3.66438 | 0.117778 | ||||||||
\(969\) | −5.25644 | −0.168861 | ||||||||
\(970\) | 11.4059 | 0.366222 | ||||||||
\(971\) | −4.88648 | −0.156815 | −0.0784073 | − | 0.996921i | \(-0.524983\pi\) | ||||
−0.0784073 | + | 0.996921i | \(0.524983\pi\) | |||||||
\(972\) | 1.75460 | 0.0562789 | ||||||||
\(973\) | 12.8418 | 0.411690 | ||||||||
\(974\) | 0.877960 | 0.0281317 | ||||||||
\(975\) | 45.4063 | 1.45417 | ||||||||
\(976\) | 13.8999 | 0.444926 | ||||||||
\(977\) | 43.4594 | 1.39039 | 0.695195 | − | 0.718821i | \(-0.255318\pi\) | ||||
0.695195 | + | 0.718821i | \(0.255318\pi\) | |||||||
\(978\) | −7.18078 | −0.229616 | ||||||||
\(979\) | 30.9153 | 0.988056 | ||||||||
\(980\) | −43.9066 | −1.40255 | ||||||||
\(981\) | 12.5951 | 0.402129 | ||||||||
\(982\) | 9.06903 | 0.289404 | ||||||||
\(983\) | 16.8858 | 0.538573 | 0.269287 | − | 0.963060i | \(-0.413212\pi\) | ||||
0.269287 | + | 0.963060i | \(0.413212\pi\) | |||||||
\(984\) | −10.7029 | −0.341196 | ||||||||
\(985\) | 82.7473 | 2.63655 | ||||||||
\(986\) | 1.17989 | 0.0375755 | ||||||||
\(987\) | 9.93364 | 0.316191 | ||||||||
\(988\) | 40.1943 | 1.27875 | ||||||||
\(989\) | −9.11516 | −0.289845 | ||||||||
\(990\) | 7.00544 | 0.222647 | ||||||||
\(991\) | 18.3162 | 0.581835 | 0.290917 | − | 0.956748i | \(-0.406040\pi\) | ||||
0.290917 | + | 0.956748i | \(0.406040\pi\) | |||||||
\(992\) | 16.3708 | 0.519774 | ||||||||
\(993\) | 3.69932 | 0.117394 | ||||||||
\(994\) | −3.46652 | −0.109951 | ||||||||
\(995\) | −88.5582 | −2.80748 | ||||||||
\(996\) | 14.7607 | 0.467710 | ||||||||
\(997\) | −11.4370 | −0.362213 | −0.181107 | − | 0.983463i | \(-0.557968\pi\) | ||||
−0.181107 | + | 0.983463i | \(0.557968\pi\) | |||||||
\(998\) | 6.76519 | 0.214148 | ||||||||
\(999\) | 8.28956 | 0.262270 |
(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 | 4029.2.a.i.1.12 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.i.1.12 | ✓ | 25 | 1.1 | even | 1 | trivial |