Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [503,2,Mod(1,503)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(503, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("503.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 503.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: | \(4.01647522167\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.858231\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 503.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58686 | −1.82919 | −0.914593 | − | 0.404375i | \(-0.867489\pi\) | ||||
−0.914593 | + | 0.404375i | \(0.867489\pi\) | |||||||
\(3\) | −1.85823 | −1.07285 | −0.536425 | − | 0.843948i | \(-0.680226\pi\) | ||||
−0.536425 | + | 0.843948i | \(0.680226\pi\) | |||||||
\(4\) | 4.69185 | 2.34592 | ||||||||
\(5\) | 1.44291 | 0.645289 | 0.322644 | − | 0.946520i | \(-0.395428\pi\) | ||||
0.322644 | + | 0.946520i | \(0.395428\pi\) | |||||||
\(6\) | 4.80698 | 1.96244 | ||||||||
\(7\) | −1.96509 | −0.742734 | −0.371367 | − | 0.928486i | \(-0.621111\pi\) | ||||
−0.371367 | + | 0.928486i | \(0.621111\pi\) | |||||||
\(8\) | −6.96343 | −2.46194 | ||||||||
\(9\) | 0.453023 | 0.151008 | ||||||||
\(10\) | −3.73261 | −1.18035 | ||||||||
\(11\) | 2.85614 | 0.861160 | 0.430580 | − | 0.902552i | \(-0.358309\pi\) | ||||
0.430580 | + | 0.902552i | \(0.358309\pi\) | |||||||
\(12\) | −8.71853 | −2.51682 | ||||||||
\(13\) | −3.84427 | −1.06621 | −0.533104 | − | 0.846050i | \(-0.678974\pi\) | ||||
−0.533104 | + | 0.846050i | \(0.678974\pi\) | |||||||
\(14\) | 5.08341 | 1.35860 | ||||||||
\(15\) | −2.68126 | −0.692298 | ||||||||
\(16\) | 8.62972 | 2.15743 | ||||||||
\(17\) | 1.30329 | 0.316095 | 0.158047 | − | 0.987432i | \(-0.449480\pi\) | ||||
0.158047 | + | 0.987432i | \(0.449480\pi\) | |||||||
\(18\) | −1.17191 | −0.276221 | ||||||||
\(19\) | 3.53196 | 0.810287 | 0.405143 | − | 0.914253i | \(-0.367222\pi\) | ||||
0.405143 | + | 0.914253i | \(0.367222\pi\) | |||||||
\(20\) | 6.76991 | 1.51380 | ||||||||
\(21\) | 3.65159 | 0.796842 | ||||||||
\(22\) | −7.38845 | −1.57522 | ||||||||
\(23\) | 4.20650 | 0.877115 | 0.438558 | − | 0.898703i | \(-0.355490\pi\) | ||||
0.438558 | + | 0.898703i | \(0.355490\pi\) | |||||||
\(24\) | 12.9397 | 2.64130 | ||||||||
\(25\) | −2.91801 | −0.583602 | ||||||||
\(26\) | 9.94458 | 1.95029 | ||||||||
\(27\) | 4.73287 | 0.910842 | ||||||||
\(28\) | −9.21989 | −1.74240 | ||||||||
\(29\) | −1.10402 | −0.205011 | −0.102506 | − | 0.994732i | \(-0.532686\pi\) | ||||
−0.102506 | + | 0.994732i | \(0.532686\pi\) | |||||||
\(30\) | 6.93604 | 1.26634 | ||||||||
\(31\) | −3.53201 | −0.634368 | −0.317184 | − | 0.948364i | \(-0.602737\pi\) | ||||
−0.317184 | + | 0.948364i | \(0.602737\pi\) | |||||||
\(32\) | −8.39703 | −1.48440 | ||||||||
\(33\) | −5.30738 | −0.923896 | ||||||||
\(34\) | −3.37144 | −0.578196 | ||||||||
\(35\) | −2.83545 | −0.479278 | ||||||||
\(36\) | 2.12551 | 0.354252 | ||||||||
\(37\) | −6.61903 | −1.08816 | −0.544081 | − | 0.839033i | \(-0.683121\pi\) | ||||
−0.544081 | + | 0.839033i | \(0.683121\pi\) | |||||||
\(38\) | −9.13668 | −1.48217 | ||||||||
\(39\) | 7.14353 | 1.14388 | ||||||||
\(40\) | −10.0476 | −1.58866 | ||||||||
\(41\) | 0.671095 | 0.104807 | 0.0524037 | − | 0.998626i | \(-0.483312\pi\) | ||||
0.0524037 | + | 0.998626i | \(0.483312\pi\) | |||||||
\(42\) | −9.44615 | −1.45757 | ||||||||
\(43\) | −4.32289 | −0.659235 | −0.329617 | − | 0.944115i | \(-0.606920\pi\) | ||||
−0.329617 | + | 0.944115i | \(0.606920\pi\) | |||||||
\(44\) | 13.4006 | 2.02021 | ||||||||
\(45\) | 0.653672 | 0.0974436 | ||||||||
\(46\) | −10.8816 | −1.60441 | ||||||||
\(47\) | −0.378524 | −0.0552134 | −0.0276067 | − | 0.999619i | \(-0.508789\pi\) | ||||
−0.0276067 | + | 0.999619i | \(0.508789\pi\) | |||||||
\(48\) | −16.0360 | −2.31460 | ||||||||
\(49\) | −3.13843 | −0.448347 | ||||||||
\(50\) | 7.54849 | 1.06752 | ||||||||
\(51\) | −2.42182 | −0.339122 | ||||||||
\(52\) | −18.0367 | −2.50124 | ||||||||
\(53\) | −7.13700 | −0.980342 | −0.490171 | − | 0.871626i | \(-0.663066\pi\) | ||||
−0.490171 | + | 0.871626i | \(0.663066\pi\) | |||||||
\(54\) | −12.2433 | −1.66610 | ||||||||
\(55\) | 4.12116 | 0.555697 | ||||||||
\(56\) | 13.6838 | 1.82857 | ||||||||
\(57\) | −6.56319 | −0.869316 | ||||||||
\(58\) | 2.85594 | 0.375004 | ||||||||
\(59\) | −13.8806 | −1.80709 | −0.903547 | − | 0.428489i | \(-0.859046\pi\) | ||||
−0.903547 | + | 0.428489i | \(0.859046\pi\) | |||||||
\(60\) | −12.5801 | −1.62408 | ||||||||
\(61\) | −6.51374 | −0.833999 | −0.417000 | − | 0.908907i | \(-0.636918\pi\) | ||||
−0.417000 | + | 0.908907i | \(0.636918\pi\) | |||||||
\(62\) | 9.13682 | 1.16038 | ||||||||
\(63\) | −0.890231 | −0.112159 | ||||||||
\(64\) | 4.46249 | 0.557812 | ||||||||
\(65\) | −5.54693 | −0.688012 | ||||||||
\(66\) | 13.7294 | 1.68998 | ||||||||
\(67\) | −7.55189 | −0.922610 | −0.461305 | − | 0.887242i | \(-0.652619\pi\) | ||||
−0.461305 | + | 0.887242i | \(0.652619\pi\) | |||||||
\(68\) | 6.11485 | 0.741534 | ||||||||
\(69\) | −7.81664 | −0.941013 | ||||||||
\(70\) | 7.33490 | 0.876688 | ||||||||
\(71\) | 0.0744967 | 0.00884113 | 0.00442057 | − | 0.999990i | \(-0.498593\pi\) | ||||
0.00442057 | + | 0.999990i | \(0.498593\pi\) | |||||||
\(72\) | −3.15459 | −0.371772 | ||||||||
\(73\) | 3.29052 | 0.385126 | 0.192563 | − | 0.981285i | \(-0.438320\pi\) | ||||
0.192563 | + | 0.981285i | \(0.438320\pi\) | |||||||
\(74\) | 17.1225 | 1.99045 | ||||||||
\(75\) | 5.42234 | 0.626118 | ||||||||
\(76\) | 16.5714 | 1.90087 | ||||||||
\(77\) | −5.61258 | −0.639612 | ||||||||
\(78\) | −18.4793 | −2.09237 | ||||||||
\(79\) | 8.57578 | 0.964850 | 0.482425 | − | 0.875937i | \(-0.339756\pi\) | ||||
0.482425 | + | 0.875937i | \(0.339756\pi\) | |||||||
\(80\) | 12.4519 | 1.39217 | ||||||||
\(81\) | −10.1538 | −1.12820 | ||||||||
\(82\) | −1.73603 | −0.191712 | ||||||||
\(83\) | 14.8165 | 1.62632 | 0.813158 | − | 0.582042i | \(-0.197746\pi\) | ||||
0.813158 | + | 0.582042i | \(0.197746\pi\) | |||||||
\(84\) | 17.1327 | 1.86933 | ||||||||
\(85\) | 1.88053 | 0.203973 | ||||||||
\(86\) | 11.1827 | 1.20586 | ||||||||
\(87\) | 2.05152 | 0.219946 | ||||||||
\(88\) | −19.8886 | −2.12013 | ||||||||
\(89\) | −17.5415 | −1.85940 | −0.929700 | − | 0.368318i | \(-0.879934\pi\) | ||||
−0.929700 | + | 0.368318i | \(0.879934\pi\) | |||||||
\(90\) | −1.69096 | −0.178243 | ||||||||
\(91\) | 7.55432 | 0.791908 | ||||||||
\(92\) | 19.7362 | 2.05764 | ||||||||
\(93\) | 6.56329 | 0.680582 | ||||||||
\(94\) | 0.979188 | 0.100996 | ||||||||
\(95\) | 5.09630 | 0.522869 | ||||||||
\(96\) | 15.6036 | 1.59254 | ||||||||
\(97\) | −8.01702 | −0.814005 | −0.407003 | − | 0.913427i | \(-0.633426\pi\) | ||||
−0.407003 | + | 0.913427i | \(0.633426\pi\) | |||||||
\(98\) | 8.11867 | 0.820110 | ||||||||
\(99\) | 1.29390 | 0.130042 | ||||||||
\(100\) | −13.6909 | −1.36909 | ||||||||
\(101\) | 9.11148 | 0.906626 | 0.453313 | − | 0.891351i | \(-0.350242\pi\) | ||||
0.453313 | + | 0.891351i | \(0.350242\pi\) | |||||||
\(102\) | 6.26491 | 0.620318 | ||||||||
\(103\) | −15.2943 | −1.50699 | −0.753494 | − | 0.657455i | \(-0.771633\pi\) | ||||
−0.753494 | + | 0.657455i | \(0.771633\pi\) | |||||||
\(104\) | 26.7693 | 2.62494 | ||||||||
