Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.844390 | 0.487509 | 0.243754 | − | 0.969837i | \(-0.421621\pi\) | ||||
0.243754 | + | 0.969837i | \(0.421621\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.22697 | 1.89036 | 0.945178 | − | 0.326555i | \(-0.105888\pi\) | ||||
0.945178 | + | 0.326555i | \(0.105888\pi\) | |||||||
\(6\) | 0.844390 | 0.344721 | ||||||||
\(7\) | −3.69998 | −1.39846 | −0.699231 | − | 0.714896i | \(-0.746474\pi\) | ||||
−0.699231 | + | 0.714896i | \(0.746474\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.28700 | −0.762335 | ||||||||
\(10\) | 4.22697 | 1.33668 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0.844390 | 0.243754 | ||||||||
\(13\) | −2.61015 | −0.723926 | −0.361963 | − | 0.932193i | \(-0.617893\pi\) | ||||
−0.361963 | + | 0.932193i | \(0.617893\pi\) | |||||||
\(14\) | −3.69998 | −0.988862 | ||||||||
\(15\) | 3.56921 | 0.921566 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.89660 | 0.945065 | 0.472532 | − | 0.881313i | \(-0.343340\pi\) | ||||
0.472532 | + | 0.881313i | \(0.343340\pi\) | |||||||
\(18\) | −2.28700 | −0.539052 | ||||||||
\(19\) | 6.44454 | 1.47848 | 0.739239 | − | 0.673443i | \(-0.235185\pi\) | ||||
0.739239 | + | 0.673443i | \(0.235185\pi\) | |||||||
\(20\) | 4.22697 | 0.945178 | ||||||||
\(21\) | −3.12423 | −0.681763 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 3.21484 | 0.670340 | 0.335170 | − | 0.942158i | \(-0.391206\pi\) | ||||
0.335170 | + | 0.942158i | \(0.391206\pi\) | |||||||
\(24\) | 0.844390 | 0.172360 | ||||||||
\(25\) | 12.8672 | 2.57345 | ||||||||
\(26\) | −2.61015 | −0.511893 | ||||||||
\(27\) | −4.46430 | −0.859154 | ||||||||
\(28\) | −3.69998 | −0.699231 | ||||||||
\(29\) | 6.10309 | 1.13332 | 0.566658 | − | 0.823953i | \(-0.308236\pi\) | ||||
0.566658 | + | 0.823953i | \(0.308236\pi\) | |||||||
\(30\) | 3.56921 | 0.651645 | ||||||||
\(31\) | 8.08890 | 1.45281 | 0.726404 | − | 0.687267i | \(-0.241190\pi\) | ||||
0.726404 | + | 0.687267i | \(0.241190\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.844390 | −0.146989 | ||||||||
\(34\) | 3.89660 | 0.668262 | ||||||||
\(35\) | −15.6397 | −2.64359 | ||||||||
\(36\) | −2.28700 | −0.381167 | ||||||||
\(37\) | −9.72230 | −1.59834 | −0.799168 | − | 0.601108i | \(-0.794726\pi\) | ||||
−0.799168 | + | 0.601108i | \(0.794726\pi\) | |||||||
\(38\) | 6.44454 | 1.04544 | ||||||||
\(39\) | −2.20399 | −0.352920 | ||||||||
\(40\) | 4.22697 | 0.668342 | ||||||||
\(41\) | 5.54084 | 0.865334 | 0.432667 | − | 0.901554i | \(-0.357573\pi\) | ||||
0.432667 | + | 0.901554i | \(0.357573\pi\) | |||||||
\(42\) | −3.12423 | −0.482079 | ||||||||
\(43\) | 1.26532 | 0.192959 | 0.0964795 | − | 0.995335i | \(-0.469242\pi\) | ||||
0.0964795 | + | 0.995335i | \(0.469242\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −9.66709 | −1.44109 | ||||||||
\(46\) | 3.21484 | 0.474002 | ||||||||
\(47\) | 4.11895 | 0.600810 | 0.300405 | − | 0.953812i | \(-0.402878\pi\) | ||||
0.300405 | + | 0.953812i | \(0.402878\pi\) | |||||||
\(48\) | 0.844390 | 0.121877 | ||||||||
\(49\) | 6.68987 | 0.955696 | ||||||||
\(50\) | 12.8672 | 1.81970 | ||||||||
\(51\) | 3.29025 | 0.460728 | ||||||||
\(52\) | −2.61015 | −0.361963 | ||||||||
\(53\) | −10.5440 | −1.44832 | −0.724162 | − | 0.689630i | \(-0.757773\pi\) | ||||
−0.724162 | + | 0.689630i | \(0.757773\pi\) | |||||||
\(54\) | −4.46430 | −0.607514 | ||||||||
\(55\) | −4.22697 | −0.569964 | ||||||||
\(56\) | −3.69998 | −0.494431 | ||||||||
\(57\) | 5.44170 | 0.720771 | ||||||||
\(58\) | 6.10309 | 0.801375 | ||||||||
\(59\) | −0.892335 | −0.116172 | −0.0580860 | − | 0.998312i | \(-0.518500\pi\) | ||||
−0.0580860 | + | 0.998312i | \(0.518500\pi\) | |||||||
\(60\) | 3.56921 | 0.460783 | ||||||||
\(61\) | 8.76256 | 1.12193 | 0.560966 | − | 0.827839i | \(-0.310430\pi\) | ||||
0.560966 | + | 0.827839i | \(0.310430\pi\) | |||||||
\(62\) | 8.08890 | 1.02729 | ||||||||
\(63\) | 8.46188 | 1.06610 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −11.0330 | −1.36848 | ||||||||
\(66\) | −0.844390 | −0.103937 | ||||||||
\(67\) | 4.58290 | 0.559891 | 0.279945 | − | 0.960016i | \(-0.409684\pi\) | ||||
0.279945 | + | 0.960016i | \(0.409684\pi\) | |||||||
\(68\) | 3.89660 | 0.472532 | ||||||||
\(69\) | 2.71458 | 0.326797 | ||||||||
\(70\) | −15.6397 | −1.86930 | ||||||||
\(71\) | 4.06852 | 0.482844 | 0.241422 | − | 0.970420i | \(-0.422386\pi\) | ||||
0.241422 | + | 0.970420i | \(0.422386\pi\) | |||||||
\(72\) | −2.28700 | −0.269526 | ||||||||
\(73\) | −8.29482 | −0.970836 | −0.485418 | − | 0.874282i | \(-0.661333\pi\) | ||||
−0.485418 | + | 0.874282i | \(0.661333\pi\) | |||||||
\(74\) | −9.72230 | −1.13019 | ||||||||
\(75\) | 10.8650 | 1.25458 | ||||||||
\(76\) | 6.44454 | 0.739239 | ||||||||
\(77\) | 3.69998 | 0.421652 | ||||||||
\(78\) | −2.20399 | −0.249552 | ||||||||
\(79\) | 13.7390 | 1.54576 | 0.772879 | − | 0.634554i | \(-0.218816\pi\) | ||||
0.772879 | + | 0.634554i | \(0.218816\pi\) | |||||||
\(80\) | 4.22697 | 0.472589 | ||||||||
\(81\) | 3.09141 | 0.343490 | ||||||||
\(82\) | 5.54084 | 0.611884 | ||||||||
\(83\) | 8.88633 | 0.975401 | 0.487701 | − | 0.873011i | \(-0.337836\pi\) | ||||
0.487701 | + | 0.873011i | \(0.337836\pi\) | |||||||
\(84\) | −3.12423 | −0.340881 | ||||||||
\(85\) | 16.4708 | 1.78651 | ||||||||
\(86\) | 1.26532 | 0.136443 | ||||||||
\(87\) | 5.15339 | 0.552501 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −16.2682 | −1.72442 | −0.862212 | − | 0.506547i | \(-0.830922\pi\) | ||||
−0.862212 | + | 0.506547i | \(0.830922\pi\) | |||||||
\(90\) | −9.66709 | −1.01900 | ||||||||
\(91\) | 9.65751 | 1.01238 | ||||||||
\(92\) | 3.21484 | 0.335170 | ||||||||
\(93\) | 6.83019 | 0.708257 | ||||||||
\(94\) | 4.11895 | 0.424837 | ||||||||
\(95\) | 27.2408 | 2.79485 | ||||||||
\(96\) | 0.844390 | 0.0861802 | ||||||||
\(97\) | 3.99233 | 0.405359 | 0.202680 | − | 0.979245i | \(-0.435035\pi\) | ||||
0.202680 | + | 0.979245i | \(0.435035\pi\) | |||||||
\(98\) | 6.68987 | 0.675779 | ||||||||
\(99\) | 2.28700 | 0.229853 | ||||||||
\(100\) | 12.8672 | 1.28672 | ||||||||
\(101\) | 6.93369 | 0.689928 | 0.344964 | − | 0.938616i | \(-0.387891\pi\) | ||||
0.344964 | + | 0.938616i | \(0.387891\pi\) | |||||||
\(102\) | 3.29025 | 0.325784 | ||||||||
\(103\) | −13.7159 | −1.35147 | −0.675733 | − | 0.737146i | \(-0.736173\pi\) | ||||
−0.675733 | + | 0.737146i | \(0.736173\pi\) | |||||||
\(104\) | −2.61015 | −0.255946 | ||||||||
\(105\) | −13.2060 | −1.28877 | ||||||||
\(106\) | −10.5440 | −1.02412 | ||||||||
\(107\) | 2.82180 | 0.272794 | 0.136397 | − | 0.990654i | \(-0.456448\pi\) | ||||
0.136397 | + | 0.990654i | \(0.456448\pi\) | |||||||
\(108\) | −4.46430 | −0.429577 | ||||||||
\(109\) | −10.1850 | −0.975546 | −0.487773 | − | 0.872970i | \(-0.662191\pi\) | ||||
−0.487773 | + | 0.872970i | \(0.662191\pi\) | |||||||
\(110\) | −4.22697 | −0.403025 | ||||||||
\(111\) | −8.20941 | −0.779203 | ||||||||
\(112\) | −3.69998 | −0.349615 | ||||||||
\(113\) | −0.545928 | −0.0513566 | −0.0256783 | − | 0.999670i | \(-0.508175\pi\) | ||||
−0.0256783 | + | 0.999670i | \(0.508175\pi\) | |||||||
