Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, 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("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.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: | \(48.2376278611\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71866 | −1.92238 | −0.961191 | − | 0.275884i | \(-0.911030\pi\) | ||||
−0.961191 | + | 0.275884i | \(0.911030\pi\) | |||||||
\(3\) | −0.898623 | −0.518820 | −0.259410 | − | 0.965767i | \(-0.583528\pi\) | ||||
−0.259410 | + | 0.965767i | \(0.583528\pi\) | |||||||
\(4\) | 5.39111 | 2.69555 | ||||||||
\(5\) | 3.58669 | 1.60402 | 0.802009 | − | 0.597312i | \(-0.203765\pi\) | ||||
0.802009 | + | 0.597312i | \(0.203765\pi\) | |||||||
\(6\) | 2.44305 | 0.997371 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −9.21926 | −3.25950 | ||||||||
\(9\) | −2.19248 | −0.730826 | ||||||||
\(10\) | −9.75100 | −3.08354 | ||||||||
\(11\) | −6.15231 | −1.85499 | −0.927496 | − | 0.373834i | \(-0.878043\pi\) | ||||
−0.927496 | + | 0.373834i | \(0.878043\pi\) | |||||||
\(12\) | −4.84457 | −1.39851 | ||||||||
\(13\) | 0.437075 | 0.121223 | 0.0606114 | − | 0.998161i | \(-0.480695\pi\) | ||||
0.0606114 | + | 0.998161i | \(0.480695\pi\) | |||||||
\(14\) | −2.71866 | −0.726592 | ||||||||
\(15\) | −3.22309 | −0.832197 | ||||||||
\(16\) | 14.2818 | 3.57045 | ||||||||
\(17\) | −4.15017 | −1.00656 | −0.503281 | − | 0.864123i | \(-0.667874\pi\) | ||||
−0.503281 | + | 0.864123i | \(0.667874\pi\) | |||||||
\(18\) | 5.96060 | 1.40493 | ||||||||
\(19\) | −2.98619 | −0.685078 | −0.342539 | − | 0.939504i | \(-0.611287\pi\) | ||||
−0.342539 | + | 0.939504i | \(0.611287\pi\) | |||||||
\(20\) | 19.3362 | 4.32372 | ||||||||
\(21\) | −0.898623 | −0.196096 | ||||||||
\(22\) | 16.7260 | 3.56600 | ||||||||
\(23\) | 3.64443 | 0.759916 | 0.379958 | − | 0.925004i | \(-0.375939\pi\) | ||||
0.379958 | + | 0.925004i | \(0.375939\pi\) | |||||||
\(24\) | 8.28464 | 1.69110 | ||||||||
\(25\) | 7.86437 | 1.57287 | ||||||||
\(26\) | −1.18826 | −0.233037 | ||||||||
\(27\) | 4.66608 | 0.897987 | ||||||||
\(28\) | 5.39111 | 1.01882 | ||||||||
\(29\) | −7.47833 | −1.38869 | −0.694345 | − | 0.719642i | \(-0.744306\pi\) | ||||
−0.694345 | + | 0.719642i | \(0.744306\pi\) | |||||||
\(30\) | 8.76247 | 1.59980 | ||||||||
\(31\) | −0.0845463 | −0.0151850 | −0.00759248 | − | 0.999971i | \(-0.502417\pi\) | ||||
−0.00759248 | + | 0.999971i | \(0.502417\pi\) | |||||||
\(32\) | −20.3889 | −3.60427 | ||||||||
\(33\) | 5.52861 | 0.962407 | ||||||||
\(34\) | 11.2829 | 1.93500 | ||||||||
\(35\) | 3.58669 | 0.606262 | ||||||||
\(36\) | −11.8199 | −1.96998 | ||||||||
\(37\) | 4.52200 | 0.743412 | 0.371706 | − | 0.928351i | \(-0.378773\pi\) | ||||
0.371706 | + | 0.928351i | \(0.378773\pi\) | |||||||
\(38\) | 8.11843 | 1.31698 | ||||||||
\(39\) | −0.392766 | −0.0628929 | ||||||||
\(40\) | −33.0667 | −5.22830 | ||||||||
\(41\) | 5.05744 | 0.789839 | 0.394920 | − | 0.918716i | \(-0.370772\pi\) | ||||
0.394920 | + | 0.918716i | \(0.370772\pi\) | |||||||
\(42\) | 2.44305 | 0.376971 | ||||||||
\(43\) | 11.2055 | 1.70882 | 0.854410 | − | 0.519600i | \(-0.173919\pi\) | ||||
0.854410 | + | 0.519600i | \(0.173919\pi\) | |||||||
\(44\) | −33.1678 | −5.00023 | ||||||||
\(45\) | −7.86374 | −1.17226 | ||||||||
\(46\) | −9.90795 | −1.46085 | ||||||||
\(47\) | −6.30676 | −0.919935 | −0.459967 | − | 0.887936i | \(-0.652139\pi\) | ||||
−0.459967 | + | 0.887936i | \(0.652139\pi\) | |||||||
\(48\) | −12.8340 | −1.85242 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −21.3805 | −3.02366 | ||||||||