\(105\) | 5.26891 | 0.514193 | ||||||||
\(106\) | 18.4624 | 1.79323 | ||||||||
\(107\) | 3.50420 | 0.338764 | 0.169382 | − | 0.985550i | \(-0.445823\pi\) | ||||
0.169382 | + | 0.985550i | \(0.445823\pi\) | |||||||
\(108\) | 22.2059 | 2.13676 | ||||||||
\(109\) | 2.49301 | 0.238787 | 0.119393 | − | 0.992847i | \(-0.461905\pi\) | ||||
0.119393 | + | 0.992847i | \(0.461905\pi\) | |||||||
\(110\) | −10.6609 | −1.01647 | ||||||||
\(111\) | 12.2997 | 1.16743 | ||||||||
\(112\) | −16.9582 | −1.60240 | ||||||||
\(113\) | −14.5343 | −1.36727 | −0.683634 | − | 0.729825i | \(-0.739601\pi\) | ||||
−0.683634 | + | 0.729825i | \(0.739601\pi\) | |||||||
\(114\) | 16.9781 | 1.59014 | ||||||||
\(115\) | 6.06959 | 0.565993 | ||||||||
\(116\) | −5.17989 | −0.480941 | ||||||||
\(117\) | −1.74154 | −0.161006 | ||||||||
\(118\) | 35.9070 | 3.30551 | ||||||||
\(119\) | −2.56109 | −0.234774 | ||||||||
\(120\) | 18.6708 | 1.70440 | ||||||||
\(121\) | −2.84244 | −0.258404 | ||||||||
\(122\) | 16.8501 | 1.52554 | ||||||||
\(123\) | −1.24705 | −0.112443 | ||||||||
\(124\) | −16.5716 | −1.48818 | ||||||||
\(125\) | −11.4250 | −1.02188 | ||||||||
\(126\) | 2.30290 | 0.205159 | ||||||||
\(127\) | 5.52702 | 0.490443 | 0.245222 | − | 0.969467i | \(-0.421139\pi\) | ||||
0.245222 | + | 0.969467i | \(0.421139\pi\) | |||||||
\(128\) | 5.25021 | 0.464057 | ||||||||
\(129\) | 8.03293 | 0.707260 | ||||||||
\(130\) | 14.3491 | 1.25850 | ||||||||
\(131\) | −21.2174 | −1.85377 | −0.926885 | − | 0.375346i | \(-0.877524\pi\) | ||||
−0.926885 | + | 0.375346i | \(0.877524\pi\) | |||||||
\(132\) | −24.9014 | −2.16739 | ||||||||
\(133\) | −6.94061 | −0.601827 | ||||||||
\(134\) | 19.5357 | 1.68763 | ||||||||
\(135\) | 6.82911 | 0.587756 | ||||||||
\(136\) | −9.07538 | −0.778208 | ||||||||
\(137\) | 11.6794 | 0.997835 | 0.498917 | − | 0.866650i | \(-0.333731\pi\) | ||||
0.498917 | + | 0.866650i | \(0.333731\pi\) | |||||||
\(138\) | 20.2206 | 1.72129 | ||||||||
\(139\) | −10.8676 | −0.921778 | −0.460889 | − | 0.887458i | \(-0.652469\pi\) | ||||
−0.460889 | + | 0.887458i | \(0.652469\pi\) | |||||||
\(140\) | −13.3035 | −1.12435 | ||||||||
\(141\) | 0.703385 | 0.0592357 | ||||||||
\(142\) | −0.192713 | −0.0161721 | ||||||||
\(143\) | −10.9798 | −0.918175 | ||||||||
\(144\) | 3.90946 | 0.325789 | ||||||||
\(145\) | −1.59300 | −0.132292 | ||||||||
\(146\) | −8.51212 | −0.704468 | ||||||||
\(147\) | 5.83192 | 0.481009 | ||||||||
\(148\) | −31.0555 | −2.55274 | ||||||||
\(149\) | −7.40209 | −0.606403 | −0.303202 | − | 0.952926i | \(-0.598056\pi\) | ||||
−0.303202 | + | 0.952926i | \(0.598056\pi\) | |||||||
\(150\) | −14.0268 | −1.14529 | ||||||||
\(151\) | 6.09188 | 0.495750 | 0.247875 | − | 0.968792i | \(-0.420268\pi\) | ||||
0.247875 | + | 0.968792i | \(0.420268\pi\) | |||||||
\(152\) | −24.5945 | −1.99488 | ||||||||
\(153\) | 0.590422 | 0.0477328 | ||||||||
\(154\) | 14.5189 | 1.16997 | ||||||||
\(155\) | −5.09637 | −0.409350 | ||||||||
\(156\) | 33.5164 | 2.68346 | ||||||||
\(157\) | 2.22790 | 0.177806 | 0.0889028 | − | 0.996040i | \(-0.471664\pi\) | ||||
0.0889028 | + | 0.996040i | \(0.471664\pi\) | |||||||
\(158\) | −22.1843 | −1.76489 | ||||||||
\(159\) | 13.2622 | 1.05176 | ||||||||
\(160\) | −12.1162 | −0.957866 | ||||||||
\(161\) | −8.26614 | −0.651463 | ||||||||
\(162\) | 26.2666 | 2.06370 | ||||||||
\(163\) | −18.7370 | −1.46759 | −0.733797 | − | 0.679368i | \(-0.762254\pi\) | ||||
−0.733797 | + | 0.679368i | \(0.762254\pi\) | |||||||
\(164\) | 3.14867 | 0.245870 | ||||||||
\(165\) | −7.65807 | −0.596180 | ||||||||
\(166\) | −38.3281 | −2.97484 | ||||||||
\(167\) | 22.7237 | 1.75841 | 0.879205 | − | 0.476443i | \(-0.158074\pi\) | ||||
0.879205 | + | 0.476443i | \(0.158074\pi\) | |||||||
\(168\) | −25.4276 | −1.96178 | ||||||||
\(169\) | 1.77838 | 0.136798 | ||||||||
\(170\) | −4.86468 | −0.373104 | ||||||||
\(171\) | 1.60006 | 0.122360 | ||||||||
\(172\) | −20.2823 | −1.54651 | ||||||||
\(173\) | −2.25141 | −0.171172 | −0.0855859 | − | 0.996331i | \(-0.527276\pi\) | ||||
−0.0855859 | + | 0.996331i | \(0.527276\pi\) | |||||||
\(174\) | −5.30701 | −0.402323 | ||||||||
\(175\) | 5.73415 | 0.433461 | ||||||||
\(176\) | 24.6477 | 1.85789 | ||||||||
\(177\) | 25.7933 | 1.93874 | ||||||||
\(178\) | 45.3775 | 3.40119 | ||||||||
\(179\) | 15.8986 | 1.18832 | 0.594159 | − | 0.804348i | \(-0.297485\pi\) | ||||
0.594159 | + | 0.804348i | \(0.297485\pi\) | |||||||
\(180\) | 3.06693 | 0.228595 | ||||||||
\(181\) | 16.5942 | 1.23344 | 0.616718 | − | 0.787184i | \(-0.288462\pi\) | ||||
0.616718 | + | 0.787184i | \(0.288462\pi\) | |||||||
\(182\) | −19.5420 | −1.44855 | ||||||||
\(183\) | 12.1040 | 0.894756 | ||||||||
\(184\) | −29.2916 | −2.15941 | ||||||||
\(185\) | −9.55066 | −0.702179 | ||||||||
\(186\) | −16.9783 | −1.24491 | ||||||||
\(187\) | 3.72239 | 0.272208 | ||||||||
\(188\) | −1.77598 | −0.129526 | ||||||||
\(189\) | −9.30051 | −0.676513 | ||||||||
\(190\) | −13.1834 | −0.956425 | ||||||||
\(191\) | −2.03640 | −0.147348 | −0.0736742 | − | 0.997282i | \(-0.523473\pi\) | ||||
−0.0736742 | + | 0.997282i | \(0.523473\pi\) | |||||||
\(192\) | −8.29235 | −0.598448 | ||||||||
\(193\) | −15.1384 | −1.08968 | −0.544841 | − | 0.838539i | \(-0.683410\pi\) | ||||
−0.544841 | + | 0.838539i | \(0.683410\pi\) | |||||||
\(194\) | 20.7389 | 1.48897 | ||||||||
\(195\) | 10.3075 | 0.738134 | ||||||||
\(196\) | −14.7250 | −1.05179 | ||||||||
\(197\) | −6.01285 | −0.428398 | −0.214199 | − | 0.976790i | \(-0.568714\pi\) | ||||
−0.214199 | + | 0.976790i | \(0.568714\pi\) | |||||||
\(198\) | −3.34714 | −0.237871 | ||||||||
\(199\) | 23.5513 | 1.66951 | 0.834753 | − | 0.550624i | \(-0.185610\pi\) | ||||
0.834753 | + | 0.550624i | \(0.185610\pi\) | |||||||
\(200\) | 20.3194 | 1.43680 | ||||||||
\(201\) | 14.0332 | 0.989823 | ||||||||
\(202\) | −23.5701 | −1.65839 | ||||||||
\(203\) | 2.16950 | 0.152269 | ||||||||
\(204\) | −11.3628 | −0.795555 | ||||||||
\(205\) | 0.968329 | 0.0676311 | ||||||||
\(206\) | 39.5641 | 2.75656 | ||||||||
\(207\) | 1.90564 | 0.132451 | ||||||||
\(208\) | −33.1749 | −2.30027 | ||||||||
\(209\) | 10.0878 | 0.697786 | ||||||||
\(210\) | −13.6299 | −0.940555 | ||||||||
\(211\) | 2.35555 | 0.162163 | 0.0810814 | − | 0.996707i | \(-0.474163\pi\) | ||||
0.0810814 | + | 0.996707i | \(0.474163\pi\) | |||||||
\(212\) | −33.4857 | −2.29981 | ||||||||
\(213\) | −0.138432 | −0.00948521 | ||||||||
\(214\) | −9.06488 | −0.619662 | ||||||||
\(215\) | −6.23754 | −0.425397 | ||||||||
\(216\) | −32.9570 | −2.24244 | ||||||||
\(217\) | 6.94071 | 0.471166 | ||||||||
\(218\) | −6.44906 | −0.436785 | ||||||||
\(219\) | −6.11455 | −0.413183 | ||||||||
\(220\) | 19.3358 | 1.30362 | ||||||||
\(221\) | −5.01020 | −0.337023 | ||||||||
\(222\) | −31.8176 | −2.13546 | ||||||||
\(223\) | 13.6268 | 0.912519 | 0.456260 | − | 0.889847i | \(-0.349189\pi\) | ||||
0.456260 | + | 0.889847i | \(0.349189\pi\) | |||||||
\(224\) | 16.5009 | 1.10251 | ||||||||
\(225\) | −1.32193 | −0.0881285 | ||||||||
\(226\) | 37.5981 | 2.50099 | ||||||||
\(227\) | 11.9812 | 0.795218 | 0.397609 | − | 0.917555i | \(-0.369840\pi\) | ||||
0.397609 | + | 0.917555i | \(0.369840\pi\) | |||||||
\(228\) | −30.7935 | −2.03935 | ||||||||