\(114\) | 5.44170 | 0.509662 | ||||||||
\(115\) | 13.5890 | 1.26718 | ||||||||
\(116\) | 6.10309 | 0.566658 | ||||||||
\(117\) | 5.96943 | 0.551874 | ||||||||
\(118\) | −0.892335 | −0.0821461 | ||||||||
\(119\) | −14.4174 | −1.32164 | ||||||||
\(120\) | 3.56921 | 0.325823 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.76256 | 0.793325 | ||||||||
\(123\) | 4.67863 | 0.421858 | ||||||||
\(124\) | 8.08890 | 0.726404 | ||||||||
\(125\) | 33.2546 | 2.97438 | ||||||||
\(126\) | 8.46188 | 0.753844 | ||||||||
\(127\) | 7.73124 | 0.686036 | 0.343018 | − | 0.939329i | \(-0.388551\pi\) | ||||
0.343018 | + | 0.939329i | \(0.388551\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.06842 | 0.0940692 | ||||||||
\(130\) | −11.0330 | −0.967660 | ||||||||
\(131\) | 5.94221 | 0.519174 | 0.259587 | − | 0.965720i | \(-0.416414\pi\) | ||||
0.259587 | + | 0.965720i | \(0.416414\pi\) | |||||||
\(132\) | −0.844390 | −0.0734947 | ||||||||
\(133\) | −23.8447 | −2.06760 | ||||||||
\(134\) | 4.58290 | 0.395903 | ||||||||
\(135\) | −18.8704 | −1.62411 | ||||||||
\(136\) | 3.89660 | 0.334131 | ||||||||
\(137\) | −21.4264 | −1.83058 | −0.915292 | − | 0.402792i | \(-0.868040\pi\) | ||||
−0.915292 | + | 0.402792i | \(0.868040\pi\) | |||||||
\(138\) | 2.71458 | 0.231080 | ||||||||
\(139\) | 11.9196 | 1.01101 | 0.505504 | − | 0.862824i | \(-0.331306\pi\) | ||||
0.505504 | + | 0.862824i | \(0.331306\pi\) | |||||||
\(140\) | −15.6397 | −1.32180 | ||||||||
\(141\) | 3.47800 | 0.292900 | ||||||||
\(142\) | 4.06852 | 0.341422 | ||||||||
\(143\) | 2.61015 | 0.218272 | ||||||||
\(144\) | −2.28700 | −0.190584 | ||||||||
\(145\) | 25.7976 | 2.14237 | ||||||||
\(146\) | −8.29482 | −0.686484 | ||||||||
\(147\) | 5.64886 | 0.465910 | ||||||||
\(148\) | −9.72230 | −0.799168 | ||||||||
\(149\) | 10.4390 | 0.855199 | 0.427600 | − | 0.903968i | \(-0.359359\pi\) | ||||
0.427600 | + | 0.903968i | \(0.359359\pi\) | |||||||
\(150\) | 10.8650 | 0.887121 | ||||||||
\(151\) | −11.5544 | −0.940283 | −0.470142 | − | 0.882591i | \(-0.655797\pi\) | ||||
−0.470142 | + | 0.882591i | \(0.655797\pi\) | |||||||
\(152\) | 6.44454 | 0.522721 | ||||||||
\(153\) | −8.91155 | −0.720456 | ||||||||
\(154\) | 3.69998 | 0.298153 | ||||||||
\(155\) | 34.1915 | 2.74633 | ||||||||
\(156\) | −2.20399 | −0.176460 | ||||||||
\(157\) | −22.4382 | −1.79076 | −0.895381 | − | 0.445302i | \(-0.853096\pi\) | ||||
−0.895381 | + | 0.445302i | \(0.853096\pi\) | |||||||
\(158\) | 13.7390 | 1.09302 | ||||||||
\(159\) | −8.90321 | −0.706071 | ||||||||
\(160\) | 4.22697 | 0.334171 | ||||||||
\(161\) | −11.8948 | −0.937445 | ||||||||
\(162\) | 3.09141 | 0.242884 | ||||||||
\(163\) | −24.3335 | −1.90595 | −0.952973 | − | 0.303056i | \(-0.901993\pi\) | ||||
−0.952973 | + | 0.303056i | \(0.901993\pi\) | |||||||
\(164\) | 5.54084 | 0.432667 | ||||||||
\(165\) | −3.56921 | −0.277863 | ||||||||
\(166\) | 8.88633 | 0.689713 | ||||||||
\(167\) | −7.53899 | −0.583385 | −0.291692 | − | 0.956512i | \(-0.594218\pi\) | ||||
−0.291692 | + | 0.956512i | \(0.594218\pi\) | |||||||
\(168\) | −3.12423 | −0.241040 | ||||||||
\(169\) | −6.18711 | −0.475932 | ||||||||
\(170\) | 16.4708 | 1.26325 | ||||||||
\(171\) | −14.7387 | −1.12710 | ||||||||
\(172\) | 1.26532 | 0.0964795 | ||||||||
\(173\) | 5.63897 | 0.428723 | 0.214361 | − | 0.976754i | \(-0.431233\pi\) | ||||
0.214361 | + | 0.976754i | \(0.431233\pi\) | |||||||
\(174\) | 5.15339 | 0.390677 | ||||||||
\(175\) | −47.6086 | −3.59887 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −0.753479 | −0.0566349 | ||||||||
\(178\) | −16.2682 | −1.21935 | ||||||||
\(179\) | 9.90420 | 0.740275 | 0.370137 | − | 0.928977i | \(-0.379311\pi\) | ||||
0.370137 | + | 0.928977i | \(0.379311\pi\) | |||||||
\(180\) | −9.66709 | −0.720543 | ||||||||
\(181\) | −19.7201 | −1.46578 | −0.732892 | − | 0.680345i | \(-0.761830\pi\) | ||||
−0.732892 | + | 0.680345i | \(0.761830\pi\) | |||||||
\(182\) | 9.65751 | 0.715863 | ||||||||
\(183\) | 7.39902 | 0.546952 | ||||||||
\(184\) | 3.21484 | 0.237001 | ||||||||
\(185\) | −41.0958 | −3.02142 | ||||||||
\(186\) | 6.83019 | 0.500814 | ||||||||
\(187\) | −3.89660 | −0.284948 | ||||||||
\(188\) | 4.11895 | 0.300405 | ||||||||
\(189\) | 16.5178 | 1.20149 | ||||||||
\(190\) | 27.2408 | 1.97626 | ||||||||
\(191\) | −12.0678 | −0.873195 | −0.436598 | − | 0.899657i | \(-0.643817\pi\) | ||||
−0.436598 | + | 0.899657i | \(0.643817\pi\) | |||||||
\(192\) | 0.844390 | 0.0609386 | ||||||||
\(193\) | −7.02489 | −0.505663 | −0.252831 | − | 0.967510i | \(-0.581362\pi\) | ||||
−0.252831 | + | 0.967510i | \(0.581362\pi\) | |||||||
\(194\) | 3.99233 | 0.286632 | ||||||||
\(195\) | −9.31618 | −0.667145 | ||||||||
\(196\) | 6.68987 | 0.477848 | ||||||||
\(197\) | −1.00000 | −0.0712470 | ||||||||
\(198\) | 2.28700 | 0.162530 | ||||||||
\(199\) | −3.09241 | −0.219215 | −0.109608 | − | 0.993975i | \(-0.534959\pi\) | ||||
−0.109608 | + | 0.993975i | \(0.534959\pi\) | |||||||
\(200\) | 12.8672 | 0.909851 | ||||||||
\(201\) | 3.86976 | 0.272952 | ||||||||
\(202\) | 6.93369 | 0.487852 | ||||||||
\(203\) | −22.5813 | −1.58490 | ||||||||
\(204\) | 3.29025 | 0.230364 | ||||||||
\(205\) | 23.4210 | 1.63579 | ||||||||
\(206\) | −13.7159 | −0.955631 | ||||||||
\(207\) | −7.35235 | −0.511023 | ||||||||
\(208\) | −2.61015 | −0.180981 | ||||||||
\(209\) | −6.44454 | −0.445778 | ||||||||
\(210\) | −13.2060 | −0.911301 | ||||||||
\(211\) | −1.18835 | −0.0818097 | −0.0409049 | − | 0.999163i | \(-0.513024\pi\) | ||||
−0.0409049 | + | 0.999163i | \(0.513024\pi\) | |||||||
\(212\) | −10.5440 | −0.724162 | ||||||||
\(213\) | 3.43541 | 0.235391 | ||||||||
\(214\) | 2.82180 | 0.192895 | ||||||||
\(215\) | 5.34845 | 0.364761 | ||||||||
\(216\) | −4.46430 | −0.303757 | ||||||||
\(217\) | −29.9288 | −2.03170 | ||||||||
\(218\) | −10.1850 | −0.689815 | ||||||||
\(219\) | −7.00407 | −0.473291 | ||||||||
\(220\) | −4.22697 | −0.284982 | ||||||||
\(221\) | −10.1707 | −0.684157 | ||||||||
\(222\) | −8.20941 | −0.550980 | ||||||||
\(223\) | 21.4276 | 1.43490 | 0.717450 | − | 0.696610i | \(-0.245309\pi\) | ||||
0.717450 | + | 0.696610i | \(0.245309\pi\) | |||||||
\(224\) | −3.69998 | −0.247215 | ||||||||
\(225\) | −29.4274 | −1.96183 | ||||||||
\(226\) | −0.545928 | −0.0363146 | ||||||||
\(227\) | −0.337056 | −0.0223712 | −0.0111856 | − | 0.999937i | \(-0.503561\pi\) | ||||
−0.0111856 | + | 0.999937i | \(0.503561\pi\) | |||||||
\(228\) | 5.44170 | 0.360386 | ||||||||
\(229\) | 19.0636 | 1.25976 | 0.629881 | − | 0.776692i | \(-0.283104\pi\) | ||||
0.629881 | + | 0.776692i | \(0.283104\pi\) | |||||||
\(230\) | 13.5890 | 0.896032 | ||||||||
\(231\) | 3.12423 | 0.205559 | ||||||||
\(232\) | 6.10309 | 0.400687 | ||||||||
\(233\) | 6.56520 | 0.430101 | 0.215050 | − | 0.976603i | \(-0.431008\pi\) | ||||
0.215050 | + | 0.976603i | \(0.431008\pi\) | |||||||
\(234\) | 5.96943 | 0.390234 | ||||||||
\(235\) | 17.4106 | 1.13575 | ||||||||
\(236\) | −0.892335 | −0.0580860 | ||||||||
\(237\) | 11.6011 | 0.753570 | ||||||||
\(238\) | −14.4174 | −0.934539 | ||||||||
\(239\) | 0.818578 | 0.0529494 | 0.0264747 | − | 0.999649i | \(-0.491572\pi\) | ||||