\(51\) | 3.72943 | 0.522225 | ||||||||
\(52\) | 2.35632 | 0.326763 | ||||||||
\(53\) | −10.0023 | −1.37393 | −0.686964 | − | 0.726692i | \(-0.741057\pi\) | ||||
−0.686964 | + | 0.726692i | \(0.741057\pi\) | |||||||
\(54\) | −12.6855 | −1.72627 | ||||||||
\(55\) | −22.0665 | −2.97544 | ||||||||
\(56\) | −9.21926 | −1.23198 | ||||||||
\(57\) | 2.68346 | 0.355433 | ||||||||
\(58\) | 20.3310 | 2.66959 | ||||||||
\(59\) | 1.07947 | 0.140536 | 0.0702678 | − | 0.997528i | \(-0.477615\pi\) | ||||
0.0702678 | + | 0.997528i | \(0.477615\pi\) | |||||||
\(60\) | −17.3760 | −2.24323 | ||||||||
\(61\) | −5.39020 | −0.690145 | −0.345072 | − | 0.938576i | \(-0.612146\pi\) | ||||
−0.345072 | + | 0.938576i | \(0.612146\pi\) | |||||||
\(62\) | 0.229853 | 0.0291913 | ||||||||
\(63\) | −2.19248 | −0.276226 | ||||||||
\(64\) | 26.8667 | 3.35834 | ||||||||
\(65\) | 1.56766 | 0.194444 | ||||||||
\(66\) | −15.0304 | −1.85011 | ||||||||
\(67\) | 0.429232 | 0.0524391 | 0.0262195 | − | 0.999656i | \(-0.491653\pi\) | ||||
0.0262195 | + | 0.999656i | \(0.491653\pi\) | |||||||
\(68\) | −22.3740 | −2.71324 | ||||||||
\(69\) | −3.27497 | −0.394260 | ||||||||
\(70\) | −9.75100 | −1.16547 | ||||||||
\(71\) | 13.6946 | 1.62525 | 0.812627 | − | 0.582784i | \(-0.198037\pi\) | ||||
0.812627 | + | 0.582784i | \(0.198037\pi\) | |||||||
\(72\) | 20.2130 | 2.38213 | ||||||||
\(73\) | −13.2913 | −1.55563 | −0.777816 | − | 0.628492i | \(-0.783672\pi\) | ||||
−0.777816 | + | 0.628492i | \(0.783672\pi\) | |||||||
\(74\) | −12.2938 | −1.42912 | ||||||||
\(75\) | −7.06710 | −0.816039 | ||||||||
\(76\) | −16.0989 | −1.84667 | ||||||||
\(77\) | −6.15231 | −0.701121 | ||||||||
\(78\) | 1.06780 | 0.120904 | ||||||||
\(79\) | 4.10176 | 0.461484 | 0.230742 | − | 0.973015i | \(-0.425885\pi\) | ||||
0.230742 | + | 0.973015i | \(0.425885\pi\) | |||||||
\(80\) | 51.2245 | 5.72707 | ||||||||
\(81\) | 2.38438 | 0.264932 | ||||||||
\(82\) | −13.7494 | −1.51837 | ||||||||
\(83\) | −1.17732 | −0.129227 | −0.0646137 | − | 0.997910i | \(-0.520582\pi\) | ||||
−0.0646137 | + | 0.997910i | \(0.520582\pi\) | |||||||
\(84\) | −4.84457 | −0.528586 | ||||||||
\(85\) | −14.8854 | −1.61455 | ||||||||
\(86\) | −30.4639 | −3.28500 | ||||||||
\(87\) | 6.72020 | 0.720481 | ||||||||
\(88\) | 56.7198 | 6.04635 | ||||||||
\(89\) | −14.0167 | −1.48577 | −0.742885 | − | 0.669419i | \(-0.766543\pi\) | ||||
−0.742885 | + | 0.669419i | \(0.766543\pi\) | |||||||
\(90\) | 21.3788 | 2.25353 | ||||||||
\(91\) | 0.437075 | 0.0458179 | ||||||||
\(92\) | 19.6475 | 2.04839 | ||||||||
\(93\) | 0.0759753 | 0.00787827 | ||||||||
\(94\) | 17.1459 | 1.76847 | ||||||||
\(95\) | −10.7105 | −1.09888 | ||||||||
\(96\) | 18.3219 | 1.86997 | ||||||||
\(97\) | 2.83308 | 0.287655 | 0.143828 | − | 0.989603i | \(-0.454059\pi\) | ||||
0.143828 | + | 0.989603i | \(0.454059\pi\) | |||||||
\(98\) | −2.71866 | −0.274626 | ||||||||
\(99\) | 13.4888 | 1.35568 | ||||||||
\(100\) | 42.3976 | 4.23976 | ||||||||
\(101\) | 10.2894 | 1.02384 | 0.511918 | − | 0.859034i | \(-0.328935\pi\) | ||||
0.511918 | + | 0.859034i | \(0.328935\pi\) | |||||||
\(102\) | −10.1391 | −1.00392 | ||||||||
\(103\) | 6.29641 | 0.620404 | 0.310202 | − | 0.950671i | \(-0.399603\pi\) | ||||
0.310202 | + | 0.950671i | \(0.399603\pi\) | |||||||
\(104\) | −4.02951 | −0.395126 | ||||||||
\(105\) | −3.22309 | −0.314541 | ||||||||
\(106\) | 27.1930 | 2.64121 | ||||||||
\(107\) | −13.8880 | −1.34261 | −0.671303 | − | 0.741183i | \(-0.734265\pi\) | ||||
−0.671303 | + | 0.741183i | \(0.734265\pi\) | |||||||
\(108\) | 25.1553 | 2.42057 | ||||||||