\(229\) | 27.2066 | 1.79786 | 0.898932 | − | 0.438087i | \(-0.144344\pi\) | ||||
0.898932 | + | 0.438087i | \(0.144344\pi\) | |||||||
\(230\) | −15.7012 | −1.03531 | ||||||||
\(231\) | 10.4295 | 0.686208 | ||||||||
\(232\) | 7.68776 | 0.504726 | ||||||||
\(233\) | 14.4504 | 0.946679 | 0.473339 | − | 0.880880i | \(-0.343048\pi\) | ||||
0.473339 | + | 0.880880i | \(0.343048\pi\) | |||||||
\(234\) | 4.50512 | 0.294509 | ||||||||
\(235\) | −0.546176 | −0.0356286 | ||||||||
\(236\) | −65.1254 | −4.23930 | ||||||||
\(237\) | −15.9358 | −1.03514 | ||||||||
\(238\) | 6.62517 | 0.429446 | ||||||||
\(239\) | −23.9361 | −1.54830 | −0.774148 | − | 0.633005i | \(-0.781821\pi\) | ||||
−0.774148 | + | 0.633005i | \(0.781821\pi\) | |||||||
\(240\) | −23.1385 | −1.49359 | ||||||||
\(241\) | −13.7734 | −0.887224 | −0.443612 | − | 0.896219i | \(-0.646303\pi\) | ||||
−0.443612 | + | 0.896219i | \(0.646303\pi\) | |||||||
\(242\) | 7.35300 | 0.472668 | ||||||||
\(243\) | 4.66957 | 0.299553 | ||||||||
\(244\) | −30.5615 | −1.95650 | ||||||||
\(245\) | −4.52847 | −0.289313 | ||||||||
\(246\) | 3.22594 | 0.205679 | ||||||||
\(247\) | −13.5778 | −0.863934 | ||||||||
\(248\) | 24.5949 | 1.56178 | ||||||||
\(249\) | −27.5324 | −1.74479 | ||||||||
\(250\) | 29.5548 | 1.86921 | ||||||||
\(251\) | −8.26975 | −0.521982 | −0.260991 | − | 0.965341i | \(-0.584049\pi\) | ||||
−0.260991 | + | 0.965341i | \(0.584049\pi\) | |||||||
\(252\) | −4.17682 | −0.263115 | ||||||||
\(253\) | 12.0144 | 0.755336 | ||||||||
\(254\) | −14.2976 | −0.897112 | ||||||||
\(255\) | −3.49447 | −0.218832 | ||||||||
\(256\) | −22.5065 | −1.40666 | ||||||||
\(257\) | −20.1486 | −1.25684 | −0.628418 | − | 0.777876i | \(-0.716297\pi\) | ||||
−0.628418 | + | 0.777876i | \(0.716297\pi\) | |||||||
\(258\) | −20.7801 | −1.29371 | ||||||||
\(259\) | 13.0070 | 0.808214 | ||||||||
\(260\) | −26.0253 | −1.61402 | ||||||||
\(261\) | −0.500147 | −0.0309583 | ||||||||
\(262\) | 54.8863 | 3.39089 | ||||||||
\(263\) | −27.9229 | −1.72180 | −0.860900 | − | 0.508774i | \(-0.830099\pi\) | ||||
−0.860900 | + | 0.508774i | \(0.830099\pi\) | |||||||
\(264\) | 36.9575 | 2.27458 | ||||||||
\(265\) | −10.2980 | −0.632604 | ||||||||
\(266\) | 17.9544 | 1.10085 | ||||||||
\(267\) | 32.5962 | 1.99486 | ||||||||
\(268\) | −35.4323 | −2.16437 | ||||||||
\(269\) | 11.6165 | 0.708269 | 0.354135 | − | 0.935194i | \(-0.384775\pi\) | ||||
0.354135 | + | 0.935194i | \(0.384775\pi\) | |||||||
\(270\) | −17.6659 | −1.07512 | ||||||||
\(271\) | −3.27787 | −0.199117 | −0.0995583 | − | 0.995032i | \(-0.531743\pi\) | ||||
−0.0995583 | + | 0.995032i | \(0.531743\pi\) | |||||||
\(272\) | 11.2471 | 0.681953 | ||||||||
\(273\) | −14.0377 | −0.849599 | ||||||||
\(274\) | −30.2129 | −1.82523 | ||||||||
\(275\) | −8.33426 | −0.502575 | ||||||||
\(276\) | −36.6745 | −2.20754 | ||||||||
\(277\) | 10.1157 | 0.607795 | 0.303897 | − | 0.952705i | \(-0.401712\pi\) | ||||
0.303897 | + | 0.952705i | \(0.401712\pi\) | |||||||
\(278\) | 28.1130 | 1.68610 | ||||||||
\(279\) | −1.60008 | −0.0957944 | ||||||||
\(280\) | 19.7444 | 1.17995 | ||||||||
\(281\) | 16.7656 | 1.00015 | 0.500077 | − | 0.865981i | \(-0.333305\pi\) | ||||
0.500077 | + | 0.865981i | \(0.333305\pi\) | |||||||
\(282\) | −1.81956 | −0.108353 | ||||||||
\(283\) | 15.4382 | 0.917705 | 0.458852 | − | 0.888513i | \(-0.348261\pi\) | ||||
0.458852 | + | 0.888513i | \(0.348261\pi\) | |||||||
\(284\) | 0.349527 | 0.0207406 | ||||||||
\(285\) | −9.47010 | −0.560960 | ||||||||
\(286\) | 28.4031 | 1.67951 | ||||||||
\(287\) | −1.31876 | −0.0778440 | ||||||||
\(288\) | −3.80405 | −0.224156 | ||||||||
\(289\) | −15.3014 | −0.900084 | ||||||||
\(290\) | 4.12087 | 0.241986 | ||||||||
\(291\) | 14.8975 | 0.873306 | ||||||||
\(292\) | 15.4386 | 0.903477 | ||||||||
\(293\) | −7.52887 | −0.439841 | −0.219921 | − | 0.975518i | \(-0.570580\pi\) | ||||
−0.219921 | + | 0.975518i | \(0.570580\pi\) | |||||||
\(294\) | −15.0864 | −0.879855 | ||||||||
\(295\) | −20.0284 | −1.16610 | ||||||||
\(296\) | 46.0911 | 2.67899 | ||||||||
\(297\) | 13.5178 | 0.784380 | ||||||||
\(298\) | 19.1482 | 1.10922 | ||||||||
\(299\) | −16.1709 | −0.935187 | ||||||||
\(300\) | 25.4408 | 1.46882 | ||||||||
\(301\) | 8.49487 | 0.489636 | ||||||||
\(302\) | −15.7588 | −0.906819 | ||||||||
\(303\) | −16.9312 | −0.972674 | ||||||||
\(304\) | 30.4798 | 1.74814 | ||||||||
\(305\) | −9.39874 | −0.538170 | ||||||||
\(306\) | −1.52734 | −0.0873121 | ||||||||
\(307\) | 17.1932 | 0.981265 | 0.490632 | − | 0.871367i | \(-0.336766\pi\) | ||||
0.490632 | + | 0.871367i | \(0.336766\pi\) | |||||||
\(308\) | −26.3333 | −1.50048 | ||||||||
\(309\) | 28.4203 | 1.61677 | ||||||||
\(310\) | 13.1836 | 0.748778 | ||||||||
\(311\) | 10.1595 | 0.576094 | 0.288047 | − | 0.957616i | \(-0.406994\pi\) | ||||
0.288047 | + | 0.957616i | \(0.406994\pi\) | |||||||
\(312\) | −49.7435 | −2.81617 | ||||||||
\(313\) | 26.6909 | 1.50866 | 0.754329 | − | 0.656496i | \(-0.227962\pi\) | ||||
0.754329 | + | 0.656496i | \(0.227962\pi\) | |||||||
\(314\) | −5.76326 | −0.325240 | ||||||||
\(315\) | −1.28452 | −0.0723746 | ||||||||
\(316\) | 40.2362 | 2.26346 | ||||||||
\(317\) | 19.3855 | 1.08880 | 0.544398 | − | 0.838827i | \(-0.316758\pi\) | ||||
0.544398 | + | 0.838827i | \(0.316758\pi\) | |||||||
\(318\) | −34.3074 | −1.92386 | ||||||||
\(319\) | −3.15324 | −0.176548 | ||||||||
\(320\) | 6.43898 | 0.359950 | ||||||||
\(321\) | −6.51161 | −0.363443 | ||||||||
\(322\) | 21.3833 | 1.19165 | ||||||||
\(323\) | 4.60317 | 0.256127 | ||||||||
\(324\) | −47.6402 | −2.64668 | ||||||||
\(325\) | 11.2176 | 0.622241 | ||||||||
\(326\) | 48.4700 | 2.68450 | ||||||||
\(327\) | −4.63258 | −0.256182 | ||||||||
\(328\) | −4.67312 | −0.258030 | ||||||||
\(329\) | 0.743833 | 0.0410088 | ||||||||
\(330\) | 19.8103 | 1.09052 | ||||||||
\(331\) | −26.0579 | −1.43227 | −0.716135 | − | 0.697962i | \(-0.754090\pi\) | ||||
−0.716135 | + | 0.697962i | \(0.754090\pi\) | |||||||
\(332\) | 69.5165 | 3.81521 | ||||||||
\(333\) | −2.99857 | −0.164321 | ||||||||
\(334\) | −58.7830 | −3.21646 | ||||||||
\(335\) | −10.8967 | −0.595350 | ||||||||
\(336\) | 31.5122 | 1.71913 | ||||||||
\(337\) | −11.6240 | −0.633199 | −0.316600 | − | 0.948559i | \(-0.602541\pi\) | ||||
−0.316600 | + | 0.948559i | \(0.602541\pi\) | |||||||
\(338\) | −4.60042 | −0.250230 | ||||||||
\(339\) | 27.0080 | 1.46687 | ||||||||
\(340\) | 8.82317 | 0.478504 | ||||||||
\(341\) | −10.0879 | −0.546292 | ||||||||
\(342\) | −4.13913 | −0.223818 | ||||||||
\(343\) | 19.9229 | 1.07574 | ||||||||
\(344\) | 30.1021 | 1.62300 | ||||||||
\(345\) | −11.2787 | −0.607225 | ||||||||
\(346\) | 5.82409 | 0.313105 | ||||||||
\(347\) | 24.5102 | 1.31578 | 0.657888 | − | 0.753115i | \(-0.271450\pi\) | ||||
0.657888 | + | 0.753115i | \(0.271450\pi\) | |||||||
\(348\) | 9.62543 | 0.515977 | ||||||||
\(349\) | 10.6510 | 0.570133 | 0.285066 | − | 0.958508i | \(-0.407984\pi\) | ||||
0.285066 | + | 0.958508i | \(0.407984\pi\) | |||||||
\(350\) | −14.8334 | −0.792881 | ||||||||
\(351\) | −18.1944 | −0.971146 | ||||||||
\(352\) | −23.9831 | −1.27830 | ||||||||
\(353\) | 1.04651 | 0.0557003 | 0.0278501 | − | 0.999612i | \(-0.491134\pi\) | ||||