0.0264747 | + | 0.999649i | \(0.491572\pi\) | |||||||
\(240\) | 3.56921 | 0.230391 | ||||||||
\(241\) | 7.99971 | 0.515307 | 0.257653 | − | 0.966237i | \(-0.417051\pi\) | ||||
0.257653 | + | 0.966237i | \(0.417051\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 16.0032 | 1.02661 | ||||||||
\(244\) | 8.76256 | 0.560966 | ||||||||
\(245\) | 28.2779 | 1.80661 | ||||||||
\(246\) | 4.67863 | 0.298299 | ||||||||
\(247\) | −16.8212 | −1.07031 | ||||||||
\(248\) | 8.08890 | 0.513645 | ||||||||
\(249\) | 7.50353 | 0.475517 | ||||||||
\(250\) | 33.2546 | 2.10320 | ||||||||
\(251\) | −11.2651 | −0.711047 | −0.355524 | − | 0.934667i | \(-0.615697\pi\) | ||||
−0.355524 | + | 0.934667i | \(0.615697\pi\) | |||||||
\(252\) | 8.46188 | 0.533048 | ||||||||
\(253\) | −3.21484 | −0.202115 | ||||||||
\(254\) | 7.73124 | 0.485101 | ||||||||
\(255\) | 13.9078 | 0.870939 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.11751 | −0.319221 | −0.159611 | − | 0.987180i | \(-0.551024\pi\) | ||||
−0.159611 | + | 0.987180i | \(0.551024\pi\) | |||||||
\(258\) | 1.06842 | 0.0665170 | ||||||||
\(259\) | 35.9723 | 2.23521 | ||||||||
\(260\) | −11.0330 | −0.684239 | ||||||||
\(261\) | −13.9578 | −0.863966 | ||||||||
\(262\) | 5.94221 | 0.367111 | ||||||||
\(263\) | 1.99141 | 0.122795 | 0.0613977 | − | 0.998113i | \(-0.480444\pi\) | ||||
0.0613977 | + | 0.998113i | \(0.480444\pi\) | |||||||
\(264\) | −0.844390 | −0.0519686 | ||||||||
\(265\) | −44.5689 | −2.73785 | ||||||||
\(266\) | −23.8447 | −1.46201 | ||||||||
\(267\) | −13.7367 | −0.840673 | ||||||||
\(268\) | 4.58290 | 0.279945 | ||||||||
\(269\) | 3.83213 | 0.233649 | 0.116825 | − | 0.993153i | \(-0.462728\pi\) | ||||
0.116825 | + | 0.993153i | \(0.462728\pi\) | |||||||
\(270\) | −18.8704 | −1.14842 | ||||||||
\(271\) | −12.4814 | −0.758192 | −0.379096 | − | 0.925357i | \(-0.623765\pi\) | ||||
−0.379096 | + | 0.925357i | \(0.623765\pi\) | |||||||
\(272\) | 3.89660 | 0.236266 | ||||||||
\(273\) | 8.15471 | 0.493546 | ||||||||
\(274\) | −21.4264 | −1.29442 | ||||||||
\(275\) | −12.8672 | −0.775924 | ||||||||
\(276\) | 2.71458 | 0.163398 | ||||||||
\(277\) | −4.92043 | −0.295640 | −0.147820 | − | 0.989014i | \(-0.547226\pi\) | ||||
−0.147820 | + | 0.989014i | \(0.547226\pi\) | |||||||
\(278\) | 11.9196 | 0.714891 | ||||||||
\(279\) | −18.4993 | −1.10753 | ||||||||
\(280\) | −15.6397 | −0.934651 | ||||||||
\(281\) | 31.2854 | 1.86633 | 0.933167 | − | 0.359444i | \(-0.117034\pi\) | ||||
0.933167 | + | 0.359444i | \(0.117034\pi\) | |||||||
\(282\) | 3.47800 | 0.207112 | ||||||||
\(283\) | −22.4086 | −1.33205 | −0.666027 | − | 0.745928i | \(-0.732006\pi\) | ||||
−0.666027 | + | 0.745928i | \(0.732006\pi\) | |||||||
\(284\) | 4.06852 | 0.241422 | ||||||||
\(285\) | 23.0019 | 1.36251 | ||||||||
\(286\) | 2.61015 | 0.154341 | ||||||||
\(287\) | −20.5010 | −1.21014 | ||||||||
\(288\) | −2.28700 | −0.134763 | ||||||||
\(289\) | −1.81649 | −0.106852 | ||||||||
\(290\) | 25.7976 | 1.51488 | ||||||||
\(291\) | 3.37108 | 0.197616 | ||||||||
\(292\) | −8.29482 | −0.485418 | ||||||||
\(293\) | −20.5399 | −1.19995 | −0.599976 | − | 0.800018i | \(-0.704823\pi\) | ||||
−0.599976 | + | 0.800018i | \(0.704823\pi\) | |||||||
\(294\) | 5.64886 | 0.329448 | ||||||||
\(295\) | −3.77187 | −0.219607 | ||||||||
\(296\) | −9.72230 | −0.565097 | ||||||||
\(297\) | 4.46430 | 0.259045 | ||||||||
\(298\) | 10.4390 | 0.604717 | ||||||||
\(299\) | −8.39121 | −0.485276 | ||||||||
\(300\) | 10.8650 | 0.627290 | ||||||||
\(301\) | −4.68165 | −0.269846 | ||||||||
\(302\) | −11.5544 | −0.664881 | ||||||||
\(303\) | 5.85474 | 0.336346 | ||||||||
\(304\) | 6.44454 | 0.369619 | ||||||||
\(305\) | 37.0391 | 2.12085 | ||||||||
\(306\) | −8.91155 | −0.509439 | ||||||||
\(307\) | −24.0190 | −1.37084 | −0.685418 | − | 0.728149i | \(-0.740381\pi\) | ||||
−0.685418 | + | 0.728149i | \(0.740381\pi\) | |||||||
\(308\) | 3.69998 | 0.210826 | ||||||||
\(309\) | −11.5816 | −0.658852 | ||||||||
\(310\) | 34.1915 | 1.94195 | ||||||||
\(311\) | 14.8044 | 0.839481 | 0.419740 | − | 0.907644i | \(-0.362121\pi\) | ||||
0.419740 | + | 0.907644i | \(0.362121\pi\) | |||||||
\(312\) | −2.20399 | −0.124776 | ||||||||
\(313\) | −29.6240 | −1.67445 | −0.837224 | − | 0.546860i | \(-0.815823\pi\) | ||||
−0.837224 | + | 0.546860i | \(0.815823\pi\) | |||||||
\(314\) | −22.4382 | −1.26626 | ||||||||
\(315\) | 35.7681 | 2.01530 | ||||||||
\(316\) | 13.7390 | 0.772879 | ||||||||
\(317\) | 6.88637 | 0.386777 | 0.193389 | − | 0.981122i | \(-0.438052\pi\) | ||||
0.193389 | + | 0.981122i | \(0.438052\pi\) | |||||||
\(318\) | −8.90321 | −0.499267 | ||||||||
\(319\) | −6.10309 | −0.341707 | ||||||||
\(320\) | 4.22697 | 0.236295 | ||||||||
\(321\) | 2.38270 | 0.132990 | ||||||||
\(322\) | −11.8948 | −0.662873 | ||||||||
\(323\) | 25.1118 | 1.39726 | ||||||||
\(324\) | 3.09141 | 0.171745 | ||||||||
\(325\) | −33.5855 | −1.86299 | ||||||||
\(326\) | −24.3335 | −1.34771 | ||||||||
\(327\) | −8.60012 | −0.475587 | ||||||||
\(328\) | 5.54084 | 0.305942 | ||||||||
\(329\) | −15.2400 | −0.840210 | ||||||||
\(330\) | −3.56921 | −0.196479 | ||||||||
\(331\) | −4.84184 | −0.266132 | −0.133066 | − | 0.991107i | \(-0.542482\pi\) | ||||
−0.133066 | + | 0.991107i | \(0.542482\pi\) | |||||||
\(332\) | 8.88633 | 0.487701 | ||||||||
\(333\) | 22.2349 | 1.21847 | ||||||||
\(334\) | −7.53899 | −0.412515 | ||||||||
\(335\) | 19.3718 | 1.05839 | ||||||||
\(336\) | −3.12423 | −0.170441 | ||||||||
\(337\) | −27.4794 | −1.49690 | −0.748450 | − | 0.663191i | \(-0.769202\pi\) | ||||
−0.748450 | + | 0.663191i | \(0.769202\pi\) | |||||||
\(338\) | −6.18711 | −0.336534 | ||||||||
\(339\) | −0.460976 | −0.0250368 | ||||||||
\(340\) | 16.4708 | 0.893255 | ||||||||
\(341\) | −8.08890 | −0.438038 | ||||||||
\(342\) | −14.7387 | −0.796977 | ||||||||
\(343\) | 1.14747 | 0.0619575 | ||||||||
\(344\) | 1.26532 | 0.0682213 | ||||||||
\(345\) | 11.4744 | 0.617762 | ||||||||
\(346\) | 5.63897 | 0.303153 | ||||||||
\(347\) | 7.78099 | 0.417705 | 0.208853 | − | 0.977947i | \(-0.433027\pi\) | ||||
0.208853 | + | 0.977947i | \(0.433027\pi\) | |||||||
\(348\) | 5.15339 | 0.276251 | ||||||||
\(349\) | 20.7381 | 1.11008 | 0.555042 | − | 0.831822i | \(-0.312702\pi\) | ||||
0.555042 | + | 0.831822i | \(0.312702\pi\) | |||||||
\(350\) | −47.6086 | −2.54479 | ||||||||
\(351\) | 11.6525 | 0.621964 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −2.88777 | −0.153701 | −0.0768503 | − | 0.997043i | \(-0.524486\pi\) | ||||
−0.0768503 | + | 0.997043i | \(0.524486\pi\) | |||||||
\(354\) | −0.753479 | −0.0400469 | ||||||||
\(355\) | 17.1975 | 0.912747 | ||||||||
\(356\) | −16.2682 | −0.862212 | ||||||||
\(357\) | −12.1739 | −0.644310 | ||||||||
\(358\) | 9.90420 | 0.523453 | ||||||||
\(359\) | 15.2377 | 0.804212 | 0.402106 | − | 0.915593i | \(-0.368278\pi\) | ||||
0.402106 | + | 0.915593i | \(0.368278\pi\) | |||||||
\(360\) | −9.66709 | −0.509501 | ||||||||
\(361\) | 22.5320 | 1.18590 | ||||||||
\(362\) | −19.7201 | −1.03647 | ||||||||
\(363\) | 0.844390 | 0.0443190 | ||||||||
\(364\) | 9.65751 | 0.506191 | ||||||||