\(109\) | 8.66578 | 0.830031 | 0.415015 | − | 0.909814i | \(-0.363776\pi\) | ||||
0.415015 | + | 0.909814i | \(0.363776\pi\) | |||||||
\(110\) | 59.9912 | 5.71993 | ||||||||
\(111\) | −4.06357 | −0.385697 | ||||||||
\(112\) | 14.2818 | 1.34950 | ||||||||
\(113\) | 12.1592 | 1.14384 | 0.571921 | − | 0.820308i | \(-0.306198\pi\) | ||||
0.571921 | + | 0.820308i | \(0.306198\pi\) | |||||||
\(114\) | −7.29540 | −0.683277 | ||||||||
\(115\) | 13.0714 | 1.21892 | ||||||||
\(116\) | −40.3164 | −3.74329 | ||||||||
\(117\) | −0.958277 | −0.0885928 | ||||||||
\(118\) | −2.93472 | −0.270163 | ||||||||
\(119\) | −4.15017 | −0.380445 | ||||||||
\(120\) | 29.7145 | 2.71255 | ||||||||
\(121\) | 26.8509 | 2.44099 | ||||||||
\(122\) | 14.6541 | 1.32672 | ||||||||
\(123\) | −4.54473 | −0.409784 | ||||||||
\(124\) | −0.455798 | −0.0409319 | ||||||||
\(125\) | 10.2736 | 0.918900 | ||||||||
\(126\) | 5.96060 | 0.531012 | ||||||||
\(127\) | −11.9245 | −1.05813 | −0.529064 | − | 0.848582i | \(-0.677457\pi\) | ||||
−0.529064 | + | 0.848582i | \(0.677457\pi\) | |||||||
\(128\) | −32.2637 | −2.85174 | ||||||||
\(129\) | −10.0695 | −0.886570 | ||||||||
\(130\) | −4.26192 | −0.373795 | ||||||||
\(131\) | 10.5085 | 0.918135 | 0.459068 | − | 0.888401i | \(-0.348184\pi\) | ||||
0.459068 | + | 0.888401i | \(0.348184\pi\) | |||||||
\(132\) | 29.8053 | 2.59422 | ||||||||
\(133\) | −2.98619 | −0.258935 | ||||||||
\(134\) | −1.16694 | −0.100808 | ||||||||
\(135\) | 16.7358 | 1.44039 | ||||||||
\(136\) | 38.2615 | 3.28089 | ||||||||
\(137\) | 4.88617 | 0.417454 | 0.208727 | − | 0.977974i | \(-0.433068\pi\) | ||||
0.208727 | + | 0.977974i | \(0.433068\pi\) | |||||||
\(138\) | 8.90352 | 0.757918 | ||||||||
\(139\) | −16.0765 | −1.36359 | −0.681795 | − | 0.731543i | \(-0.738801\pi\) | ||||
−0.681795 | + | 0.731543i | \(0.738801\pi\) | |||||||
\(140\) | 19.3362 | 1.63421 | ||||||||
\(141\) | 5.66740 | 0.477281 | ||||||||
\(142\) | −37.2310 | −3.12436 | ||||||||
\(143\) | −2.68902 | −0.224867 | ||||||||
\(144\) | −31.3125 | −2.60938 | ||||||||
\(145\) | −26.8225 | −2.22748 | ||||||||
\(146\) | 36.1346 | 2.99052 | ||||||||
\(147\) | −0.898623 | −0.0741172 | ||||||||
\(148\) | 24.3786 | 2.00391 | ||||||||
\(149\) | 16.2761 | 1.33339 | 0.666694 | − | 0.745332i | \(-0.267709\pi\) | ||||
0.666694 | + | 0.745332i | \(0.267709\pi\) | |||||||
\(150\) | 19.2130 | 1.56874 | ||||||||
\(151\) | −12.4912 | −1.01652 | −0.508259 | − | 0.861204i | \(-0.669711\pi\) | ||||
−0.508259 | + | 0.861204i | \(0.669711\pi\) | |||||||
\(152\) | 27.5304 | 2.23301 | ||||||||
\(153\) | 9.09914 | 0.735622 | ||||||||
\(154\) | 16.7260 | 1.34782 | ||||||||
\(155\) | −0.303242 | −0.0243570 | ||||||||
\(156\) | −2.11744 | −0.169531 | ||||||||
\(157\) | 19.2088 | 1.53303 | 0.766516 | − | 0.642225i | \(-0.221989\pi\) | ||||
0.766516 | + | 0.642225i | \(0.221989\pi\) | |||||||
\(158\) | −11.1513 | −0.887148 | ||||||||
\(159\) | 8.98834 | 0.712822 | ||||||||
\(160\) | −73.1286 | −5.78132 | ||||||||
\(161\) | 3.64443 | 0.287221 | ||||||||
\(162\) | −6.48233 | −0.509300 | ||||||||
\(163\) | −4.70230 | −0.368313 | −0.184156 | − | 0.982897i | \(-0.558955\pi\) | ||||
−0.184156 | + | 0.982897i | \(0.558955\pi\) | |||||||
\(164\) | 27.2652 | 2.12905 | ||||||||
\(165\) | 19.8294 | 1.54372 | ||||||||
\(166\) | 3.20073 | 0.248424 | ||||||||
\(167\) | 16.3733 | 1.26701 | 0.633503 | − | 0.773740i | \(-0.281616\pi\) | ||||
0.633503 | + | 0.773740i | \(0.281616\pi\) | |||||||
\(168\) | 8.28464 | 0.639174 | ||||||||
\(169\) | −12.8090 | −0.985305 | ||||||||
\(170\) | 40.4682 | 3.10377 | ||||||||