0.0278501 | + | 0.999612i | \(0.491134\pi\) | |||||||
\(354\) | −66.7236 | −3.54632 | ||||||||
\(355\) | 0.107492 | 0.00570508 | ||||||||
\(356\) | −82.3022 | −4.36201 | ||||||||
\(357\) | 4.75909 | 0.251878 | ||||||||
\(358\) | −41.1275 | −2.17365 | ||||||||
\(359\) | −24.0194 | −1.26769 | −0.633847 | − | 0.773459i | \(-0.718525\pi\) | ||||
−0.633847 | + | 0.773459i | \(0.718525\pi\) | |||||||
\(360\) | −4.55179 | −0.239901 | ||||||||
\(361\) | −6.52528 | −0.343436 | ||||||||
\(362\) | −42.9268 | −2.25618 | ||||||||
\(363\) | 5.28191 | 0.277228 | ||||||||
\(364\) | 35.4437 | 1.85776 | ||||||||
\(365\) | 4.74793 | 0.248518 | ||||||||
\(366\) | −31.3115 | −1.63668 | ||||||||
\(367\) | −18.6963 | −0.975937 | −0.487969 | − | 0.872861i | \(-0.662262\pi\) | ||||
−0.487969 | + | 0.872861i | \(0.662262\pi\) | |||||||
\(368\) | 36.3009 | 1.89231 | ||||||||
\(369\) | 0.304022 | 0.0158267 | ||||||||
\(370\) | 24.7062 | 1.28442 | ||||||||
\(371\) | 14.0248 | 0.728133 | ||||||||
\(372\) | 30.7939 | 1.59659 | ||||||||
\(373\) | −23.3008 | −1.20647 | −0.603235 | − | 0.797564i | \(-0.706122\pi\) | ||||
−0.603235 | + | 0.797564i | \(0.706122\pi\) | |||||||
\(374\) | −9.62931 | −0.497920 | ||||||||
\(375\) | 21.2302 | 1.09633 | ||||||||
\(376\) | 2.63582 | 0.135932 | ||||||||
\(377\) | 4.24415 | 0.218585 | ||||||||
\(378\) | 24.0591 | 1.23747 | ||||||||
\(379\) | −9.79951 | −0.503367 | −0.251683 | − | 0.967810i | \(-0.580984\pi\) | ||||
−0.251683 | + | 0.967810i | \(0.580984\pi\) | |||||||
\(380\) | 23.9110 | 1.22661 | ||||||||
\(381\) | −10.2705 | −0.526172 | ||||||||
\(382\) | 5.26787 | 0.269528 | ||||||||
\(383\) | −1.97295 | −0.100813 | −0.0504066 | − | 0.998729i | \(-0.516052\pi\) | ||||
−0.0504066 | + | 0.998729i | \(0.516052\pi\) | |||||||
\(384\) | −9.75610 | −0.497864 | ||||||||
\(385\) | −8.09844 | −0.412735 | ||||||||
\(386\) | 39.1608 | 1.99323 | ||||||||
\(387\) | −1.95837 | −0.0995496 | ||||||||
\(388\) | −37.6146 | −1.90959 | ||||||||
\(389\) | −6.61202 | −0.335243 | −0.167621 | − | 0.985851i | \(-0.553609\pi\) | ||||
−0.167621 | + | 0.985851i | \(0.553609\pi\) | |||||||
\(390\) | −26.6640 | −1.35018 | ||||||||
\(391\) | 5.48230 | 0.277252 | ||||||||
\(392\) | 21.8542 | 1.10380 | ||||||||
\(393\) | 39.4268 | 1.98882 | ||||||||
\(394\) | 15.5544 | 0.783619 | ||||||||
\(395\) | 12.3741 | 0.622607 | ||||||||
\(396\) | 6.07078 | 0.305068 | ||||||||
\(397\) | −7.61750 | −0.382311 | −0.191156 | − | 0.981560i | \(-0.561224\pi\) | ||||
−0.191156 | + | 0.981560i | \(0.561224\pi\) | |||||||
\(398\) | −60.9239 | −3.05384 | ||||||||
\(399\) | 12.8973 | 0.645670 | ||||||||
\(400\) | −25.1816 | −1.25908 | ||||||||
\(401\) | 25.8162 | 1.28920 | 0.644601 | − | 0.764519i | \(-0.277024\pi\) | ||||
0.644601 | + | 0.764519i | \(0.277024\pi\) | |||||||
\(402\) | −36.3018 | −1.81057 | ||||||||
\(403\) | 13.5780 | 0.676368 | ||||||||
\(404\) | 42.7497 | 2.12687 | ||||||||
\(405\) | −14.6511 | −0.728018 | ||||||||
\(406\) | −5.61218 | −0.278528 | ||||||||
\(407\) | −18.9049 | −0.937081 | ||||||||
\(408\) | 16.8642 | 0.834900 | ||||||||
\(409\) | −13.6924 | −0.677044 | −0.338522 | − | 0.940958i | \(-0.609927\pi\) | ||||
−0.338522 | + | 0.940958i | \(0.609927\pi\) | |||||||
\(410\) | −2.50493 | −0.123710 | ||||||||
\(411\) | −21.7029 | −1.07053 | ||||||||
\(412\) | −71.7583 | −3.53528 | ||||||||
\(413\) | 27.2765 | 1.34219 | ||||||||
\(414\) | −4.92962 | −0.242278 | ||||||||
\(415\) | 21.3788 | 1.04944 | ||||||||
\(416\) | 32.2804 | 1.58268 | ||||||||
\(417\) | 20.1945 | 0.988930 | ||||||||
\(418\) | −26.0957 | −1.27638 | ||||||||
\(419\) | 24.0027 | 1.17261 | 0.586305 | − | 0.810091i | \(-0.300582\pi\) | ||||
0.586305 | + | 0.810091i | \(0.300582\pi\) | |||||||
\(420\) | 24.7209 | 1.20626 | ||||||||
\(421\) | 31.1293 | 1.51715 | 0.758573 | − | 0.651588i | \(-0.225897\pi\) | ||||
0.758573 | + | 0.651588i | \(0.225897\pi\) | |||||||
\(422\) | −6.09348 | −0.296626 | ||||||||
\(423\) | −0.171480 | −0.00833765 | ||||||||
\(424\) | 49.6979 | 2.41355 | ||||||||
\(425\) | −3.80302 | −0.184474 | ||||||||
\(426\) | 0.358104 | 0.0173502 | ||||||||
\(427\) | 12.8001 | 0.619439 | ||||||||
\(428\) | 16.4412 | 0.794714 | ||||||||
\(429\) | 20.4030 | 0.985064 | ||||||||
\(430\) | 16.1357 | 0.778130 | ||||||||
\(431\) | 28.0585 | 1.35153 | 0.675766 | − | 0.737116i | \(-0.263813\pi\) | ||||
0.675766 | + | 0.737116i | \(0.263813\pi\) | |||||||
\(432\) | 40.8434 | 1.96508 | ||||||||
\(433\) | −20.6011 | −0.990026 | −0.495013 | − | 0.868886i | \(-0.664837\pi\) | ||||
−0.495013 | + | 0.868886i | \(0.664837\pi\) | |||||||
\(434\) | −17.9547 | −0.861851 | ||||||||
\(435\) | 2.96016 | 0.141929 | ||||||||
\(436\) | 11.6968 | 0.560175 | ||||||||
\(437\) | 14.8572 | 0.710715 | ||||||||
\(438\) | 15.8175 | 0.755789 | ||||||||
\(439\) | −36.4050 | −1.73752 | −0.868758 | − | 0.495238i | \(-0.835081\pi\) | ||||
−0.868758 | + | 0.495238i | \(0.835081\pi\) | |||||||
\(440\) | −28.6974 | −1.36809 | ||||||||
\(441\) | −1.42178 | −0.0677038 | ||||||||
\(442\) | 12.9607 | 0.616477 | ||||||||
\(443\) | −28.1192 | −1.33598 | −0.667992 | − | 0.744169i | \(-0.732846\pi\) | ||||
−0.667992 | + | 0.744169i | \(0.732846\pi\) | |||||||
\(444\) | 57.7082 | 2.73871 | ||||||||
\(445\) | −25.3109 | −1.19985 | ||||||||
\(446\) | −35.2507 | −1.66917 | ||||||||
\(447\) | 13.7548 | 0.650580 | ||||||||
\(448\) | −8.76920 | −0.414306 | ||||||||
\(449\) | −12.9493 | −0.611116 | −0.305558 | − | 0.952173i | \(-0.598843\pi\) | ||||
−0.305558 | + | 0.952173i | \(0.598843\pi\) | |||||||
\(450\) | 3.41964 | 0.161203 | ||||||||
\(451\) | 1.91674 | 0.0902559 | ||||||||
\(452\) | −68.1925 | −3.20750 | ||||||||
\(453\) | −11.3201 | −0.531866 | ||||||||
\(454\) | −30.9936 | −1.45460 | ||||||||
\(455\) | 10.9002 | 0.511010 | ||||||||
\(456\) | 45.7023 | 2.14021 | ||||||||
\(457\) | 0.149626 | 0.00699919 | 0.00349960 | − | 0.999994i | \(-0.498886\pi\) | ||||
0.00349960 | + | 0.999994i | \(0.498886\pi\) | |||||||
\(458\) | −70.3797 | −3.28863 | ||||||||
\(459\) | 6.16832 | 0.287912 | ||||||||
\(460\) | 28.4776 | 1.32777 | ||||||||
\(461\) | 38.9917 | 1.81603 | 0.908013 | − | 0.418942i | \(-0.137599\pi\) | ||||
0.908013 | + | 0.418942i | \(0.137599\pi\) | |||||||
\(462\) | −26.9796 | −1.25520 | ||||||||
\(463\) | −20.1386 | −0.935918 | −0.467959 | − | 0.883750i | \(-0.655011\pi\) | ||||
−0.467959 | + | 0.883750i | \(0.655011\pi\) | |||||||
\(464\) | −9.52738 | −0.442298 | ||||||||
\(465\) | 9.47024 | 0.439172 | ||||||||
\(466\) | −37.3812 | −1.73165 | ||||||||
\(467\) | 14.8664 | 0.687936 | 0.343968 | − | 0.938981i | \(-0.388229\pi\) | ||||
0.343968 | + | 0.938981i | \(0.388229\pi\) | |||||||
\(468\) | −8.17104 | −0.377707 | ||||||||
\(469\) | 14.8401 | 0.685254 | ||||||||
\(470\) | 1.41288 | 0.0651713 | ||||||||
\(471\) | −4.13995 | −0.190759 | ||||||||
\(472\) | 96.6562 | 4.44896 | ||||||||
\(473\) | −12.3468 | −0.567707 | ||||||||
\(474\) | 41.2236 | 1.89346 | ||||||||
\(475\) | −10.3063 | −0.472885 | ||||||||
\(476\) | −12.0162 | −0.550762 | ||||||||
\(477\) | −3.23322 | −0.148039 | ||||||||
\(478\) | 61.9193 | 2.83212 | ||||||||
\(479\) | −35.2515 | −1.61068 | −0.805342 | − | 0.592810i | \(-0.798018\pi\) | ||||
−0.805342 | + | 0.592810i | \(0.798018\pi\) | |||||||