\(365\) | −35.0619 | −1.83523 | ||||||||
\(366\) | 7.39902 | 0.386753 | ||||||||
\(367\) | 16.7576 | 0.874738 | 0.437369 | − | 0.899282i | \(-0.355910\pi\) | ||||
0.437369 | + | 0.899282i | \(0.355910\pi\) | |||||||
\(368\) | 3.21484 | 0.167585 | ||||||||
\(369\) | −12.6719 | −0.659675 | ||||||||
\(370\) | −41.0958 | −2.13647 | ||||||||
\(371\) | 39.0124 | 2.02542 | ||||||||
\(372\) | 6.83019 | 0.354129 | ||||||||
\(373\) | −35.4758 | −1.83687 | −0.918433 | − | 0.395577i | \(-0.870545\pi\) | ||||
−0.918433 | + | 0.395577i | \(0.870545\pi\) | |||||||
\(374\) | −3.89660 | −0.201488 | ||||||||
\(375\) | 28.0798 | 1.45004 | ||||||||
\(376\) | 4.11895 | 0.212418 | ||||||||
\(377\) | −15.9300 | −0.820436 | ||||||||
\(378\) | 16.5178 | 0.849585 | ||||||||
\(379\) | 2.08275 | 0.106984 | 0.0534919 | − | 0.998568i | \(-0.482965\pi\) | ||||
0.0534919 | + | 0.998568i | \(0.482965\pi\) | |||||||
\(380\) | 27.2408 | 1.39743 | ||||||||
\(381\) | 6.52818 | 0.334449 | ||||||||
\(382\) | −12.0678 | −0.617442 | ||||||||
\(383\) | −3.98661 | −0.203706 | −0.101853 | − | 0.994799i | \(-0.532477\pi\) | ||||
−0.101853 | + | 0.994799i | \(0.532477\pi\) | |||||||
\(384\) | 0.844390 | 0.0430901 | ||||||||
\(385\) | 15.6397 | 0.797073 | ||||||||
\(386\) | −7.02489 | −0.357557 | ||||||||
\(387\) | −2.89378 | −0.147099 | ||||||||
\(388\) | 3.99233 | 0.202680 | ||||||||
\(389\) | 30.6751 | 1.55529 | 0.777644 | − | 0.628705i | \(-0.216415\pi\) | ||||
0.777644 | + | 0.628705i | \(0.216415\pi\) | |||||||
\(390\) | −9.31618 | −0.471743 | ||||||||
\(391\) | 12.5269 | 0.633515 | ||||||||
\(392\) | 6.68987 | 0.337890 | ||||||||
\(393\) | 5.01755 | 0.253102 | ||||||||
\(394\) | −1.00000 | −0.0503793 | ||||||||
\(395\) | 58.0742 | 2.92203 | ||||||||
\(396\) | 2.28700 | 0.114926 | ||||||||
\(397\) | 28.2667 | 1.41866 | 0.709332 | − | 0.704875i | \(-0.248997\pi\) | ||||
0.709332 | + | 0.704875i | \(0.248997\pi\) | |||||||
\(398\) | −3.09241 | −0.155008 | ||||||||
\(399\) | −20.1342 | −1.00797 | ||||||||
\(400\) | 12.8672 | 0.643362 | ||||||||
\(401\) | −7.18828 | −0.358966 | −0.179483 | − | 0.983761i | \(-0.557442\pi\) | ||||
−0.179483 | + | 0.983761i | \(0.557442\pi\) | |||||||
\(402\) | 3.86976 | 0.193006 | ||||||||
\(403\) | −21.1132 | −1.05173 | ||||||||
\(404\) | 6.93369 | 0.344964 | ||||||||
\(405\) | 13.0673 | 0.649318 | ||||||||
\(406\) | −22.5813 | −1.12069 | ||||||||
\(407\) | 9.72230 | 0.481916 | ||||||||
\(408\) | 3.29025 | 0.162892 | ||||||||
\(409\) | −27.2450 | −1.34718 | −0.673590 | − | 0.739106i | \(-0.735248\pi\) | ||||
−0.673590 | + | 0.739106i | \(0.735248\pi\) | |||||||
\(410\) | 23.4210 | 1.15668 | ||||||||
\(411\) | −18.0923 | −0.892426 | ||||||||
\(412\) | −13.7159 | −0.675733 | ||||||||
\(413\) | 3.30162 | 0.162462 | ||||||||
\(414\) | −7.35235 | −0.361348 | ||||||||
\(415\) | 37.5622 | 1.84386 | ||||||||
\(416\) | −2.61015 | −0.127973 | ||||||||
\(417\) | 10.0648 | 0.492876 | ||||||||
\(418\) | −6.44454 | −0.315213 | ||||||||
\(419\) | −14.4906 | −0.707915 | −0.353957 | − | 0.935262i | \(-0.615164\pi\) | ||||
−0.353957 | + | 0.935262i | \(0.615164\pi\) | |||||||
\(420\) | −13.2060 | −0.644387 | ||||||||
\(421\) | −34.0129 | −1.65769 | −0.828844 | − | 0.559480i | \(-0.811001\pi\) | ||||
−0.828844 | + | 0.559480i | \(0.811001\pi\) | |||||||
\(422\) | −1.18835 | −0.0578482 | ||||||||
\(423\) | −9.42005 | −0.458018 | ||||||||
\(424\) | −10.5440 | −0.512060 | ||||||||
\(425\) | 50.1385 | 2.43208 | ||||||||
\(426\) | 3.43541 | 0.166446 | ||||||||
\(427\) | −32.4213 | −1.56898 | ||||||||
\(428\) | 2.82180 | 0.136397 | ||||||||
\(429\) | 2.20399 | 0.106409 | ||||||||
\(430\) | 5.34845 | 0.257925 | ||||||||
\(431\) | −6.65099 | −0.320367 | −0.160183 | − | 0.987087i | \(-0.551209\pi\) | ||||
−0.160183 | + | 0.987087i | \(0.551209\pi\) | |||||||
\(432\) | −4.46430 | −0.214789 | ||||||||
\(433\) | −39.0712 | −1.87764 | −0.938821 | − | 0.344405i | \(-0.888081\pi\) | ||||
−0.938821 | + | 0.344405i | \(0.888081\pi\) | |||||||
\(434\) | −29.9288 | −1.43663 | ||||||||
\(435\) | 21.7832 | 1.04442 | ||||||||
\(436\) | −10.1850 | −0.487773 | ||||||||
\(437\) | 20.7181 | 0.991083 | ||||||||
\(438\) | −7.00407 | −0.334667 | ||||||||
\(439\) | −12.9506 | −0.618097 | −0.309048 | − | 0.951046i | \(-0.600010\pi\) | ||||
−0.309048 | + | 0.951046i | \(0.600010\pi\) | |||||||
\(440\) | −4.22697 | −0.201513 | ||||||||
\(441\) | −15.2998 | −0.728560 | ||||||||
\(442\) | −10.1707 | −0.483772 | ||||||||
\(443\) | −13.3359 | −0.633607 | −0.316804 | − | 0.948491i | \(-0.602610\pi\) | ||||
−0.316804 | + | 0.948491i | \(0.602610\pi\) | |||||||
\(444\) | −8.20941 | −0.389602 | ||||||||
\(445\) | −68.7651 | −3.25978 | ||||||||
\(446\) | 21.4276 | 1.01463 | ||||||||
\(447\) | 8.81462 | 0.416917 | ||||||||
\(448\) | −3.69998 | −0.174808 | ||||||||
\(449\) | 3.42835 | 0.161794 | 0.0808969 | − | 0.996722i | \(-0.474222\pi\) | ||||
0.0808969 | + | 0.996722i | \(0.474222\pi\) | |||||||
\(450\) | −29.4274 | −1.38722 | ||||||||
\(451\) | −5.54084 | −0.260908 | ||||||||
\(452\) | −0.545928 | −0.0256783 | ||||||||
\(453\) | −9.75642 | −0.458396 | ||||||||
\(454\) | −0.337056 | −0.0158188 | ||||||||
\(455\) | 40.8220 | 1.91376 | ||||||||
\(456\) | 5.44170 | 0.254831 | ||||||||
\(457\) | −4.61725 | −0.215986 | −0.107993 | − | 0.994152i | \(-0.534442\pi\) | ||||
−0.107993 | + | 0.994152i | \(0.534442\pi\) | |||||||
\(458\) | 19.0636 | 0.890786 | ||||||||
\(459\) | −17.3956 | −0.811956 | ||||||||
\(460\) | 13.5890 | 0.633591 | ||||||||
\(461\) | −13.8104 | −0.643215 | −0.321608 | − | 0.946873i | \(-0.604223\pi\) | ||||
−0.321608 | + | 0.946873i | \(0.604223\pi\) | |||||||
\(462\) | 3.12423 | 0.145352 | ||||||||
\(463\) | 29.0450 | 1.34984 | 0.674918 | − | 0.737892i | \(-0.264179\pi\) | ||||
0.674918 | + | 0.737892i | \(0.264179\pi\) | |||||||
\(464\) | 6.10309 | 0.283329 | ||||||||
\(465\) | 28.8710 | 1.33886 | ||||||||
\(466\) | 6.56520 | 0.304127 | ||||||||
\(467\) | −1.59622 | −0.0738643 | −0.0369321 | − | 0.999318i | \(-0.511759\pi\) | ||||
−0.0369321 | + | 0.999318i | \(0.511759\pi\) | |||||||
\(468\) | 5.96943 | 0.275937 | ||||||||
\(469\) | −16.9567 | −0.782986 | ||||||||
\(470\) | 17.4106 | 0.803093 | ||||||||
\(471\) | −18.9466 | −0.873012 | ||||||||
\(472\) | −0.892335 | −0.0410730 | ||||||||
\(473\) | −1.26532 | −0.0581793 | ||||||||
\(474\) | 11.6011 | 0.532855 | ||||||||
\(475\) | 82.9234 | 3.80479 | ||||||||
\(476\) | −14.4174 | −0.660819 | ||||||||
\(477\) | 24.1141 | 1.10411 | ||||||||
\(478\) | 0.818578 | 0.0374409 | ||||||||
\(479\) | −24.1500 | −1.10344 | −0.551721 | − | 0.834029i | \(-0.686029\pi\) | ||||
−0.551721 | + | 0.834029i | \(0.686029\pi\) | |||||||
\(480\) | 3.56921 | 0.162911 | ||||||||
\(481\) | 25.3767 | 1.15708 | ||||||||
\(482\) | 7.99971 | 0.364377 | ||||||||
\(483\) | −10.0439 | −0.457013 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 16.8754 | 0.766274 | ||||||||
\(486\) | 16.0032 | 0.725922 | ||||||||
\(487\) | 40.0418 | 1.81447 | 0.907234 | − | 0.420625i | \(-0.138189\pi\) | ||||
0.907234 | + | 0.420625i | \(0.138189\pi\) | |||||||
\(488\) | 8.76256 | 0.396663 | ||||||||