\(171\) | 6.54715 | 0.500673 | ||||||||
\(172\) | 60.4099 | 4.60621 | ||||||||
\(173\) | −0.149213 | −0.0113444 | −0.00567222 | − | 0.999984i | \(-0.501806\pi\) | ||||
−0.00567222 | + | 0.999984i | \(0.501806\pi\) | |||||||
\(174\) | −18.2699 | −1.38504 | ||||||||
\(175\) | 7.86437 | 0.594490 | ||||||||
\(176\) | −87.8662 | −6.62316 | ||||||||
\(177\) | −0.970041 | −0.0729127 | ||||||||
\(178\) | 38.1067 | 2.85622 | ||||||||
\(179\) | −8.21822 | −0.614258 | −0.307129 | − | 0.951668i | \(-0.599368\pi\) | ||||
−0.307129 | + | 0.951668i | \(0.599368\pi\) | |||||||
\(180\) | −42.3943 | −3.15988 | ||||||||
\(181\) | 21.2890 | 1.58240 | 0.791198 | − | 0.611561i | \(-0.209458\pi\) | ||||
0.791198 | + | 0.611561i | \(0.209458\pi\) | |||||||
\(182\) | −1.18826 | −0.0880796 | ||||||||
\(183\) | 4.84376 | 0.358061 | ||||||||
\(184\) | −33.5989 | −2.47695 | ||||||||
\(185\) | 16.2190 | 1.19245 | ||||||||
\(186\) | −0.206551 | −0.0151450 | ||||||||
\(187\) | 25.5331 | 1.86717 | ||||||||
\(188\) | −34.0004 | −2.47973 | ||||||||
\(189\) | 4.66608 | 0.339407 | ||||||||
\(190\) | 29.1183 | 2.11246 | ||||||||
\(191\) | 19.2441 | 1.39245 | 0.696226 | − | 0.717823i | \(-0.254861\pi\) | ||||
0.696226 | + | 0.717823i | \(0.254861\pi\) | |||||||
\(192\) | −24.1430 | −1.74237 | ||||||||
\(193\) | 1.70644 | 0.122832 | 0.0614160 | − | 0.998112i | \(-0.480438\pi\) | ||||
0.0614160 | + | 0.998112i | \(0.480438\pi\) | |||||||
\(194\) | −7.70217 | −0.552984 | ||||||||
\(195\) | −1.40873 | −0.100881 | ||||||||
\(196\) | 5.39111 | 0.385079 | ||||||||
\(197\) | −11.3972 | −0.812016 | −0.406008 | − | 0.913869i | \(-0.633080\pi\) | ||||
−0.406008 | + | 0.913869i | \(0.633080\pi\) | |||||||
\(198\) | −36.6714 | −2.60613 | ||||||||
\(199\) | 18.3993 | 1.30429 | 0.652144 | − | 0.758095i | \(-0.273870\pi\) | ||||
0.652144 | + | 0.758095i | \(0.273870\pi\) | |||||||
\(200\) | −72.5037 | −5.12678 | ||||||||
\(201\) | −0.385718 | −0.0272064 | ||||||||
\(202\) | −27.9734 | −1.96820 | ||||||||
\(203\) | −7.47833 | −0.524876 | ||||||||
\(204\) | 20.1058 | 1.40769 | ||||||||
\(205\) | 18.1395 | 1.26692 | ||||||||
\(206\) | −17.1178 | −1.19265 | ||||||||
\(207\) | −7.99032 | −0.555366 | ||||||||
\(208\) | 6.24223 | 0.432821 | ||||||||
\(209\) | 18.3720 | 1.27081 | ||||||||
\(210\) | 8.76247 | 0.604668 | ||||||||
\(211\) | 5.86906 | 0.404043 | 0.202021 | − | 0.979381i | \(-0.435249\pi\) | ||||
0.202021 | + | 0.979381i | \(0.435249\pi\) | |||||||
\(212\) | −53.9237 | −3.70350 | ||||||||
\(213\) | −12.3063 | −0.843214 | ||||||||
\(214\) | 37.7568 | 2.58100 | ||||||||
\(215\) | 40.1906 | 2.74098 | ||||||||
\(216\) | −43.0178 | −2.92699 | ||||||||
\(217\) | −0.0845463 | −0.00573938 | ||||||||
\(218\) | −23.5593 | −1.59564 | ||||||||
\(219\) | 11.9439 | 0.807093 | ||||||||
\(220\) | −118.963 | −8.02046 | ||||||||
\(221\) | −1.81393 | −0.122018 | ||||||||
\(222\) | 11.0475 | 0.741457 | ||||||||
\(223\) | −0.238872 | −0.0159960 | −0.00799802 | − | 0.999968i | \(-0.502546\pi\) | ||||
−0.00799802 | + | 0.999968i | \(0.502546\pi\) | |||||||
\(224\) | −20.3889 | −1.36229 | ||||||||
\(225\) | −17.2424 | −1.14950 | ||||||||
\(226\) | −33.0568 | −2.19890 | ||||||||
\(227\) | −23.3285 | −1.54837 | −0.774183 | − | 0.632962i | \(-0.781839\pi\) | ||||
−0.774183 | + | 0.632962i | \(0.781839\pi\) | |||||||
\(228\) | 14.4668 | 0.958087 | ||||||||
\(229\) | −22.6685 | −1.49798 | −0.748989 | − | 0.662582i | \(-0.769461\pi\) | ||||
−0.748989 | + | 0.662582i | \(0.769461\pi\) | |||||||
\(230\) | −35.5368 | −2.34323 | ||||||||
\(231\) | 5.52861 | 0.363756 | ||||||||