\(480\) | 22.5146 | 1.02765 | ||||||||
\(481\) | 25.4453 | 1.16021 | ||||||||
\(482\) | 35.6299 | 1.62290 | ||||||||
\(483\) | 15.3604 | 0.698922 | ||||||||
\(484\) | −13.3363 | −0.606195 | ||||||||
\(485\) | −11.5678 | −0.525268 | ||||||||
\(486\) | −12.0795 | −0.547938 | ||||||||
\(487\) | 27.4362 | 1.24325 | 0.621626 | − | 0.783314i | \(-0.286472\pi\) | ||||
0.621626 | + | 0.783314i | \(0.286472\pi\) | |||||||
\(488\) | 45.3580 | 2.05326 | ||||||||
\(489\) | 34.8177 | 1.57451 | ||||||||
\(490\) | 11.7145 | 0.529208 | ||||||||
\(491\) | −4.83937 | −0.218398 | −0.109199 | − | 0.994020i | \(-0.534829\pi\) | ||||
−0.109199 | + | 0.994020i | \(0.534829\pi\) | |||||||
\(492\) | −5.85096 | −0.263782 | ||||||||
\(493\) | −1.43886 | −0.0648030 | ||||||||
\(494\) | 35.1238 | 1.58030 | ||||||||
\(495\) | 1.86698 | 0.0839145 | ||||||||
\(496\) | −30.4803 | −1.36860 | ||||||||
\(497\) | −0.146393 | −0.00656661 | ||||||||
\(498\) | 71.2225 | 3.19155 | ||||||||
\(499\) | 16.7739 | 0.750904 | 0.375452 | − | 0.926842i | \(-0.377488\pi\) | ||||
0.375452 | + | 0.926842i | \(0.377488\pi\) | |||||||
\(500\) | −53.6042 | −2.39725 | ||||||||
\(501\) | −42.2258 | −1.88651 | ||||||||
\(502\) | 21.3927 | 0.954803 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 6.19906 | 0.276128 | ||||||||
\(505\) | 13.1470 | 0.585036 | ||||||||
\(506\) | −31.0795 | −1.38165 | ||||||||
\(507\) | −3.30464 | −0.146764 | ||||||||
\(508\) | 25.9319 | 1.15054 | ||||||||
\(509\) | −27.5401 | −1.22069 | −0.610347 | − | 0.792134i | \(-0.708970\pi\) | ||||
−0.610347 | + | 0.792134i | \(0.708970\pi\) | |||||||
\(510\) | 9.03970 | 0.400284 | ||||||||
\(511\) | −6.46617 | −0.286046 | ||||||||
\(512\) | 47.7209 | 2.10898 | ||||||||
\(513\) | 16.7163 | 0.738043 | ||||||||
\(514\) | 52.1216 | 2.29899 | ||||||||
\(515\) | −22.0682 | −0.972443 | ||||||||
\(516\) | 37.6893 | 1.65918 | ||||||||
\(517\) | −1.08112 | −0.0475475 | ||||||||
\(518\) | −33.6472 | −1.47837 | ||||||||
\(519\) | 4.18365 | 0.183642 | ||||||||
\(520\) | 38.6256 | 1.69385 | ||||||||
\(521\) | 25.7250 | 1.12703 | 0.563515 | − | 0.826106i | \(-0.309449\pi\) | ||||
0.563515 | + | 0.826106i | \(0.309449\pi\) | |||||||
\(522\) | 1.29381 | 0.0566285 | ||||||||
\(523\) | −29.5746 | −1.29321 | −0.646605 | − | 0.762825i | \(-0.723812\pi\) | ||||
−0.646605 | + | 0.762825i | \(0.723812\pi\) | |||||||
\(524\) | −99.5486 | −4.34880 | ||||||||
\(525\) | −10.6554 | −0.465039 | ||||||||
\(526\) | 72.2327 | 3.14949 | ||||||||
\(527\) | −4.60324 | −0.200520 | ||||||||
\(528\) | −45.8012 | −1.99324 | ||||||||
\(529\) | −5.30539 | −0.230669 | ||||||||
\(530\) | 26.6396 | 1.15715 | ||||||||
\(531\) | −6.28821 | −0.272885 | ||||||||
\(532\) | −32.5643 | −1.41184 | ||||||||
\(533\) | −2.57987 | −0.111746 | ||||||||
\(534\) | −84.3219 | −3.64897 | ||||||||
\(535\) | 5.05624 | 0.218601 | ||||||||
\(536\) | 52.5870 | 2.27141 | ||||||||
\(537\) | −29.5433 | −1.27489 | ||||||||
\(538\) | −30.0502 | −1.29556 | ||||||||
\(539\) | −8.96380 | −0.386098 | ||||||||
\(540\) | 32.0411 | 1.37883 | ||||||||
\(541\) | −13.1889 | −0.567035 | −0.283517 | − | 0.958967i | \(-0.591501\pi\) | ||||
−0.283517 | + | 0.958967i | \(0.591501\pi\) | |||||||
\(542\) | 8.47940 | 0.364222 | ||||||||
\(543\) | −30.8358 | −1.32329 | ||||||||
\(544\) | −10.9438 | −0.469211 | ||||||||
\(545\) | 3.59718 | 0.154086 | ||||||||
\(546\) | 36.3135 | 1.55407 | ||||||||
\(547\) | −17.9543 | −0.767673 | −0.383836 | − | 0.923401i | \(-0.625397\pi\) | ||||
−0.383836 | + | 0.923401i | \(0.625397\pi\) | |||||||
\(548\) | 54.7977 | 2.34084 | ||||||||
\(549\) | −2.95088 | −0.125940 | ||||||||
\(550\) | 21.5596 | 0.919303 | ||||||||
\(551\) | −3.89935 | −0.166118 | ||||||||
\(552\) | 54.4306 | 2.31672 | ||||||||
\(553\) | −16.8522 | −0.716627 | ||||||||
\(554\) | −26.1680 | −1.11177 | ||||||||
\(555\) | 17.7473 | 0.753332 | ||||||||
\(556\) | −50.9891 | −2.16242 | ||||||||
\(557\) | 9.47412 | 0.401431 | 0.200716 | − | 0.979650i | \(-0.435673\pi\) | ||||
0.200716 | + | 0.979650i | \(0.435673\pi\) | |||||||
\(558\) | 4.13919 | 0.175226 | ||||||||
\(559\) | 16.6183 | 0.702881 | ||||||||
\(560\) | −24.4691 | −1.03401 | ||||||||
\(561\) | −6.91706 | −0.292039 | ||||||||
\(562\) | −43.3703 | −1.82947 | ||||||||
\(563\) | −33.2995 | −1.40341 | −0.701704 | − | 0.712469i | \(-0.747577\pi\) | ||||
−0.701704 | + | 0.712469i | \(0.747577\pi\) | |||||||
\(564\) | 3.30017 | 0.138962 | ||||||||
\(565\) | −20.9716 | −0.882283 | ||||||||
\(566\) | −39.9364 | −1.67865 | ||||||||
\(567\) | 19.9532 | 0.837955 | ||||||||
\(568\) | −0.518752 | −0.0217664 | ||||||||
\(569\) | −28.8525 | −1.20956 | −0.604780 | − | 0.796393i | \(-0.706739\pi\) | ||||
−0.604780 | + | 0.796393i | \(0.706739\pi\) | |||||||
\(570\) | 24.4978 | 1.02610 | ||||||||
\(571\) | 22.7379 | 0.951550 | 0.475775 | − | 0.879567i | \(-0.342168\pi\) | ||||
0.475775 | + | 0.879567i | \(0.342168\pi\) | |||||||
\(572\) | −51.5154 | −2.15397 | ||||||||
\(573\) | 3.78409 | 0.158083 | ||||||||
\(574\) | 3.41145 | 0.142391 | ||||||||
\(575\) | −12.2746 | −0.511886 | ||||||||
\(576\) | 2.02161 | 0.0842339 | ||||||||
\(577\) | −4.60031 | −0.191513 | −0.0957567 | − | 0.995405i | \(-0.530527\pi\) | ||||
−0.0957567 | + | 0.995405i | \(0.530527\pi\) | |||||||
\(578\) | 39.5827 | 1.64642 | ||||||||
\(579\) | 28.1306 | 1.16907 | ||||||||
\(580\) | −7.47411 | −0.310346 | ||||||||
\(581\) | −29.1156 | −1.20792 | ||||||||
\(582\) | −38.5377 | −1.59744 | ||||||||
\(583\) | −20.3843 | −0.844231 | ||||||||
\(584\) | −22.9133 | −0.948159 | ||||||||
\(585\) | −2.51289 | −0.103895 | ||||||||
\(586\) | 19.4761 | 0.804552 | ||||||||
\(587\) | 32.6537 | 1.34776 | 0.673881 | − | 0.738839i | \(-0.264626\pi\) | ||||
0.673881 | + | 0.738839i | \(0.264626\pi\) | |||||||
\(588\) | 27.3625 | 1.12841 | ||||||||
\(589\) | −12.4749 | −0.514020 | ||||||||
\(590\) | 51.8106 | 2.13301 | ||||||||
\(591\) | 11.1733 | 0.459607 | ||||||||
\(592\) | −57.1204 | −2.34763 | ||||||||
\(593\) | −36.4077 | −1.49509 | −0.747543 | − | 0.664214i | \(-0.768767\pi\) | ||||
−0.747543 | + | 0.664214i | \(0.768767\pi\) | |||||||
\(594\) | −34.9686 | −1.43478 | ||||||||
\(595\) | −3.69542 | −0.151497 | ||||||||
\(596\) | −34.7295 | −1.42257 | ||||||||
\(597\) | −43.7637 | −1.79113 | ||||||||
\(598\) | 41.8318 | 1.71063 | ||||||||
\(599\) | −40.2375 | −1.64406 | −0.822031 | − | 0.569443i | \(-0.807159\pi\) | ||||
−0.822031 | + | 0.569443i | \(0.807159\pi\) | |||||||
\(600\) | −37.7581 | −1.54147 | ||||||||
\(601\) | 8.80257 | 0.359065 | 0.179532 | − | 0.983752i | \(-0.442542\pi\) | ||||
0.179532 | + | 0.983752i | \(0.442542\pi\) | |||||||
\(602\) | −21.9750 | −0.895635 | ||||||||
\(603\) | −3.42118 | −0.139321 | ||||||||
\(604\) | 28.5822 | 1.16299 | ||||||||
\(605\) | −4.10139 | −0.166745 | ||||||||
\(606\) | 43.7987 | 1.77920 | ||||||||
\(607\) | 13.3824 | 0.543176 | 0.271588 | − | 0.962414i | \(-0.412451\pi\) | ||||
0.271588 | + | 0.962414i | \(0.412451\pi\) | |||||||
\(608\) | −29.6579 | −1.20279 | ||||||||
\(609\) | −4.03143 | −0.163362 | ||||||||
\(610\) | 24.3132 | 0.984414 | ||||||||
\(611\) | 1.45515 | 0.0588689 | ||||||||
\(612\) | 2.77017 | 0.111977 | ||||||||