\(489\) | −20.5470 | −0.929166 | ||||||||
\(490\) | 28.2779 | 1.27746 | ||||||||
\(491\) | −38.6205 | −1.74292 | −0.871459 | − | 0.490469i | \(-0.836826\pi\) | ||||
−0.871459 | + | 0.490469i | \(0.836826\pi\) | |||||||
\(492\) | 4.67863 | 0.210929 | ||||||||
\(493\) | 23.7813 | 1.07106 | ||||||||
\(494\) | −16.8212 | −0.756822 | ||||||||
\(495\) | 9.66709 | 0.434503 | ||||||||
\(496\) | 8.08890 | 0.363202 | ||||||||
\(497\) | −15.0534 | −0.675239 | ||||||||
\(498\) | 7.50353 | 0.336241 | ||||||||
\(499\) | 35.1589 | 1.57393 | 0.786964 | − | 0.616998i | \(-0.211652\pi\) | ||||
0.786964 | + | 0.616998i | \(0.211652\pi\) | |||||||
\(500\) | 33.2546 | 1.48719 | ||||||||
\(501\) | −6.36585 | −0.284405 | ||||||||
\(502\) | −11.2651 | −0.502786 | ||||||||
\(503\) | −8.99226 | −0.400945 | −0.200473 | − | 0.979699i | \(-0.564248\pi\) | ||||
−0.200473 | + | 0.979699i | \(0.564248\pi\) | |||||||
\(504\) | 8.46188 | 0.376922 | ||||||||
\(505\) | 29.3085 | 1.30421 | ||||||||
\(506\) | −3.21484 | −0.142917 | ||||||||
\(507\) | −5.22434 | −0.232021 | ||||||||
\(508\) | 7.73124 | 0.343018 | ||||||||
\(509\) | 41.3096 | 1.83102 | 0.915508 | − | 0.402300i | \(-0.131789\pi\) | ||||
0.915508 | + | 0.402300i | \(0.131789\pi\) | |||||||
\(510\) | 13.9078 | 0.615847 | ||||||||
\(511\) | 30.6907 | 1.35768 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −28.7703 | −1.27024 | ||||||||
\(514\) | −5.11751 | −0.225723 | ||||||||
\(515\) | −57.9766 | −2.55475 | ||||||||
\(516\) | 1.06842 | 0.0470346 | ||||||||
\(517\) | −4.11895 | −0.181151 | ||||||||
\(518\) | 35.9723 | 1.58053 | ||||||||
\(519\) | 4.76149 | 0.209006 | ||||||||
\(520\) | −11.0330 | −0.483830 | ||||||||
\(521\) | 26.3354 | 1.15378 | 0.576888 | − | 0.816823i | \(-0.304267\pi\) | ||||
0.576888 | + | 0.816823i | \(0.304267\pi\) | |||||||
\(522\) | −13.9578 | −0.610916 | ||||||||
\(523\) | −22.6110 | −0.988711 | −0.494355 | − | 0.869260i | \(-0.664596\pi\) | ||||
−0.494355 | + | 0.869260i | \(0.664596\pi\) | |||||||
\(524\) | 5.94221 | 0.259587 | ||||||||
\(525\) | −40.2002 | −1.75448 | ||||||||
\(526\) | 1.99141 | 0.0868295 | ||||||||
\(527\) | 31.5192 | 1.37300 | ||||||||
\(528\) | −0.844390 | −0.0367474 | ||||||||
\(529\) | −12.6648 | −0.550645 | ||||||||
\(530\) | −44.5689 | −1.93595 | ||||||||
\(531\) | 2.04077 | 0.0885620 | ||||||||
\(532\) | −23.8447 | −1.03380 | ||||||||
\(533\) | −14.4624 | −0.626438 | ||||||||
\(534\) | −13.7367 | −0.594445 | ||||||||
\(535\) | 11.9277 | 0.515678 | ||||||||
\(536\) | 4.58290 | 0.197951 | ||||||||
\(537\) | 8.36301 | 0.360891 | ||||||||
\(538\) | 3.83213 | 0.165215 | ||||||||
\(539\) | −6.68987 | −0.288153 | ||||||||
\(540\) | −18.8704 | −0.812054 | ||||||||
\(541\) | −22.0328 | −0.947264 | −0.473632 | − | 0.880723i | \(-0.657057\pi\) | ||||
−0.473632 | + | 0.880723i | \(0.657057\pi\) | |||||||
\(542\) | −12.4814 | −0.536123 | ||||||||
\(543\) | −16.6515 | −0.714583 | ||||||||
\(544\) | 3.89660 | 0.167065 | ||||||||
\(545\) | −43.0517 | −1.84413 | ||||||||
\(546\) | 8.15471 | 0.348989 | ||||||||
\(547\) | 38.2504 | 1.63547 | 0.817735 | − | 0.575595i | \(-0.195229\pi\) | ||||
0.817735 | + | 0.575595i | \(0.195229\pi\) | |||||||
\(548\) | −21.4264 | −0.915292 | ||||||||
\(549\) | −20.0400 | −0.855287 | ||||||||
\(550\) | −12.8672 | −0.548661 | ||||||||
\(551\) | 39.3316 | 1.67558 | ||||||||
\(552\) | 2.71458 | 0.115540 | ||||||||
\(553\) | −50.8340 | −2.16168 | ||||||||
\(554\) | −4.92043 | −0.209049 | ||||||||
\(555\) | −34.7009 | −1.47297 | ||||||||
\(556\) | 11.9196 | 0.505504 | ||||||||
\(557\) | 32.6703 | 1.38428 | 0.692142 | − | 0.721761i | \(-0.256667\pi\) | ||||
0.692142 | + | 0.721761i | \(0.256667\pi\) | |||||||
\(558\) | −18.4993 | −0.783140 | ||||||||
\(559\) | −3.30267 | −0.139688 | ||||||||
\(560\) | −15.6397 | −0.660898 | ||||||||
\(561\) | −3.29025 | −0.138915 | ||||||||
\(562\) | 31.2854 | 1.31970 | ||||||||
\(563\) | −33.7102 | −1.42071 | −0.710357 | − | 0.703842i | \(-0.751466\pi\) | ||||
−0.710357 | + | 0.703842i | \(0.751466\pi\) | |||||||
\(564\) | 3.47800 | 0.146450 | ||||||||
\(565\) | −2.30762 | −0.0970822 | ||||||||
\(566\) | −22.4086 | −0.941904 | ||||||||
\(567\) | −11.4382 | −0.480357 | ||||||||
\(568\) | 4.06852 | 0.170711 | ||||||||
\(569\) | −26.7251 | −1.12037 | −0.560187 | − | 0.828366i | \(-0.689271\pi\) | ||||
−0.560187 | + | 0.828366i | \(0.689271\pi\) | |||||||
\(570\) | 23.0019 | 0.963443 | ||||||||
\(571\) | 45.0811 | 1.88659 | 0.943293 | − | 0.331962i | \(-0.107711\pi\) | ||||
0.943293 | + | 0.331962i | \(0.107711\pi\) | |||||||
\(572\) | 2.61015 | 0.109136 | ||||||||
\(573\) | −10.1899 | −0.425691 | ||||||||
\(574\) | −20.5010 | −0.855696 | ||||||||
\(575\) | 41.3661 | 1.72508 | ||||||||
\(576\) | −2.28700 | −0.0952919 | ||||||||
\(577\) | 1.46900 | 0.0611554 | 0.0305777 | − | 0.999532i | \(-0.490265\pi\) | ||||
0.0305777 | + | 0.999532i | \(0.490265\pi\) | |||||||
\(578\) | −1.81649 | −0.0755561 | ||||||||
\(579\) | −5.93175 | −0.246515 | ||||||||
\(580\) | 25.7976 | 1.07119 | ||||||||
\(581\) | −32.8793 | −1.36406 | ||||||||
\(582\) | 3.37108 | 0.139736 | ||||||||
\(583\) | 10.5440 | 0.436686 | ||||||||
\(584\) | −8.29482 | −0.343242 | ||||||||
\(585\) | 25.2326 | 1.04324 | ||||||||
\(586\) | −20.5399 | −0.848494 | ||||||||
\(587\) | −1.12752 | −0.0465377 | −0.0232688 | − | 0.999729i | \(-0.507407\pi\) | ||||
−0.0232688 | + | 0.999729i | \(0.507407\pi\) | |||||||
\(588\) | 5.64886 | 0.232955 | ||||||||
\(589\) | 52.1292 | 2.14795 | ||||||||
\(590\) | −3.77187 | −0.155285 | ||||||||
\(591\) | −0.844390 | −0.0347336 | ||||||||
\(592\) | −9.72230 | −0.399584 | ||||||||
\(593\) | 37.5248 | 1.54096 | 0.770479 | − | 0.637465i | \(-0.220017\pi\) | ||||
0.770479 | + | 0.637465i | \(0.220017\pi\) | |||||||
\(594\) | 4.46430 | 0.183172 | ||||||||
\(595\) | −60.9417 | −2.49837 | ||||||||
\(596\) | 10.4390 | 0.427600 | ||||||||
\(597\) | −2.61120 | −0.106869 | ||||||||
\(598\) | −8.39121 | −0.343142 | ||||||||
\(599\) | 24.8692 | 1.01613 | 0.508065 | − | 0.861319i | \(-0.330361\pi\) | ||||
0.508065 | + | 0.861319i | \(0.330361\pi\) | |||||||
\(600\) | 10.8650 | 0.443561 | ||||||||
\(601\) | −17.5955 | −0.717734 | −0.358867 | − | 0.933389i | \(-0.616837\pi\) | ||||
−0.358867 | + | 0.933389i | \(0.616837\pi\) | |||||||
\(602\) | −4.68165 | −0.190810 | ||||||||
\(603\) | −10.4811 | −0.426824 | ||||||||
\(604\) | −11.5544 | −0.470142 | ||||||||
\(605\) | 4.22697 | 0.171851 | ||||||||
\(606\) | 5.85474 | 0.237832 | ||||||||
\(607\) | −39.8949 | −1.61929 | −0.809643 | − | 0.586923i | \(-0.800339\pi\) | ||||
−0.809643 | + | 0.586923i | \(0.800339\pi\) | |||||||
\(608\) | 6.44454 | 0.261360 | ||||||||
\(609\) | −19.0675 | −0.772652 | ||||||||
\(610\) | 37.0391 | 1.49967 | ||||||||
\(611\) | −10.7511 | −0.434942 | ||||||||
\(612\) | −8.91155 | −0.360228 | ||||||||
\(613\) | −44.3957 | −1.79313 | −0.896563 | − | 0.442916i | \(-0.853944\pi\) | ||||
−0.896563 | + | 0.442916i | \(0.853944\pi\) | |||||||
\(614\) | −24.0190 | −0.969328 | ||||||||
\(615\) | 19.7764 | 0.797462 | ||||||||
\(616\) | 3.69998 | 0.149077 | ||||||||