\(232\) | 68.9446 | 4.52644 | ||||||||
\(233\) | −11.7360 | −0.768849 | −0.384424 | − | 0.923156i | \(-0.625600\pi\) | ||||
−0.384424 | + | 0.923156i | \(0.625600\pi\) | |||||||
\(234\) | 2.60523 | 0.170309 | ||||||||
\(235\) | −22.6204 | −1.47559 | ||||||||
\(236\) | 5.81956 | 0.378821 | ||||||||
\(237\) | −3.68593 | −0.239427 | ||||||||
\(238\) | 11.2829 | 0.731361 | ||||||||
\(239\) | 25.4338 | 1.64518 | 0.822588 | − | 0.568638i | \(-0.192530\pi\) | ||||
0.822588 | + | 0.568638i | \(0.192530\pi\) | |||||||
\(240\) | −46.0315 | −2.97132 | ||||||||
\(241\) | −4.81627 | −0.310244 | −0.155122 | − | 0.987895i | \(-0.549577\pi\) | ||||
−0.155122 | + | 0.987895i | \(0.549577\pi\) | |||||||
\(242\) | −72.9985 | −4.69252 | ||||||||
\(243\) | −16.1409 | −1.03544 | ||||||||
\(244\) | −29.0592 | −1.86032 | ||||||||
\(245\) | 3.58669 | 0.229145 | ||||||||
\(246\) | 12.3556 | 0.787762 | ||||||||
\(247\) | −1.30519 | −0.0830472 | ||||||||
\(248\) | 0.779455 | 0.0494954 | ||||||||
\(249\) | 1.05796 | 0.0670458 | ||||||||
\(250\) | −27.9305 | −1.76648 | ||||||||
\(251\) | 18.2117 | 1.14951 | 0.574757 | − | 0.818324i | \(-0.305097\pi\) | ||||
0.574757 | + | 0.818324i | \(0.305097\pi\) | |||||||
\(252\) | −11.8199 | −0.744582 | ||||||||
\(253\) | −22.4217 | −1.40964 | ||||||||
\(254\) | 32.4186 | 2.03412 | ||||||||
\(255\) | 13.3763 | 0.837659 | ||||||||
\(256\) | 33.9806 | 2.12379 | ||||||||
\(257\) | −1.85367 | −0.115629 | −0.0578144 | − | 0.998327i | \(-0.518413\pi\) | ||||
−0.0578144 | + | 0.998327i | \(0.518413\pi\) | |||||||
\(258\) | 27.3755 | 1.70433 | ||||||||
\(259\) | 4.52200 | 0.280983 | ||||||||
\(260\) | 8.45139 | 0.524133 | ||||||||
\(261\) | 16.3961 | 1.01489 | ||||||||
\(262\) | −28.5691 | −1.76501 | ||||||||
\(263\) | −15.3998 | −0.949591 | −0.474795 | − | 0.880096i | \(-0.657478\pi\) | ||||
−0.474795 | + | 0.880096i | \(0.657478\pi\) | |||||||
\(264\) | −50.9697 | −3.13697 | ||||||||
\(265\) | −35.8753 | −2.20381 | ||||||||
\(266\) | 8.11843 | 0.497773 | ||||||||
\(267\) | 12.5958 | 0.770848 | ||||||||
\(268\) | 2.31404 | 0.141352 | ||||||||
\(269\) | −18.4640 | −1.12577 | −0.562884 | − | 0.826536i | \(-0.690308\pi\) | ||||
−0.562884 | + | 0.826536i | \(0.690308\pi\) | |||||||
\(270\) | −45.4989 | −2.76898 | ||||||||
\(271\) | 1.99413 | 0.121135 | 0.0605673 | − | 0.998164i | \(-0.480709\pi\) | ||||
0.0605673 | + | 0.998164i | \(0.480709\pi\) | |||||||
\(272\) | −59.2719 | −3.59389 | ||||||||
\(273\) | −0.392766 | −0.0237713 | ||||||||
\(274\) | −13.2838 | −0.802506 | ||||||||
\(275\) | −48.3840 | −2.91767 | ||||||||
\(276\) | −17.6557 | −1.06275 | ||||||||
\(277\) | 27.2755 | 1.63882 | 0.819412 | − | 0.573205i | \(-0.194300\pi\) | ||||
0.819412 | + | 0.573205i | \(0.194300\pi\) | |||||||
\(278\) | 43.7065 | 2.62134 | ||||||||
\(279\) | 0.185366 | 0.0110976 | ||||||||
\(280\) | −33.0667 | −1.97611 | ||||||||
\(281\) | 21.7734 | 1.29889 | 0.649447 | − | 0.760407i | \(-0.275000\pi\) | ||||
0.649447 | + | 0.760407i | \(0.275000\pi\) | |||||||
\(282\) | −15.4077 | −0.917516 | ||||||||
\(283\) | 15.5606 | 0.924983 | 0.462491 | − | 0.886624i | \(-0.346956\pi\) | ||||
0.462491 | + | 0.886624i | \(0.346956\pi\) | |||||||
\(284\) | 73.8292 | 4.38096 | ||||||||
\(285\) | 9.62474 | 0.570120 | ||||||||
\(286\) | 7.31054 | 0.432281 | ||||||||
\(287\) | 5.05744 | 0.298531 | ||||||||
\(288\) | 44.7021 | 2.63410 | ||||||||
\(289\) | 0.223872 | 0.0131689 | ||||||||
\(290\) | 72.9211 | 4.28208 | ||||||||
\(291\) | −2.54587 | −0.149241 | ||||||||
\(292\) | −71.6549 | −4.19329 | ||||||||