\(613\) | −15.6160 | −0.630725 | −0.315363 | − | 0.948971i | \(-0.602126\pi\) | ||||
−0.315363 | + | 0.948971i | \(0.602126\pi\) | |||||||
\(614\) | −44.4763 | −1.79492 | ||||||||
\(615\) | −1.79938 | −0.0725580 | ||||||||
\(616\) | 39.0828 | 1.57469 | ||||||||
\(617\) | 4.29634 | 0.172964 | 0.0864820 | − | 0.996253i | \(-0.472437\pi\) | ||||
0.0864820 | + | 0.996253i | \(0.472437\pi\) | |||||||
\(618\) | −73.5193 | −2.95738 | ||||||||
\(619\) | −10.8380 | −0.435614 | −0.217807 | − | 0.975992i | \(-0.569890\pi\) | ||||
−0.217807 | + | 0.975992i | \(0.569890\pi\) | |||||||
\(620\) | −23.9114 | −0.960305 | ||||||||
\(621\) | 19.9088 | 0.798913 | ||||||||
\(622\) | −26.2813 | −1.05378 | ||||||||
\(623\) | 34.4707 | 1.38104 | ||||||||
\(624\) | 61.6467 | 2.46784 | ||||||||
\(625\) | −1.89515 | −0.0758062 | ||||||||
\(626\) | −69.0456 | −2.75962 | ||||||||
\(627\) | −18.7454 | −0.748620 | ||||||||
\(628\) | 10.4529 | 0.417118 | ||||||||
\(629\) | −8.62653 | −0.343962 | ||||||||
\(630\) | 3.32288 | 0.132387 | ||||||||
\(631\) | 29.5073 | 1.17467 | 0.587334 | − | 0.809345i | \(-0.300178\pi\) | ||||
0.587334 | + | 0.809345i | \(0.300178\pi\) | |||||||
\(632\) | −59.7168 | −2.37541 | ||||||||
\(633\) | −4.37716 | −0.173976 | ||||||||
\(634\) | −50.1475 | −1.99161 | ||||||||
\(635\) | 7.97499 | 0.316478 | ||||||||
\(636\) | 62.2241 | 2.46735 | ||||||||
\(637\) | 12.0649 | 0.478031 | ||||||||
\(638\) | 8.15699 | 0.322938 | ||||||||
\(639\) | 0.0337487 | 0.00133508 | ||||||||
\(640\) | 7.57558 | 0.299451 | ||||||||
\(641\) | 7.72732 | 0.305211 | 0.152605 | − | 0.988287i | \(-0.451234\pi\) | ||||
0.152605 | + | 0.988287i | \(0.451234\pi\) | |||||||
\(642\) | 16.8446 | 0.664805 | ||||||||
\(643\) | 10.0167 | 0.395021 | 0.197511 | − | 0.980301i | \(-0.436714\pi\) | ||||
0.197511 | + | 0.980301i | \(0.436714\pi\) | |||||||
\(644\) | −38.7834 | −1.52828 | ||||||||
\(645\) | 11.5908 | 0.456387 | ||||||||
\(646\) | −11.9078 | −0.468505 | ||||||||
\(647\) | −13.6884 | −0.538147 | −0.269074 | − | 0.963120i | \(-0.586718\pi\) | ||||
−0.269074 | + | 0.963120i | \(0.586718\pi\) | |||||||
\(648\) | 70.7055 | 2.77758 | ||||||||
\(649\) | −39.6449 | −1.55620 | ||||||||
\(650\) | −29.0184 | −1.13819 | ||||||||
\(651\) | −12.8974 | −0.505491 | ||||||||
\(652\) | −87.9111 | −3.44286 | ||||||||
\(653\) | 38.1399 | 1.49253 | 0.746264 | − | 0.665650i | \(-0.231845\pi\) | ||||
0.746264 | + | 0.665650i | \(0.231845\pi\) | |||||||
\(654\) | 11.9838 | 0.468605 | ||||||||
\(655\) | −30.6147 | −1.19622 | ||||||||
\(656\) | 5.79136 | 0.226115 | ||||||||
\(657\) | 1.49068 | 0.0581571 | ||||||||
\(658\) | −1.92419 | −0.0750128 | ||||||||
\(659\) | 31.5253 | 1.22805 | 0.614026 | − | 0.789286i | \(-0.289549\pi\) | ||||
0.614026 | + | 0.789286i | \(0.289549\pi\) | |||||||
\(660\) | −35.9305 | −1.39859 | ||||||||
\(661\) | −30.1122 | −1.17123 | −0.585614 | − | 0.810590i | \(-0.699146\pi\) | ||||
−0.585614 | + | 0.810590i | \(0.699146\pi\) | |||||||
\(662\) | 67.4080 | 2.61989 | ||||||||
\(663\) | 9.31012 | 0.361575 | ||||||||
\(664\) | −103.173 | −4.00390 | ||||||||
\(665\) | −10.0147 | −0.388352 | ||||||||
\(666\) | 7.75689 | 0.300573 | ||||||||
\(667\) | −4.64405 | −0.179818 | ||||||||
\(668\) | 106.616 | 4.12510 | ||||||||
\(669\) | −25.3218 | −0.978996 | ||||||||
\(670\) | 28.1882 | 1.08901 | ||||||||
\(671\) | −18.6042 | −0.718207 | ||||||||
\(672\) | −30.6625 | −1.18283 | ||||||||
\(673\) | −40.7982 | −1.57265 | −0.786327 | − | 0.617810i | \(-0.788020\pi\) | ||||
−0.786327 | + | 0.617810i | \(0.788020\pi\) | |||||||
\(674\) | 30.0697 | 1.15824 | ||||||||
\(675\) | −13.8106 | −0.531569 | ||||||||
\(676\) | 8.34388 | 0.320918 | ||||||||
\(677\) | 3.18994 | 0.122599 | 0.0612997 | − | 0.998119i | \(-0.480475\pi\) | ||||
0.0612997 | + | 0.998119i | \(0.480475\pi\) | |||||||
\(678\) | −69.8659 | −2.68319 | ||||||||
\(679\) | 15.7542 | 0.604589 | ||||||||
\(680\) | −13.0950 | −0.502169 | ||||||||
\(681\) | −22.2638 | −0.853150 | ||||||||
\(682\) | 26.0961 | 0.999270 | ||||||||
\(683\) | 25.0239 | 0.957512 | 0.478756 | − | 0.877948i | \(-0.341088\pi\) | ||||
0.478756 | + | 0.877948i | \(0.341088\pi\) | |||||||
\(684\) | 7.50723 | 0.287046 | ||||||||
\(685\) | 16.8523 | 0.643892 | ||||||||
\(686\) | −51.5378 | −1.96772 | ||||||||
\(687\) | −50.5562 | −1.92884 | ||||||||
\(688\) | −37.3054 | −1.42225 | ||||||||
\(689\) | 27.4365 | 1.04525 | ||||||||
\(690\) | 29.1764 | 1.11073 | ||||||||
\(691\) | 36.5349 | 1.38985 | 0.694927 | − | 0.719081i | \(-0.255437\pi\) | ||||
0.694927 | + | 0.719081i | \(0.255437\pi\) | |||||||
\(692\) | −10.5633 | −0.401556 | ||||||||
\(693\) | −2.54263 | −0.0965864 | ||||||||
\(694\) | −63.4045 | −2.40680 | ||||||||
\(695\) | −15.6810 | −0.594813 | ||||||||
\(696\) | −14.2856 | −0.541496 | ||||||||
\(697\) | 0.874633 | 0.0331291 | ||||||||
\(698\) | −27.5525 | −1.04288 | ||||||||
\(699\) | −26.8522 | −1.01564 | ||||||||
\(700\) | 26.9037 | 1.01687 | ||||||||
\(701\) | 40.6252 | 1.53439 | 0.767196 | − | 0.641413i | \(-0.221652\pi\) | ||||
0.767196 | + | 0.641413i | \(0.221652\pi\) | |||||||
\(702\) | 47.0664 | 1.77641 | ||||||||
\(703\) | −23.3781 | −0.881723 | ||||||||
\(704\) | 12.7455 | 0.480365 | ||||||||
\(705\) | 1.01492 | 0.0382241 | ||||||||
\(706\) | −2.70718 | −0.101886 | ||||||||
\(707\) | −17.9049 | −0.673382 | ||||||||
\(708\) | 121.018 | 4.54814 | ||||||||
\(709\) | −29.3401 | −1.10189 | −0.550945 | − | 0.834542i | \(-0.685733\pi\) | ||||
−0.550945 | + | 0.834542i | \(0.685733\pi\) | |||||||
\(710\) | −0.278067 | −0.0104357 | ||||||||
\(711\) | 3.88503 | 0.145700 | ||||||||
\(712\) | 122.149 | 4.57774 | ||||||||
\(713\) | −14.8574 | −0.556414 | ||||||||
\(714\) | −12.3111 | −0.460731 | ||||||||
\(715\) | −15.8428 | −0.592488 | ||||||||
\(716\) | 74.5938 | 2.78770 | ||||||||
\(717\) | 44.4788 | 1.66109 | ||||||||
\(718\) | 62.1347 | 2.31885 | ||||||||
\(719\) | −5.69273 | −0.212303 | −0.106152 | − | 0.994350i | \(-0.533853\pi\) | ||||
−0.106152 | + | 0.994350i | \(0.533853\pi\) | |||||||
\(720\) | 5.64100 | 0.210228 | ||||||||
\(721\) | 30.0546 | 1.11929 | ||||||||
\(722\) | 16.8800 | 0.628208 | ||||||||
\(723\) | 25.5942 | 0.951858 | ||||||||
\(724\) | 77.8574 | 2.89355 | ||||||||
\(725\) | 3.22154 | 0.119645 | ||||||||
\(726\) | −13.6636 | −0.507102 | ||||||||
\(727\) | 31.4072 | 1.16483 | 0.582414 | − | 0.812892i | \(-0.302108\pi\) | ||||
0.582414 | + | 0.812892i | \(0.302108\pi\) | |||||||
\(728\) | −52.6040 | −1.94963 | ||||||||
\(729\) | 21.7844 | 0.806829 | ||||||||
\(730\) | −12.2822 | −0.454585 | ||||||||
\(731\) | −5.63399 | −0.208381 | ||||||||
\(732\) | 56.7903 | 2.09903 | ||||||||
\(733\) | 47.6365 | 1.75949 | 0.879747 | − | 0.475441i | \(-0.157712\pi\) | ||||
0.879747 | + | 0.475441i | \(0.157712\pi\) | |||||||
\(734\) | 48.3646 | 1.78517 | ||||||||
\(735\) | 8.41494 | 0.310390 | ||||||||
\(736\) | −35.3221 | −1.30199 | ||||||||
\(737\) | −21.5693 | −0.794515 | ||||||||
\(738\) | −0.786461 | −0.0289500 | ||||||||
\(739\) | 9.88794 | 0.363734 | 0.181867 | − | 0.983323i | \(-0.441786\pi\) | ||||
0.181867 | + | 0.983323i | \(0.441786\pi\) | |||||||
\(740\) | −44.8102 | −1.64726 | ||||||||
\(741\) | 25.2307 | 0.926871 | ||||||||