\(617\) | −20.3606 | −0.819689 | −0.409844 | − | 0.912155i | \(-0.634417\pi\) | ||||
−0.409844 | + | 0.912155i | \(0.634417\pi\) | |||||||
\(618\) | −11.5816 | −0.465879 | ||||||||
\(619\) | −2.32871 | −0.0935987 | −0.0467994 | − | 0.998904i | \(-0.514902\pi\) | ||||
−0.0467994 | + | 0.998904i | \(0.514902\pi\) | |||||||
\(620\) | 34.1915 | 1.37316 | ||||||||
\(621\) | −14.3520 | −0.575925 | ||||||||
\(622\) | 14.8044 | 0.593602 | ||||||||
\(623\) | 60.1920 | 2.41154 | ||||||||
\(624\) | −2.20399 | −0.0882301 | ||||||||
\(625\) | 76.2297 | 3.04919 | ||||||||
\(626\) | −29.6240 | −1.18401 | ||||||||
\(627\) | −5.44170 | −0.217321 | ||||||||
\(628\) | −22.4382 | −0.895381 | ||||||||
\(629\) | −37.8839 | −1.51053 | ||||||||
\(630\) | 35.7681 | 1.42503 | ||||||||
\(631\) | −6.46527 | −0.257378 | −0.128689 | − | 0.991685i | \(-0.541077\pi\) | ||||
−0.128689 | + | 0.991685i | \(0.541077\pi\) | |||||||
\(632\) | 13.7390 | 0.546508 | ||||||||
\(633\) | −1.00344 | −0.0398830 | ||||||||
\(634\) | 6.88637 | 0.273493 | ||||||||
\(635\) | 32.6797 | 1.29685 | ||||||||
\(636\) | −8.90321 | −0.353035 | ||||||||
\(637\) | −17.4616 | −0.691853 | ||||||||
\(638\) | −6.10309 | −0.241624 | ||||||||
\(639\) | −9.30471 | −0.368089 | ||||||||
\(640\) | 4.22697 | 0.167086 | ||||||||
\(641\) | 25.9044 | 1.02316 | 0.511581 | − | 0.859235i | \(-0.329060\pi\) | ||||
0.511581 | + | 0.859235i | \(0.329060\pi\) | |||||||
\(642\) | 2.38270 | 0.0940378 | ||||||||
\(643\) | 37.4755 | 1.47789 | 0.738946 | − | 0.673765i | \(-0.235324\pi\) | ||||
0.738946 | + | 0.673765i | \(0.235324\pi\) | |||||||
\(644\) | −11.8948 | −0.468722 | ||||||||
\(645\) | 4.51618 | 0.177824 | ||||||||
\(646\) | 25.1118 | 0.988010 | ||||||||
\(647\) | 42.4037 | 1.66706 | 0.833531 | − | 0.552472i | \(-0.186315\pi\) | ||||
0.833531 | + | 0.552472i | \(0.186315\pi\) | |||||||
\(648\) | 3.09141 | 0.121442 | ||||||||
\(649\) | 0.892335 | 0.0350272 | ||||||||
\(650\) | −33.5855 | −1.31733 | ||||||||
\(651\) | −25.2716 | −0.990471 | ||||||||
\(652\) | −24.3335 | −0.952973 | ||||||||
\(653\) | 27.7564 | 1.08619 | 0.543096 | − | 0.839671i | \(-0.317252\pi\) | ||||
0.543096 | + | 0.839671i | \(0.317252\pi\) | |||||||
\(654\) | −8.60012 | −0.336291 | ||||||||
\(655\) | 25.1175 | 0.981423 | ||||||||
\(656\) | 5.54084 | 0.216334 | ||||||||
\(657\) | 18.9703 | 0.740102 | ||||||||
\(658\) | −15.2400 | −0.594118 | ||||||||
\(659\) | −5.38453 | −0.209752 | −0.104876 | − | 0.994485i | \(-0.533445\pi\) | ||||
−0.104876 | + | 0.994485i | \(0.533445\pi\) | |||||||
\(660\) | −3.56921 | −0.138931 | ||||||||
\(661\) | −20.2828 | −0.788909 | −0.394454 | − | 0.918916i | \(-0.629066\pi\) | ||||
−0.394454 | + | 0.918916i | \(0.629066\pi\) | |||||||
\(662\) | −4.84184 | −0.188183 | ||||||||
\(663\) | −8.58806 | −0.333533 | ||||||||
\(664\) | 8.88633 | 0.344856 | ||||||||
\(665\) | −100.791 | −3.90849 | ||||||||
\(666\) | 22.2349 | 0.861586 | ||||||||
\(667\) | 19.6204 | 0.759706 | ||||||||
\(668\) | −7.53899 | −0.291692 | ||||||||
\(669\) | 18.0933 | 0.699527 | ||||||||
\(670\) | 19.3718 | 0.748397 | ||||||||
\(671\) | −8.76256 | −0.338275 | ||||||||
\(672\) | −3.12423 | −0.120520 | ||||||||
\(673\) | 26.7211 | 1.03002 | 0.515011 | − | 0.857184i | \(-0.327788\pi\) | ||||
0.515011 | + | 0.857184i | \(0.327788\pi\) | |||||||
\(674\) | −27.4794 | −1.05847 | ||||||||
\(675\) | −57.4432 | −2.21099 | ||||||||
\(676\) | −6.18711 | −0.237966 | ||||||||
\(677\) | 44.5073 | 1.71056 | 0.855278 | − | 0.518170i | \(-0.173386\pi\) | ||||
0.855278 | + | 0.518170i | \(0.173386\pi\) | |||||||
\(678\) | −0.460976 | −0.0177037 | ||||||||
\(679\) | −14.7715 | −0.566879 | ||||||||
\(680\) | 16.4708 | 0.631627 | ||||||||
\(681\) | −0.284607 | −0.0109062 | ||||||||
\(682\) | −8.08890 | −0.309740 | ||||||||
\(683\) | 37.6162 | 1.43934 | 0.719672 | − | 0.694314i | \(-0.244292\pi\) | ||||
0.719672 | + | 0.694314i | \(0.244292\pi\) | |||||||
\(684\) | −14.7387 | −0.563548 | ||||||||
\(685\) | −90.5688 | −3.46046 | ||||||||
\(686\) | 1.14747 | 0.0438106 | ||||||||
\(687\) | 16.0972 | 0.614145 | ||||||||
\(688\) | 1.26532 | 0.0482397 | ||||||||
\(689\) | 27.5213 | 1.04848 | ||||||||
\(690\) | 11.4744 | 0.436824 | ||||||||
\(691\) | −17.4575 | −0.664113 | −0.332057 | − | 0.943259i | \(-0.607743\pi\) | ||||
−0.332057 | + | 0.943259i | \(0.607743\pi\) | |||||||
\(692\) | 5.63897 | 0.214361 | ||||||||
\(693\) | −8.46188 | −0.321440 | ||||||||
\(694\) | 7.78099 | 0.295362 | ||||||||
\(695\) | 50.3838 | 1.91117 | ||||||||
\(696\) | 5.15339 | 0.195339 | ||||||||
\(697\) | 21.5905 | 0.817797 | ||||||||
\(698\) | 20.7381 | 0.784948 | ||||||||
\(699\) | 5.54359 | 0.209678 | ||||||||
\(700\) | −47.6086 | −1.79943 | ||||||||
\(701\) | 5.49542 | 0.207559 | 0.103780 | − | 0.994600i | \(-0.466906\pi\) | ||||
0.103780 | + | 0.994600i | \(0.466906\pi\) | |||||||
\(702\) | 11.6525 | 0.439795 | ||||||||
\(703\) | −62.6557 | −2.36310 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 14.7014 | 0.553686 | ||||||||
\(706\) | −2.88777 | −0.108683 | ||||||||
\(707\) | −25.6545 | −0.964838 | ||||||||
\(708\) | −0.753479 | −0.0283175 | ||||||||
\(709\) | −24.6020 | −0.923947 | −0.461974 | − | 0.886894i | \(-0.652859\pi\) | ||||
−0.461974 | + | 0.886894i | \(0.652859\pi\) | |||||||
\(710\) | 17.1975 | 0.645410 | ||||||||
\(711\) | −31.4211 | −1.17838 | ||||||||
\(712\) | −16.2682 | −0.609676 | ||||||||
\(713\) | 26.0045 | 0.973876 | ||||||||
\(714\) | −12.1739 | −0.455596 | ||||||||
\(715\) | 11.0330 | 0.412612 | ||||||||
\(716\) | 9.90420 | 0.370137 | ||||||||
\(717\) | 0.691199 | 0.0258133 | ||||||||
\(718\) | 15.2377 | 0.568664 | ||||||||
\(719\) | −38.5150 | −1.43637 | −0.718184 | − | 0.695853i | \(-0.755026\pi\) | ||||
−0.718184 | + | 0.695853i | \(0.755026\pi\) | |||||||
\(720\) | −9.66709 | −0.360271 | ||||||||
\(721\) | 50.7485 | 1.88997 | ||||||||
\(722\) | 22.5320 | 0.838556 | ||||||||
\(723\) | 6.75488 | 0.251217 | ||||||||
\(724\) | −19.7201 | −0.732892 | ||||||||
\(725\) | 78.5299 | 2.91653 | ||||||||
\(726\) | 0.844390 | 0.0313383 | ||||||||
\(727\) | −14.0857 | −0.522411 | −0.261205 | − | 0.965283i | \(-0.584120\pi\) | ||||
−0.261205 | + | 0.965283i | \(0.584120\pi\) | |||||||
\(728\) | 9.65751 | 0.357931 | ||||||||
\(729\) | 4.23876 | 0.156991 | ||||||||
\(730\) | −35.0619 | −1.29770 | ||||||||
\(731\) | 4.93043 | 0.182359 | ||||||||
\(732\) | 7.39902 | 0.273476 | ||||||||
\(733\) | −13.4321 | −0.496126 | −0.248063 | − | 0.968744i | \(-0.579794\pi\) | ||||
−0.248063 | + | 0.968744i | \(0.579794\pi\) | |||||||
\(734\) | 16.7576 | 0.618533 | ||||||||
\(735\) | 23.8776 | 0.880737 | ||||||||
\(736\) | 3.21484 | 0.118500 | ||||||||
\(737\) | −4.58290 | −0.168813 | ||||||||
\(738\) | −12.6719 | −0.466460 | ||||||||
\(739\) | −32.1784 | −1.18370 | −0.591850 | − | 0.806048i | \(-0.701602\pi\) | ||||
−0.591850 | + | 0.806048i | \(0.701602\pi\) | |||||||
\(740\) | −41.0958 | −1.51071 | ||||||||
\(741\) | −14.2037 | −0.521785 | ||||||||
\(742\) | 39.0124 | 1.43219 | ||||||||
\(743\) | 7.65039 | 0.280666 | 0.140333 | − | 0.990104i | \(-0.455183\pi\) | ||||