\(293\) | −20.3666 | −1.18983 | −0.594916 | − | 0.803788i | \(-0.702815\pi\) | ||||
−0.594916 | + | 0.803788i | \(0.702815\pi\) | |||||||
\(294\) | 2.44305 | 0.142482 | ||||||||
\(295\) | 3.87174 | 0.225422 | ||||||||
\(296\) | −41.6895 | −2.42315 | ||||||||
\(297\) | −28.7072 | −1.66576 | ||||||||
\(298\) | −44.2491 | −2.56328 | ||||||||
\(299\) | 1.59289 | 0.0921192 | ||||||||
\(300\) | −38.0995 | −2.19968 | ||||||||
\(301\) | 11.2055 | 0.645873 | ||||||||
\(302\) | 33.9593 | 1.95414 | ||||||||
\(303\) | −9.24632 | −0.531187 | ||||||||
\(304\) | −42.6482 | −2.44604 | ||||||||
\(305\) | −19.3330 | −1.10700 | ||||||||
\(306\) | −24.7375 | −1.41415 | ||||||||
\(307\) | 22.5602 | 1.28758 | 0.643788 | − | 0.765204i | \(-0.277362\pi\) | ||||
0.643788 | + | 0.765204i | \(0.277362\pi\) | |||||||
\(308\) | −33.1678 | −1.88991 | ||||||||
\(309\) | −5.65810 | −0.321878 | ||||||||
\(310\) | 0.824411 | 0.0468234 | ||||||||
\(311\) | 11.9761 | 0.679104 | 0.339552 | − | 0.940587i | \(-0.389724\pi\) | ||||
0.339552 | + | 0.940587i | \(0.389724\pi\) | |||||||
\(312\) | 3.62101 | 0.204999 | ||||||||
\(313\) | 24.1029 | 1.36237 | 0.681187 | − | 0.732109i | \(-0.261464\pi\) | ||||
0.681187 | + | 0.732109i | \(0.261464\pi\) | |||||||
\(314\) | −52.2223 | −2.94707 | ||||||||
\(315\) | −7.86374 | −0.443072 | ||||||||
\(316\) | 22.1130 | 1.24395 | ||||||||
\(317\) | 6.87592 | 0.386190 | 0.193095 | − | 0.981180i | \(-0.438147\pi\) | ||||
0.193095 | + | 0.981180i | \(0.438147\pi\) | |||||||
\(318\) | −24.4362 | −1.37032 | ||||||||
\(319\) | 46.0090 | 2.57601 | ||||||||
\(320\) | 96.3627 | 5.38684 | ||||||||
\(321\) | 12.4801 | 0.696572 | ||||||||
\(322\) | −9.90795 | −0.552149 | ||||||||
\(323\) | 12.3932 | 0.689575 | ||||||||
\(324\) | 12.8545 | 0.714137 | ||||||||
\(325\) | 3.43732 | 0.190668 | ||||||||
\(326\) | 12.7840 | 0.708038 | ||||||||
\(327\) | −7.78727 | −0.430637 | ||||||||
\(328\) | −46.6258 | −2.57448 | ||||||||
\(329\) | −6.30676 | −0.347703 | ||||||||
\(330\) | −53.9094 | −2.96762 | ||||||||
\(331\) | 30.1696 | 1.65827 | 0.829136 | − | 0.559047i | \(-0.188833\pi\) | ||||
0.829136 | + | 0.559047i | \(0.188833\pi\) | |||||||
\(332\) | −6.34704 | −0.348339 | ||||||||
\(333\) | −9.91437 | −0.543304 | ||||||||
\(334\) | −44.5135 | −2.43567 | ||||||||
\(335\) | 1.53952 | 0.0841132 | ||||||||
\(336\) | −12.8340 | −0.700150 | ||||||||
\(337\) | −31.4116 | −1.71110 | −0.855549 | − | 0.517721i | \(-0.826780\pi\) | ||||
−0.855549 | + | 0.517721i | \(0.826780\pi\) | |||||||
\(338\) | 34.8232 | 1.89413 | ||||||||
\(339\) | −10.9266 | −0.593449 | ||||||||
\(340\) | −80.2486 | −4.35209 | ||||||||
\(341\) | 0.520155 | 0.0281680 | ||||||||
\(342\) | −17.7995 | −0.962485 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −103.306 | −5.56990 | ||||||||
\(345\) | −11.7463 | −0.632400 | ||||||||
\(346\) | 0.405659 | 0.0218084 | ||||||||
\(347\) | −0.429830 | −0.0230745 | −0.0115372 | − | 0.999933i | \(-0.503673\pi\) | ||||
−0.0115372 | + | 0.999933i | \(0.503673\pi\) | |||||||
\(348\) | 36.2293 | 1.94209 | ||||||||
\(349\) | 23.7478 | 1.27119 | 0.635595 | − | 0.772023i | \(-0.280755\pi\) | ||||
0.635595 | + | 0.772023i | \(0.280755\pi\) | |||||||
\(350\) | −21.3805 | −1.14284 | ||||||||
\(351\) | 2.03943 | 0.108857 | ||||||||
\(352\) | 125.439 | 6.68590 | ||||||||
\(353\) | −1.83516 | −0.0976759 | −0.0488379 | − | 0.998807i | \(-0.515552\pi\) | ||||
−0.0488379 | + | 0.998807i | \(0.515552\pi\) | |||||||
\(354\) | 2.63721 | 0.140166 | ||||||||
\(355\) | 49.1184 | 2.60694 | ||||||||
\(356\) | −75.5657 | −4.00497 | ||||||||
\(357\) | 3.72943 | 0.197383 | ||||||||