\(742\) | −36.2803 | −1.33189 | ||||||||
\(743\) | 17.7935 | 0.652782 | 0.326391 | − | 0.945235i | \(-0.394167\pi\) | ||||
0.326391 | + | 0.945235i | \(0.394167\pi\) | |||||||
\(744\) | −45.7030 | −1.67555 | ||||||||
\(745\) | −10.6806 | −0.391305 | ||||||||
\(746\) | 60.2759 | 2.20686 | ||||||||
\(747\) | 6.71220 | 0.245586 | ||||||||
\(748\) | 17.4649 | 0.638579 | ||||||||
\(749\) | −6.88606 | −0.251611 | ||||||||
\(750\) | −54.9197 | −2.00538 | ||||||||
\(751\) | −43.7934 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(752\) | −3.26656 | −0.119119 | ||||||||
\(753\) | 15.3671 | 0.560009 | ||||||||
\(754\) | −10.9790 | −0.399832 | ||||||||
\(755\) | 8.79003 | 0.319902 | ||||||||
\(756\) | −43.6366 | −1.58705 | ||||||||
\(757\) | 0.950190 | 0.0345353 | 0.0172676 | − | 0.999851i | \(-0.494503\pi\) | ||||
0.0172676 | + | 0.999851i | \(0.494503\pi\) | |||||||
\(758\) | 25.3499 | 0.920752 | ||||||||
\(759\) | −22.3255 | −0.810363 | ||||||||
\(760\) | −35.4877 | −1.28727 | ||||||||
\(761\) | −5.00434 | −0.181407 | −0.0907035 | − | 0.995878i | \(-0.528912\pi\) | ||||
−0.0907035 | + | 0.995878i | \(0.528912\pi\) | |||||||
\(762\) | 26.5683 | 0.962467 | ||||||||
\(763\) | −4.89898 | −0.177355 | ||||||||
\(764\) | −9.55445 | −0.345668 | ||||||||
\(765\) | 0.851925 | 0.0308014 | ||||||||
\(766\) | 5.10375 | 0.184406 | ||||||||
\(767\) | 53.3605 | 1.92674 | ||||||||
\(768\) | 41.8224 | 1.50913 | ||||||||
\(769\) | 16.5794 | 0.597870 | 0.298935 | − | 0.954274i | \(-0.403369\pi\) | ||||
0.298935 | + | 0.954274i | \(0.403369\pi\) | |||||||
\(770\) | 20.9495 | 0.754969 | ||||||||
\(771\) | 37.4408 | 1.34840 | ||||||||
\(772\) | −71.0268 | −2.55631 | ||||||||
\(773\) | −30.4696 | −1.09592 | −0.547958 | − | 0.836506i | \(-0.684595\pi\) | ||||
−0.547958 | + | 0.836506i | \(0.684595\pi\) | |||||||
\(774\) | 5.06603 | 0.182095 | ||||||||
\(775\) | 10.3064 | 0.370218 | ||||||||
\(776\) | 55.8259 | 2.00403 | ||||||||
\(777\) | −24.1700 | −0.867093 | ||||||||
\(778\) | 17.1044 | 0.613221 | ||||||||
\(779\) | 2.37028 | 0.0849240 | ||||||||
\(780\) | 48.3611 | 1.73160 | ||||||||
\(781\) | 0.212773 | 0.00761363 | ||||||||
\(782\) | −14.1819 | −0.507145 | ||||||||
\(783\) | −5.22518 | −0.186733 | ||||||||
\(784\) | −27.0837 | −0.967277 | ||||||||
\(785\) | 3.21465 | 0.114736 | ||||||||
\(786\) | −101.992 | −3.63792 | ||||||||
\(787\) | 29.7903 | 1.06191 | 0.530954 | − | 0.847400i | \(-0.321834\pi\) | ||||
0.530954 | + | 0.847400i | \(0.321834\pi\) | |||||||
\(788\) | −28.2114 | −1.00499 | ||||||||
\(789\) | 51.8872 | 1.84723 | ||||||||
\(790\) | −32.0100 | −1.13886 | ||||||||
\(791\) | 28.5611 | 1.01552 | ||||||||
\(792\) | −9.00998 | −0.320156 | ||||||||
\(793\) | 25.0406 | 0.889216 | ||||||||
\(794\) | 19.7054 | 0.699318 | ||||||||
\(795\) | 19.1361 | 0.678689 | ||||||||
\(796\) | 110.499 | 3.91653 | ||||||||
\(797\) | 0.503125 | 0.0178216 | 0.00891081 | − | 0.999960i | \(-0.497164\pi\) | ||||
0.00891081 | + | 0.999960i | \(0.497164\pi\) | |||||||
\(798\) | −33.3634 | −1.18105 | ||||||||
\(799\) | −0.493327 | −0.0174527 | ||||||||
\(800\) | 24.5026 | 0.866299 | ||||||||
\(801\) | −7.94673 | −0.280784 | ||||||||
\(802\) | −66.7830 | −2.35819 | ||||||||
\(803\) | 9.39820 | 0.331655 | ||||||||
\(804\) | 65.8414 | 2.32205 | ||||||||
\(805\) | −11.9273 | −0.420382 | ||||||||
\(806\) | −35.1244 | −1.23720 | ||||||||
\(807\) | −21.5861 | −0.759867 | ||||||||
\(808\) | −63.4471 | −2.23206 | ||||||||
\(809\) | −21.1371 | −0.743142 | −0.371571 | − | 0.928405i | \(-0.621181\pi\) | ||||
−0.371571 | + | 0.928405i | \(0.621181\pi\) | |||||||
\(810\) | 37.9003 | 1.33168 | ||||||||
\(811\) | 15.7238 | 0.552139 | 0.276069 | − | 0.961138i | \(-0.410968\pi\) | ||||
0.276069 | + | 0.961138i | \(0.410968\pi\) | |||||||
\(812\) | 10.1789 | 0.357211 | ||||||||
\(813\) | 6.09105 | 0.213622 | ||||||||
\(814\) | 48.9043 | 1.71410 | ||||||||
\(815\) | −27.0358 | −0.947023 | ||||||||
\(816\) | −20.8996 | −0.731633 | ||||||||
\(817\) | −15.2683 | −0.534169 | ||||||||
\(818\) | 35.4202 | 1.23844 | ||||||||
\(819\) | 3.42228 | 0.119584 | ||||||||
\(820\) | 4.54325 | 0.158657 | ||||||||
\(821\) | −42.7588 | −1.49229 | −0.746147 | − | 0.665781i | \(-0.768098\pi\) | ||||
−0.746147 | + | 0.665781i | \(0.768098\pi\) | |||||||
\(822\) | 56.1425 | 1.95819 | ||||||||
\(823\) | −33.2920 | −1.16049 | −0.580243 | − | 0.814444i | \(-0.697042\pi\) | ||||
−0.580243 | + | 0.814444i | \(0.697042\pi\) | |||||||
\(824\) | 106.500 | 3.71012 | ||||||||
\(825\) | 15.4870 | 0.539188 | ||||||||
\(826\) | −70.5605 | −2.45511 | ||||||||
\(827\) | 14.2343 | 0.494975 | 0.247487 | − | 0.968891i | \(-0.420395\pi\) | ||||
0.247487 | + | 0.968891i | \(0.420395\pi\) | |||||||
\(828\) | 8.94097 | 0.310720 | ||||||||
\(829\) | −12.3766 | −0.429855 | −0.214928 | − | 0.976630i | \(-0.568952\pi\) | ||||
−0.214928 | + | 0.976630i | \(0.568952\pi\) | |||||||
\(830\) | −55.3040 | −1.91963 | ||||||||
\(831\) | −18.7973 | −0.652073 | ||||||||
\(832\) | −17.1550 | −0.594743 | ||||||||
\(833\) | −4.09029 | −0.141720 | ||||||||
\(834\) | −52.2404 | −1.80894 | ||||||||
\(835\) | 32.7882 | 1.13468 | ||||||||
\(836\) | 47.3303 | 1.63695 | ||||||||
\(837\) | −16.7166 | −0.577809 | ||||||||
\(838\) | −62.0917 | −2.14492 | ||||||||
\(839\) | 31.6864 | 1.09394 | 0.546969 | − | 0.837153i | \(-0.315782\pi\) | ||||
0.546969 | + | 0.837153i | \(0.315782\pi\) | |||||||
\(840\) | −36.6897 | −1.26591 | ||||||||
\(841\) | −27.7811 | −0.957970 | ||||||||
\(842\) | −80.5270 | −2.77514 | ||||||||
\(843\) | −31.1544 | −1.07301 | ||||||||
\(844\) | 11.0519 | 0.380421 | ||||||||
\(845\) | 2.56604 | 0.0882745 | ||||||||
\(846\) | 0.443595 | 0.0152511 | ||||||||
\(847\) | 5.58565 | 0.191925 | ||||||||
\(848\) | −61.5903 | −2.11502 | ||||||||
\(849\) | −28.6877 | −0.984560 | ||||||||
\(850\) | 9.83789 | 0.337437 | ||||||||
\(851\) | −27.8429 | −0.954443 | ||||||||
\(852\) | −0.649502 | −0.0222516 | ||||||||
\(853\) | 30.2234 | 1.03483 | 0.517416 | − | 0.855734i | \(-0.326894\pi\) | ||||
0.517416 | + | 0.855734i | \(0.326894\pi\) | |||||||
\(854\) | −33.1120 | −1.13307 | ||||||||
\(855\) | 2.30874 | 0.0789573 | ||||||||
\(856\) | −24.4012 | −0.834017 | ||||||||
\(857\) | −31.4206 | −1.07331 | −0.536653 | − | 0.843803i | \(-0.680312\pi\) | ||||
−0.536653 | + | 0.843803i | \(0.680312\pi\) | |||||||
\(858\) | −52.7796 | −1.80187 | ||||||||
\(859\) | 27.5866 | 0.941244 | 0.470622 | − | 0.882335i | \(-0.344030\pi\) | ||||
0.470622 | + | 0.882335i | \(0.344030\pi\) | |||||||
\(860\) | −29.2656 | −0.997948 | ||||||||
\(861\) | 2.45056 | 0.0835149 | ||||||||
\(862\) | −72.5835 | −2.47220 | ||||||||
\(863\) | 40.3690 | 1.37418 | 0.687088 | − | 0.726574i | \(-0.258889\pi\) | ||||
0.687088 | + | 0.726574i | \(0.258889\pi\) | |||||||
\(864\) | −39.7421 | −1.35205 | ||||||||
\(865\) | −3.24859 | −0.110455 | ||||||||
\(866\) | 53.2922 | 1.81094 | ||||||||
\(867\) | 28.4336 | 0.965655 | ||||||||
\(868\) | 32.5648 | 1.10532 | ||||||||
\(869\) | 24.4937 | 0.830890 | ||||||||
\(870\) | −7.65753 | −0.259615 | ||||||||
\(871\) | 29.0315 | 0.983694 | ||||||||
\(872\) | −17.3599 | −0.587879 | ||||||||
\(873\) | −3.63190 | −0.122921 | ||||||||
\(874\) | −38.4334 | −1.30003 | ||||||||