0.140333 | + | 0.990104i | \(0.455183\pi\) | |||||||
\(744\) | 6.83019 | 0.250407 | ||||||||
\(745\) | 44.1254 | 1.61663 | ||||||||
\(746\) | −35.4758 | −1.29886 | ||||||||
\(747\) | −20.3231 | −0.743583 | ||||||||
\(748\) | −3.89660 | −0.142474 | ||||||||
\(749\) | −10.4406 | −0.381492 | ||||||||
\(750\) | 28.0798 | 1.02533 | ||||||||
\(751\) | −35.3070 | −1.28837 | −0.644186 | − | 0.764869i | \(-0.722804\pi\) | ||||
−0.644186 | + | 0.764869i | \(0.722804\pi\) | |||||||
\(752\) | 4.11895 | 0.150202 | ||||||||
\(753\) | −9.51215 | −0.346642 | ||||||||
\(754\) | −15.9300 | −0.580136 | ||||||||
\(755\) | −48.8400 | −1.77747 | ||||||||
\(756\) | 16.5178 | 0.600747 | ||||||||
\(757\) | 29.0049 | 1.05420 | 0.527100 | − | 0.849803i | \(-0.323279\pi\) | ||||
0.527100 | + | 0.849803i | \(0.323279\pi\) | |||||||
\(758\) | 2.08275 | 0.0756489 | ||||||||
\(759\) | −2.71458 | −0.0985329 | ||||||||
\(760\) | 27.2408 | 0.988129 | ||||||||
\(761\) | 14.1566 | 0.513176 | 0.256588 | − | 0.966521i | \(-0.417402\pi\) | ||||
0.256588 | + | 0.966521i | \(0.417402\pi\) | |||||||
\(762\) | 6.52818 | 0.236491 | ||||||||
\(763\) | 37.6843 | 1.36426 | ||||||||
\(764\) | −12.0678 | −0.436598 | ||||||||
\(765\) | −37.6688 | −1.36192 | ||||||||
\(766\) | −3.98661 | −0.144042 | ||||||||
\(767\) | 2.32913 | 0.0841000 | ||||||||
\(768\) | 0.844390 | 0.0304693 | ||||||||
\(769\) | 19.1400 | 0.690207 | 0.345103 | − | 0.938565i | \(-0.387844\pi\) | ||||
0.345103 | + | 0.938565i | \(0.387844\pi\) | |||||||
\(770\) | 15.6397 | 0.563616 | ||||||||
\(771\) | −4.32117 | −0.155623 | ||||||||
\(772\) | −7.02489 | −0.252831 | ||||||||
\(773\) | −26.7827 | −0.963307 | −0.481654 | − | 0.876362i | \(-0.659964\pi\) | ||||
−0.481654 | + | 0.876362i | \(0.659964\pi\) | |||||||
\(774\) | −2.89378 | −0.104015 | ||||||||
\(775\) | 104.082 | 3.73873 | ||||||||
\(776\) | 3.99233 | 0.143316 | ||||||||
\(777\) | 30.3747 | 1.08969 | ||||||||
\(778\) | 30.6751 | 1.09975 | ||||||||
\(779\) | 35.7082 | 1.27938 | ||||||||
\(780\) | −9.31618 | −0.333573 | ||||||||
\(781\) | −4.06852 | −0.145583 | ||||||||
\(782\) | 12.5269 | 0.447962 | ||||||||
\(783\) | −27.2460 | −0.973693 | ||||||||
\(784\) | 6.68987 | 0.238924 | ||||||||
\(785\) | −94.8454 | −3.38518 | ||||||||
\(786\) | 5.01755 | 0.178970 | ||||||||
\(787\) | 14.7535 | 0.525906 | 0.262953 | − | 0.964809i | \(-0.415304\pi\) | ||||
0.262953 | + | 0.964809i | \(0.415304\pi\) | |||||||
\(788\) | −1.00000 | −0.0356235 | ||||||||
\(789\) | 1.68153 | 0.0598639 | ||||||||
\(790\) | 58.0742 | 2.06619 | ||||||||
\(791\) | 2.01992 | 0.0718202 | ||||||||
\(792\) | 2.28700 | 0.0812652 | ||||||||
\(793\) | −22.8716 | −0.812195 | ||||||||
\(794\) | 28.2667 | 1.00315 | ||||||||
\(795\) | −37.6336 | −1.33473 | ||||||||
\(796\) | −3.09241 | −0.109608 | ||||||||
\(797\) | −33.8080 | −1.19754 | −0.598771 | − | 0.800920i | \(-0.704344\pi\) | ||||
−0.598771 | + | 0.800920i | \(0.704344\pi\) | |||||||
\(798\) | −20.1342 | −0.712743 | ||||||||
\(799\) | 16.0499 | 0.567804 | ||||||||
\(800\) | 12.8672 | 0.454926 | ||||||||
\(801\) | 37.2054 | 1.31459 | ||||||||
\(802\) | −7.18828 | −0.253827 | ||||||||
\(803\) | 8.29482 | 0.292718 | ||||||||
\(804\) | 3.86976 | 0.136476 | ||||||||
\(805\) | −50.2791 | −1.77210 | ||||||||
\(806\) | −21.1132 | −0.743682 | ||||||||
\(807\) | 3.23581 | 0.113906 | ||||||||
\(808\) | 6.93369 | 0.243926 | ||||||||
\(809\) | 15.5360 | 0.546218 | 0.273109 | − | 0.961983i | \(-0.411948\pi\) | ||||
0.273109 | + | 0.961983i | \(0.411948\pi\) | |||||||
\(810\) | 13.0673 | 0.459137 | ||||||||
\(811\) | 5.00745 | 0.175835 | 0.0879177 | − | 0.996128i | \(-0.471979\pi\) | ||||
0.0879177 | + | 0.996128i | \(0.471979\pi\) | |||||||
\(812\) | −22.5813 | −0.792449 | ||||||||
\(813\) | −10.5392 | −0.369626 | ||||||||
\(814\) | 9.72230 | 0.340766 | ||||||||
\(815\) | −102.857 | −3.60292 | ||||||||
\(816\) | 3.29025 | 0.115182 | ||||||||
\(817\) | 8.15438 | 0.285286 | ||||||||
\(818\) | −27.2450 | −0.952599 | ||||||||
\(819\) | −22.0868 | −0.771775 | ||||||||
\(820\) | 23.4210 | 0.817895 | ||||||||
\(821\) | −7.50470 | −0.261916 | −0.130958 | − | 0.991388i | \(-0.541805\pi\) | ||||
−0.130958 | + | 0.991388i | \(0.541805\pi\) | |||||||
\(822\) | −18.0923 | −0.631040 | ||||||||
\(823\) | 20.6529 | 0.719913 | 0.359957 | − | 0.932969i | \(-0.382791\pi\) | ||||
0.359957 | + | 0.932969i | \(0.382791\pi\) | |||||||
\(824\) | −13.7159 | −0.477816 | ||||||||
\(825\) | −10.8650 | −0.378270 | ||||||||
\(826\) | 3.30162 | 0.114878 | ||||||||
\(827\) | 34.3811 | 1.19555 | 0.597775 | − | 0.801664i | \(-0.296052\pi\) | ||||
0.597775 | + | 0.801664i | \(0.296052\pi\) | |||||||
\(828\) | −7.35235 | −0.255512 | ||||||||
\(829\) | −48.8203 | −1.69560 | −0.847800 | − | 0.530316i | \(-0.822073\pi\) | ||||
−0.847800 | + | 0.530316i | \(0.822073\pi\) | |||||||
\(830\) | 37.5622 | 1.30380 | ||||||||
\(831\) | −4.15476 | −0.144127 | ||||||||
\(832\) | −2.61015 | −0.0904907 | ||||||||
\(833\) | 26.0678 | 0.903195 | ||||||||
\(834\) | 10.0648 | 0.348516 | ||||||||
\(835\) | −31.8671 | −1.10281 | ||||||||
\(836\) | −6.44454 | −0.222889 | ||||||||
\(837\) | −36.1112 | −1.24819 | ||||||||
\(838\) | −14.4906 | −0.500571 | ||||||||
\(839\) | −31.4609 | −1.08615 | −0.543076 | − | 0.839684i | \(-0.682740\pi\) | ||||
−0.543076 | + | 0.839684i | \(0.682740\pi\) | |||||||
\(840\) | −13.2060 | −0.455651 | ||||||||
\(841\) | 8.24771 | 0.284404 | ||||||||
\(842\) | −34.0129 | −1.17216 | ||||||||
\(843\) | 26.4171 | 0.909854 | ||||||||
\(844\) | −1.18835 | −0.0409049 | ||||||||
\(845\) | −26.1527 | −0.899680 | ||||||||
\(846\) | −9.42005 | −0.323868 | ||||||||
\(847\) | −3.69998 | −0.127133 | ||||||||
\(848\) | −10.5440 | −0.362081 | ||||||||
\(849\) | −18.9216 | −0.649388 | ||||||||
\(850\) | 50.1385 | 1.71974 | ||||||||
\(851\) | −31.2556 | −1.07143 | ||||||||
\(852\) | 3.43541 | 0.117695 | ||||||||
\(853\) | −26.9406 | −0.922430 | −0.461215 | − | 0.887288i | \(-0.652586\pi\) | ||||
−0.461215 | + | 0.887288i | \(0.652586\pi\) | |||||||
\(854\) | −32.4213 | −1.10944 | ||||||||
\(855\) | −62.2999 | −2.13061 | ||||||||
\(856\) | 2.82180 | 0.0964473 | ||||||||
\(857\) | 14.8118 | 0.505963 | 0.252981 | − | 0.967471i | \(-0.418589\pi\) | ||||
0.252981 | + | 0.967471i | \(0.418589\pi\) | |||||||
\(858\) | 2.20399 | 0.0752429 | ||||||||
\(859\) | 27.8216 | 0.949259 | 0.474630 | − | 0.880186i | \(-0.342582\pi\) | ||||
0.474630 | + | 0.880186i | \(0.342582\pi\) | |||||||
\(860\) | 5.34845 | 0.182381 | ||||||||
\(861\) | −17.3109 | −0.589953 | ||||||||
\(862\) | −6.65099 | −0.226533 | ||||||||
\(863\) | −20.8280 | −0.708992 | −0.354496 | − | 0.935058i | \(-0.615348\pi\) | ||||
−0.354496 | + | 0.935058i | \(0.615348\pi\) | |||||||
\(864\) | −4.46430 | −0.151878 | ||||||||
\(865\) | 23.8357 | 0.810439 | ||||||||
\(866\) | −39.0712 | −1.32769 | ||||||||
\(867\) | −1.53383 | −0.0520915 | ||||||||
\(868\) | −29.9288 | −1.01585 | ||||||||
\(869\) | −13.7390 | −0.466063 | ||||||||
\(870\) | 21.7832 | 0.738520 | ||||||||
\(871\) | −11.9621 | −0.405319 | ||||||||
\(872\) | −10.1850 | −0.344908 | ||||||||
\(873\) | −9.13047 | −0.309020 | ||||||||