\(358\) | 22.3425 | 1.18084 | ||||||||
\(359\) | 16.7364 | 0.883311 | 0.441656 | − | 0.897185i | \(-0.354391\pi\) | ||||
0.441656 | + | 0.897185i | \(0.354391\pi\) | |||||||
\(360\) | 72.4979 | 3.82097 | ||||||||
\(361\) | −10.0827 | −0.530667 | ||||||||
\(362\) | −57.8774 | −3.04197 | ||||||||
\(363\) | −24.1289 | −1.26644 | ||||||||
\(364\) | 2.35632 | 0.123505 | ||||||||
\(365\) | −47.6719 | −2.49526 | ||||||||
\(366\) | −13.1685 | −0.688330 | ||||||||
\(367\) | 31.3254 | 1.63517 | 0.817586 | − | 0.575807i | \(-0.195312\pi\) | ||||
0.817586 | + | 0.575807i | \(0.195312\pi\) | |||||||
\(368\) | 52.0490 | 2.71324 | ||||||||
\(369\) | −11.0883 | −0.577235 | ||||||||
\(370\) | −44.0940 | −2.29234 | ||||||||
\(371\) | −10.0023 | −0.519296 | ||||||||
\(372\) | 0.409591 | 0.0212363 | ||||||||
\(373\) | −5.13661 | −0.265964 | −0.132982 | − | 0.991118i | \(-0.542455\pi\) | ||||
−0.132982 | + | 0.991118i | \(0.542455\pi\) | |||||||
\(374\) | −69.4158 | −3.58941 | ||||||||
\(375\) | −9.23211 | −0.476744 | ||||||||
\(376\) | 58.1436 | 2.99853 | ||||||||
\(377\) | −3.26859 | −0.168341 | ||||||||
\(378\) | −12.6855 | −0.652471 | ||||||||
\(379\) | −2.11173 | −0.108472 | −0.0542361 | − | 0.998528i | \(-0.517272\pi\) | ||||
−0.0542361 | + | 0.998528i | \(0.517272\pi\) | |||||||
\(380\) | −57.7417 | −2.96208 | ||||||||
\(381\) | 10.7156 | 0.548978 | ||||||||
\(382\) | −52.3180 | −2.67682 | ||||||||
\(383\) | 19.5018 | 0.996494 | 0.498247 | − | 0.867035i | \(-0.333977\pi\) | ||||
0.498247 | + | 0.867035i | \(0.333977\pi\) | |||||||
\(384\) | 28.9929 | 1.47954 | ||||||||
\(385\) | −22.0665 | −1.12461 | ||||||||
\(386\) | −4.63922 | −0.236130 | ||||||||
\(387\) | −24.5678 | −1.24885 | ||||||||
\(388\) | 15.2734 | 0.775390 | ||||||||
\(389\) | −13.7410 | −0.696695 | −0.348348 | − | 0.937365i | \(-0.613257\pi\) | ||||
−0.348348 | + | 0.937365i | \(0.613257\pi\) | |||||||
\(390\) | 3.82986 | 0.193932 | ||||||||
\(391\) | −15.1250 | −0.764903 | ||||||||
\(392\) | −9.21926 | −0.465643 | ||||||||
\(393\) | −9.44321 | −0.476347 | ||||||||
\(394\) | 30.9851 | 1.56101 | ||||||||
\(395\) | 14.7118 | 0.740229 | ||||||||
\(396\) | 72.7195 | 3.65429 | ||||||||
\(397\) | 30.6331 | 1.53743 | 0.768715 | − | 0.639592i | \(-0.220897\pi\) | ||||
0.768715 | + | 0.639592i | \(0.220897\pi\) | |||||||
\(398\) | −50.0213 | −2.50734 | ||||||||
\(399\) | 2.68346 | 0.134341 | ||||||||
\(400\) | 112.317 | 5.61587 | ||||||||
\(401\) | 9.37442 | 0.468136 | 0.234068 | − | 0.972220i | \(-0.424796\pi\) | ||||
0.234068 | + | 0.972220i | \(0.424796\pi\) | |||||||
\(402\) | 1.04864 | 0.0523012 | ||||||||
\(403\) | −0.0369531 | −0.00184077 | ||||||||
\(404\) | 55.4714 | 2.75981 | ||||||||
\(405\) | 8.55205 | 0.424955 | ||||||||
\(406\) | 20.3310 | 1.00901 | ||||||||
\(407\) | −27.8207 | −1.37902 | ||||||||
\(408\) | −34.3826 | −1.70219 | ||||||||
\(409\) | 16.3209 | 0.807014 | 0.403507 | − | 0.914977i | \(-0.367791\pi\) | ||||
0.403507 | + | 0.914977i | \(0.367791\pi\) | |||||||
\(410\) | −49.3151 | −2.43550 | ||||||||
\(411\) | −4.39083 | −0.216584 | ||||||||
\(412\) | 33.9446 | 1.67233 | ||||||||
\(413\) | 1.07947 | 0.0531175 | ||||||||
\(414\) | 21.7230 | 1.06763 | ||||||||
\(415\) | −4.22268 | −0.207283 | ||||||||
\(416\) | −8.91146 | −0.436920 | ||||||||
\(417\) | 14.4467 | 0.707459 | ||||||||
\(418\) | −49.9471 | −2.44299 | ||||||||
\(419\) | 17.9286 | 0.875867 | 0.437934 | − | 0.899007i | \(-0.355711\pi\) | ||||
0.437934 | + | 0.899007i | \(0.355711\pi\) | |||||||
\(420\) | −17.3760 | −0.847862 | ||||||||