\(875\) | 22.4511 | 0.758985 | ||||||||
\(876\) | −28.6885 | −0.969295 | ||||||||
\(877\) | −0.330616 | −0.0111641 | −0.00558205 | − | 0.999984i | \(-0.501777\pi\) | ||||
−0.00558205 | + | 0.999984i | \(0.501777\pi\) | |||||||
\(878\) | 94.1746 | 3.17824 | ||||||||
\(879\) | 13.9904 | 0.471884 | ||||||||
\(880\) | 35.5644 | 1.19888 | ||||||||
\(881\) | −4.51734 | −0.152193 | −0.0760965 | − | 0.997100i | \(-0.524246\pi\) | ||||
−0.0760965 | + | 0.997100i | \(0.524246\pi\) | |||||||
\(882\) | 3.67795 | 0.123843 | ||||||||
\(883\) | −46.7445 | −1.57308 | −0.786539 | − | 0.617540i | \(-0.788129\pi\) | ||||
−0.786539 | + | 0.617540i | \(0.788129\pi\) | |||||||
\(884\) | −23.5071 | −0.790629 | ||||||||
\(885\) | 37.2174 | 1.25105 | ||||||||
\(886\) | 72.7404 | 2.44376 | ||||||||
\(887\) | −9.29057 | −0.311947 | −0.155973 | − | 0.987761i | \(-0.549851\pi\) | ||||
−0.155973 | + | 0.987761i | \(0.549851\pi\) | |||||||
\(888\) | −85.6480 | −2.87416 | ||||||||
\(889\) | −10.8611 | −0.364269 | ||||||||
\(890\) | 65.4757 | 2.19475 | ||||||||
\(891\) | −29.0008 | −0.971564 | ||||||||
\(892\) | 63.9349 | 2.14070 | ||||||||
\(893\) | −1.33693 | −0.0447387 | ||||||||
\(894\) | −35.5817 | −1.19003 | ||||||||
\(895\) | 22.9403 | 0.766808 | ||||||||
\(896\) | −10.3171 | −0.344671 | ||||||||
\(897\) | 30.0492 | 1.00332 | ||||||||
\(898\) | 33.4981 | 1.11785 | ||||||||
\(899\) | 3.89941 | 0.130053 | ||||||||
\(900\) | −6.20228 | −0.206743 | ||||||||
\(901\) | −9.30159 | −0.309881 | ||||||||
\(902\) | −4.95835 | −0.165095 | ||||||||
\(903\) | −15.7854 | −0.525306 | ||||||||
\(904\) | 101.208 | 3.36614 | ||||||||
\(905\) | 23.9439 | 0.795923 | ||||||||
\(906\) | 29.2836 | 0.972881 | ||||||||
\(907\) | −24.0423 | −0.798313 | −0.399156 | − | 0.916883i | \(-0.630697\pi\) | ||||
−0.399156 | + | 0.916883i | \(0.630697\pi\) | |||||||
\(908\) | 56.2138 | 1.86552 | ||||||||
\(909\) | 4.12771 | 0.136908 | ||||||||
\(910\) | −28.1973 | −0.934732 | ||||||||
\(911\) | 6.04735 | 0.200358 | 0.100179 | − | 0.994969i | \(-0.468059\pi\) | ||||
0.100179 | + | 0.994969i | \(0.468059\pi\) | |||||||
\(912\) | −56.6385 | −1.87549 | ||||||||
\(913\) | 42.3179 | 1.40052 | ||||||||
\(914\) | −0.387061 | −0.0128028 | ||||||||
\(915\) | 17.4650 | 0.577376 | ||||||||
\(916\) | 127.649 | 4.21765 | ||||||||
\(917\) | 41.6940 | 1.37686 | ||||||||
\(918\) | −15.9566 | −0.526645 | ||||||||
\(919\) | −34.8990 | −1.15121 | −0.575606 | − | 0.817727i | \(-0.695234\pi\) | ||||
−0.575606 | + | 0.817727i | \(0.695234\pi\) | |||||||
\(920\) | −42.2652 | −1.39344 | ||||||||
\(921\) | −31.9488 | −1.05275 | ||||||||
\(922\) | −100.866 | −3.32185 | ||||||||
\(923\) | −0.286385 | −0.00942648 | ||||||||
\(924\) | 48.9334 | 1.60979 | ||||||||
\(925\) | 19.3144 | 0.635054 | ||||||||
\(926\) | 52.0956 | 1.71197 | ||||||||
\(927\) | −6.92866 | −0.227567 | ||||||||
\(928\) | 9.27048 | 0.304319 | ||||||||
\(929\) | 39.8343 | 1.30692 | 0.653460 | − | 0.756961i | \(-0.273317\pi\) | ||||
0.653460 | + | 0.756961i | \(0.273317\pi\) | |||||||
\(930\) | −24.4982 | −0.803327 | ||||||||
\(931\) | −11.0848 | −0.363289 | ||||||||
\(932\) | 67.7992 | 2.22084 | ||||||||
\(933\) | −18.8788 | −0.618063 | ||||||||
\(934\) | −38.4573 | −1.25836 | ||||||||
\(935\) | 5.37108 | 0.175653 | ||||||||
\(936\) | 12.1271 | 0.396387 | ||||||||
\(937\) | 10.6822 | 0.348971 | 0.174485 | − | 0.984660i | \(-0.444174\pi\) | ||||
0.174485 | + | 0.984660i | \(0.444174\pi\) | |||||||
\(938\) | −38.3894 | −1.25346 | ||||||||
\(939\) | −49.5978 | −1.61856 | ||||||||
\(940\) | −2.56257 | −0.0835819 | ||||||||
\(941\) | −1.40329 | −0.0457459 | −0.0228729 | − | 0.999738i | \(-0.507281\pi\) | ||||
−0.0228729 | + | 0.999738i | \(0.507281\pi\) | |||||||
\(942\) | 10.7095 | 0.348933 | ||||||||
\(943\) | 2.82296 | 0.0919281 | ||||||||
\(944\) | −119.785 | −3.89868 | ||||||||
\(945\) | −13.4198 | −0.436546 | ||||||||
\(946\) | 31.9395 | 1.03844 | ||||||||
\(947\) | 9.93625 | 0.322885 | 0.161442 | − | 0.986882i | \(-0.448385\pi\) | ||||
0.161442 | + | 0.986882i | \(0.448385\pi\) | |||||||
\(948\) | −74.7682 | −2.42836 | ||||||||
\(949\) | −12.6496 | −0.410625 | ||||||||
\(950\) | 26.6609 | 0.864995 | ||||||||
\(951\) | −36.0227 | −1.16812 | ||||||||
\(952\) | 17.8339 | 0.578001 | ||||||||
\(953\) | 11.4560 | 0.371097 | 0.185548 | − | 0.982635i | \(-0.440594\pi\) | ||||
0.185548 | + | 0.982635i | \(0.440594\pi\) | |||||||
\(954\) | 8.36390 | 0.270791 | ||||||||
\(955\) | −2.93834 | −0.0950823 | ||||||||
\(956\) | −112.304 | −3.63218 | ||||||||
\(957\) | 5.85945 | 0.189409 | ||||||||
\(958\) | 91.1908 | 2.94624 | ||||||||
\(959\) | −22.9510 | −0.741126 | ||||||||
\(960\) | −11.9651 | −0.386172 | ||||||||
\(961\) | −18.5249 | −0.597578 | ||||||||
\(962\) | −65.8234 | −2.12223 | ||||||||
\(963\) | 1.58748 | 0.0511560 | ||||||||
\(964\) | −64.6227 | −2.08136 | ||||||||
\(965\) | −21.8433 | −0.703160 | ||||||||
\(966\) | −39.7352 | −1.27846 | ||||||||
\(967\) | −32.0337 | −1.03014 | −0.515068 | − | 0.857150i | \(-0.672233\pi\) | ||||
−0.515068 | + | 0.857150i | \(0.672233\pi\) | |||||||
\(968\) | 19.7931 | 0.636175 | ||||||||
\(969\) | −8.55376 | −0.274786 | ||||||||
\(970\) | 29.9244 | 0.960814 | ||||||||
\(971\) | −21.7771 | −0.698859 | −0.349429 | − | 0.936963i | \(-0.613625\pi\) | ||||
−0.349429 | + | 0.936963i | \(0.613625\pi\) | |||||||
\(972\) | 21.9089 | 0.702728 | ||||||||
\(973\) | 21.3558 | 0.684636 | ||||||||
\(974\) | −70.9736 | −2.27414 | ||||||||
\(975\) | −20.8449 | −0.667572 | ||||||||
\(976\) | −56.2118 | −1.79930 | ||||||||
\(977\) | 48.8640 | 1.56330 | 0.781649 | − | 0.623719i | \(-0.214379\pi\) | ||||
0.781649 | + | 0.623719i | \(0.214379\pi\) | |||||||
\(978\) | −90.0684 | −2.88007 | ||||||||
\(979\) | −50.1012 | −1.60124 | ||||||||
\(980\) | −21.2469 | −0.678706 | ||||||||
\(981\) | 1.12939 | 0.0360586 | ||||||||
\(982\) | 12.5188 | 0.399490 | ||||||||
\(983\) | 43.9288 | 1.40111 | 0.700555 | − | 0.713598i | \(-0.252936\pi\) | ||||
0.700555 | + | 0.713598i | \(0.252936\pi\) | |||||||
\(984\) | 8.68374 | 0.276827 | ||||||||
\(985\) | −8.67600 | −0.276440 | ||||||||
\(986\) | 3.72213 | 0.118537 | ||||||||
\(987\) | −1.38221 | −0.0439963 | ||||||||
\(988\) | −63.7049 | −2.02672 | ||||||||
\(989\) | −18.1842 | −0.578225 | ||||||||
\(990\) | −4.82962 | −0.153495 | ||||||||
\(991\) | 18.0715 | 0.574060 | 0.287030 | − | 0.957922i | \(-0.407332\pi\) | ||||
0.287030 | + | 0.957922i | \(0.407332\pi\) | |||||||
\(992\) | 29.6584 | 0.941655 | ||||||||
\(993\) | 48.4215 | 1.53661 | ||||||||
\(994\) | 0.378697 | 0.0120115 | ||||||||
\(995\) | 33.9824 | 1.07731 | ||||||||
\(996\) | −129.178 | −4.09315 | ||||||||
\(997\) | −36.5966 | −1.15903 | −0.579514 | − | 0.814963i | \(-0.696757\pi\) | ||||
−0.579514 | + | 0.814963i | \(0.696757\pi\) | |||||||
\(998\) | −43.3918 | −1.37354 | ||||||||
\(999\) | −31.3270 | −0.991143 |
(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 | 503.2.a.e.1.1 | ✓ | 10 | |
3.2 | odd | 2 | 4527.2.a.k.1.10 | 10 | |||
4.3 | odd | 2 | 8048.2.a.p.1.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.1 | ✓ | 10 | 1.1 | even | 1 | trivial | |
4527.2.a.k.1.10 | 10 | 3.2 | odd | 2 | |||
8048.2.a.p.1.8 | 10 | 4.3 | odd | 2 |