\(874\) | 20.7181 | 0.700801 | ||||||||
\(875\) | −123.041 | −4.15956 | ||||||||
\(876\) | −7.00407 | −0.236646 | ||||||||
\(877\) | −33.8906 | −1.14440 | −0.572202 | − | 0.820113i | \(-0.693911\pi\) | ||||
−0.572202 | + | 0.820113i | \(0.693911\pi\) | |||||||
\(878\) | −12.9506 | −0.437060 | ||||||||
\(879\) | −17.3437 | −0.584988 | ||||||||
\(880\) | −4.22697 | −0.142491 | ||||||||
\(881\) | 5.48780 | 0.184889 | 0.0924443 | − | 0.995718i | \(-0.470532\pi\) | ||||
0.0924443 | + | 0.995718i | \(0.470532\pi\) | |||||||
\(882\) | −15.2998 | −0.515170 | ||||||||
\(883\) | −39.5901 | −1.33231 | −0.666157 | − | 0.745812i | \(-0.732062\pi\) | ||||
−0.666157 | + | 0.745812i | \(0.732062\pi\) | |||||||
\(884\) | −10.1707 | −0.342078 | ||||||||
\(885\) | −3.18493 | −0.107060 | ||||||||
\(886\) | −13.3359 | −0.448028 | ||||||||
\(887\) | 32.9813 | 1.10740 | 0.553701 | − | 0.832715i | \(-0.313215\pi\) | ||||
0.553701 | + | 0.832715i | \(0.313215\pi\) | |||||||
\(888\) | −8.20941 | −0.275490 | ||||||||
\(889\) | −28.6054 | −0.959396 | ||||||||
\(890\) | −68.7651 | −2.30501 | ||||||||
\(891\) | −3.09141 | −0.103566 | ||||||||
\(892\) | 21.4276 | 0.717450 | ||||||||
\(893\) | 26.5447 | 0.888284 | ||||||||
\(894\) | 8.81462 | 0.294805 | ||||||||
\(895\) | 41.8647 | 1.39938 | ||||||||
\(896\) | −3.69998 | −0.123608 | ||||||||
\(897\) | −7.08546 | −0.236577 | ||||||||
\(898\) | 3.42835 | 0.114405 | ||||||||
\(899\) | 49.3673 | 1.64649 | ||||||||
\(900\) | −29.4274 | −0.980915 | ||||||||
\(901\) | −41.0856 | −1.36876 | ||||||||
\(902\) | −5.54084 | −0.184490 | ||||||||
\(903\) | −3.95314 | −0.131552 | ||||||||
\(904\) | −0.545928 | −0.0181573 | ||||||||
\(905\) | −83.3562 | −2.77086 | ||||||||
\(906\) | −9.75642 | −0.324135 | ||||||||
\(907\) | −3.67368 | −0.121982 | −0.0609912 | − | 0.998138i | \(-0.519426\pi\) | ||||
−0.0609912 | + | 0.998138i | \(0.519426\pi\) | |||||||
\(908\) | −0.337056 | −0.0111856 | ||||||||
\(909\) | −15.8574 | −0.525956 | ||||||||
\(910\) | 40.8220 | 1.35324 | ||||||||
\(911\) | −6.56180 | −0.217402 | −0.108701 | − | 0.994074i | \(-0.534669\pi\) | ||||
−0.108701 | + | 0.994074i | \(0.534669\pi\) | |||||||
\(912\) | 5.44170 | 0.180193 | ||||||||
\(913\) | −8.88633 | −0.294095 | ||||||||
\(914\) | −4.61725 | −0.152725 | ||||||||
\(915\) | 31.2754 | 1.03393 | ||||||||
\(916\) | 19.0636 | 0.629881 | ||||||||
\(917\) | −21.9861 | −0.726044 | ||||||||
\(918\) | −17.3956 | −0.574140 | ||||||||
\(919\) | −18.4078 | −0.607217 | −0.303608 | − | 0.952797i | \(-0.598191\pi\) | ||||
−0.303608 | + | 0.952797i | \(0.598191\pi\) | |||||||
\(920\) | 13.5890 | 0.448016 | ||||||||
\(921\) | −20.2814 | −0.668295 | ||||||||
\(922\) | −13.8104 | −0.454822 | ||||||||
\(923\) | −10.6194 | −0.349543 | ||||||||
\(924\) | 3.12423 | 0.102780 | ||||||||
\(925\) | −125.099 | −4.11323 | ||||||||
\(926\) | 29.0450 | 0.954479 | ||||||||
\(927\) | 31.3683 | 1.03027 | ||||||||
\(928\) | 6.10309 | 0.200344 | ||||||||
\(929\) | −27.4128 | −0.899385 | −0.449692 | − | 0.893183i | \(-0.648466\pi\) | ||||
−0.449692 | + | 0.893183i | \(0.648466\pi\) | |||||||
\(930\) | 28.8710 | 0.946716 | ||||||||
\(931\) | 43.1131 | 1.41298 | ||||||||
\(932\) | 6.56520 | 0.215050 | ||||||||
\(933\) | 12.5007 | 0.409254 | ||||||||
\(934\) | −1.59622 | −0.0522299 | ||||||||
\(935\) | −16.4708 | −0.538653 | ||||||||
\(936\) | 5.96943 | 0.195117 | ||||||||
\(937\) | 35.3582 | 1.15510 | 0.577551 | − | 0.816355i | \(-0.304009\pi\) | ||||
0.577551 | + | 0.816355i | \(0.304009\pi\) | |||||||
\(938\) | −16.9567 | −0.553655 | ||||||||
\(939\) | −25.0142 | −0.816309 | ||||||||
\(940\) | 17.4106 | 0.567873 | ||||||||
\(941\) | 15.7031 | 0.511907 | 0.255954 | − | 0.966689i | \(-0.417611\pi\) | ||||
0.255954 | + | 0.966689i | \(0.417611\pi\) | |||||||
\(942\) | −18.9466 | −0.617313 | ||||||||
\(943\) | 17.8129 | 0.580068 | ||||||||
\(944\) | −0.892335 | −0.0290430 | ||||||||
\(945\) | 69.8203 | 2.27125 | ||||||||
\(946\) | −1.26532 | −0.0411390 | ||||||||
\(947\) | −25.7117 | −0.835518 | −0.417759 | − | 0.908558i | \(-0.637184\pi\) | ||||
−0.417759 | + | 0.908558i | \(0.637184\pi\) | |||||||
\(948\) | 11.6011 | 0.376785 | ||||||||
\(949\) | 21.6507 | 0.702813 | ||||||||
\(950\) | 82.9234 | 2.69039 | ||||||||
\(951\) | 5.81478 | 0.188557 | ||||||||
\(952\) | −14.4174 | −0.467269 | ||||||||
\(953\) | −4.10747 | −0.133054 | −0.0665270 | − | 0.997785i | \(-0.521192\pi\) | ||||
−0.0665270 | + | 0.997785i | \(0.521192\pi\) | |||||||
\(954\) | 24.1141 | 0.780722 | ||||||||
\(955\) | −51.0102 | −1.65065 | ||||||||
\(956\) | 0.818578 | 0.0264747 | ||||||||
\(957\) | −5.15339 | −0.166585 | ||||||||
\(958\) | −24.1500 | −0.780251 | ||||||||
\(959\) | 79.2774 | 2.56000 | ||||||||
\(960\) | 3.56921 | 0.115196 | ||||||||
\(961\) | 34.4303 | 1.11065 | ||||||||
\(962\) | 25.3767 | 0.818177 | ||||||||
\(963\) | −6.45348 | −0.207960 | ||||||||
\(964\) | 7.99971 | 0.257653 | ||||||||
\(965\) | −29.6940 | −0.955883 | ||||||||
\(966\) | −10.0439 | −0.323157 | ||||||||
\(967\) | −2.07183 | −0.0666257 | −0.0333128 | − | 0.999445i | \(-0.510606\pi\) | ||||
−0.0333128 | + | 0.999445i | \(0.510606\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 21.2042 | 0.681176 | ||||||||
\(970\) | 16.8754 | 0.541837 | ||||||||
\(971\) | −16.2399 | −0.521162 | −0.260581 | − | 0.965452i | \(-0.583914\pi\) | ||||
−0.260581 | + | 0.965452i | \(0.583914\pi\) | |||||||
\(972\) | 16.0032 | 0.513304 | ||||||||
\(973\) | −44.1024 | −1.41386 | ||||||||
\(974\) | 40.0418 | 1.28302 | ||||||||
\(975\) | −28.3592 | −0.908222 | ||||||||
\(976\) | 8.76256 | 0.280483 | ||||||||
\(977\) | 55.5862 | 1.77836 | 0.889181 | − | 0.457556i | \(-0.151275\pi\) | ||||
0.889181 | + | 0.457556i | \(0.151275\pi\) | |||||||
\(978\) | −20.5470 | −0.657019 | ||||||||
\(979\) | 16.2682 | 0.519934 | ||||||||
\(980\) | 28.2779 | 0.903303 | ||||||||
\(981\) | 23.2931 | 0.743693 | ||||||||
\(982\) | −38.6205 | −1.23243 | ||||||||
\(983\) | −12.0362 | −0.383896 | −0.191948 | − | 0.981405i | \(-0.561480\pi\) | ||||
−0.191948 | + | 0.981405i | \(0.561480\pi\) | |||||||
\(984\) | 4.67863 | 0.149149 | ||||||||
\(985\) | −4.22697 | −0.134682 | ||||||||
\(986\) | 23.7813 | 0.757351 | ||||||||
\(987\) | −12.8685 | −0.409610 | ||||||||
\(988\) | −16.8212 | −0.535154 | ||||||||
\(989\) | 4.06779 | 0.129348 | ||||||||
\(990\) | 9.66709 | 0.307240 | ||||||||
\(991\) | 51.6586 | 1.64099 | 0.820495 | − | 0.571654i | \(-0.193698\pi\) | ||||
0.820495 | + | 0.571654i | \(0.193698\pi\) | |||||||
\(992\) | 8.08890 | 0.256823 | ||||||||
\(993\) | −4.08840 | −0.129742 | ||||||||
\(994\) | −15.0534 | −0.477466 | ||||||||
\(995\) | −13.0715 | −0.414395 | ||||||||
\(996\) | 7.50353 | 0.237758 | ||||||||
\(997\) | −28.4177 | −0.899998 | −0.449999 | − | 0.893029i | \(-0.648576\pi\) | ||||
−0.449999 | + | 0.893029i | \(0.648576\pi\) | |||||||
\(998\) | 35.1589 | 1.11294 | ||||||||
\(999\) | 43.4032 | 1.37322 |
(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 | 4334.2.a.f.1.14 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.f.1.14 | ✓ | 24 | 1.1 | even | 1 | trivial |