\(421\) | −9.07939 | −0.442502 | −0.221251 | − | 0.975217i | \(-0.571014\pi\) | ||||
−0.221251 | + | 0.975217i | \(0.571014\pi\) | |||||||
\(422\) | −15.9560 | −0.776725 | ||||||||
\(423\) | 13.8274 | 0.672312 | ||||||||
\(424\) | 92.2142 | 4.47832 | ||||||||
\(425\) | −32.6384 | −1.58320 | ||||||||
\(426\) | 33.4567 | 1.62098 | ||||||||
\(427\) | −5.39020 | −0.260850 | ||||||||
\(428\) | −74.8719 | −3.61907 | ||||||||
\(429\) | 2.41642 | 0.116666 | ||||||||
\(430\) | −109.265 | −5.26921 | ||||||||
\(431\) | 26.7123 | 1.28669 | 0.643344 | − | 0.765577i | \(-0.277547\pi\) | ||||
0.643344 | + | 0.765577i | \(0.277547\pi\) | |||||||
\(432\) | 66.6401 | 3.20622 | ||||||||
\(433\) | −25.7496 | −1.23745 | −0.618723 | − | 0.785609i | \(-0.712350\pi\) | ||||
−0.618723 | + | 0.785609i | \(0.712350\pi\) | |||||||
\(434\) | 0.229853 | 0.0110333 | ||||||||
\(435\) | 24.1033 | 1.15566 | ||||||||
\(436\) | 46.7181 | 2.23739 | ||||||||
\(437\) | −10.8829 | −0.520602 | ||||||||
\(438\) | −32.4714 | −1.55154 | ||||||||
\(439\) | 18.0350 | 0.860763 | 0.430381 | − | 0.902647i | \(-0.358379\pi\) | ||||
0.430381 | + | 0.902647i | \(0.358379\pi\) | |||||||
\(440\) | 203.436 | 9.69845 | ||||||||
\(441\) | −2.19248 | −0.104404 | ||||||||
\(442\) | 4.93147 | 0.234566 | ||||||||
\(443\) | 33.9536 | 1.61318 | 0.806592 | − | 0.591109i | \(-0.201310\pi\) | ||||
0.806592 | + | 0.591109i | \(0.201310\pi\) | |||||||
\(444\) | −21.9071 | −1.03967 | ||||||||
\(445\) | −50.2737 | −2.38320 | ||||||||
\(446\) | 0.649411 | 0.0307505 | ||||||||
\(447\) | −14.6261 | −0.691789 | ||||||||
\(448\) | 26.8667 | 1.26933 | ||||||||
\(449\) | 35.9164 | 1.69500 | 0.847500 | − | 0.530795i | \(-0.178107\pi\) | ||||
0.847500 | + | 0.530795i | \(0.178107\pi\) | |||||||
\(450\) | 46.8763 | 2.20977 | ||||||||
\(451\) | −31.1149 | −1.46514 | ||||||||
\(452\) | 65.5516 | 3.08329 | ||||||||
\(453\) | 11.2249 | 0.527390 | ||||||||
\(454\) | 63.4222 | 2.97655 | ||||||||
\(455\) | 1.56766 | 0.0734928 | ||||||||
\(456\) | −24.7395 | −1.15853 | ||||||||
\(457\) | 15.7647 | 0.737441 | 0.368721 | − | 0.929540i | \(-0.379796\pi\) | ||||
0.368721 | + | 0.929540i | \(0.379796\pi\) | |||||||
\(458\) | 61.6280 | 2.87969 | ||||||||
\(459\) | −19.3650 | −0.903881 | ||||||||
\(460\) | 70.4695 | 3.28566 | ||||||||
\(461\) | −1.11400 | −0.0518843 | −0.0259421 | − | 0.999663i | \(-0.508259\pi\) | ||||
−0.0259421 | + | 0.999663i | \(0.508259\pi\) | |||||||
\(462\) | −15.0304 | −0.699278 | ||||||||
\(463\) | −9.68434 | −0.450069 | −0.225035 | − | 0.974351i | \(-0.572250\pi\) | ||||
−0.225035 | + | 0.974351i | \(0.572250\pi\) | |||||||
\(464\) | −106.804 | −4.95825 | ||||||||
\(465\) | 0.272500 | 0.0126369 | ||||||||
\(466\) | 31.9061 | 1.47802 | ||||||||
\(467\) | −16.2219 | −0.750659 | −0.375329 | − | 0.926891i | \(-0.622470\pi\) | ||||
−0.375329 | + | 0.926891i | \(0.622470\pi\) | |||||||
\(468\) | −5.16617 | −0.238807 | ||||||||
\(469\) | 0.429232 | 0.0198201 | ||||||||
\(470\) | 61.4971 | 2.83665 | ||||||||
\(471\) | −17.2615 | −0.795368 | ||||||||
\(472\) | −9.95196 | −0.458076 | ||||||||
\(473\) | −68.9396 | −3.16985 | ||||||||
\(474\) | 10.0208 | 0.460271 | ||||||||
\(475\) | −23.4845 | −1.07754 | ||||||||
\(476\) | −22.3740 | −1.02551 | ||||||||
\(477\) | 21.9299 | 1.00410 | ||||||||
\(478\) | −69.1458 | −3.16266 | ||||||||
\(479\) | 24.4008 | 1.11490 | 0.557450 | − | 0.830211i | \(-0.311780\pi\) | ||||
0.557450 | + | 0.830211i | \(0.311780\pi\) | |||||||
\(480\) | 65.7150 | 2.99947 | ||||||||
\(481\) | 1.97645 | 0.0901185 | ||||||||
\(482\) | 13.0938 | 0.596407 | ||||||||
\(483\) | −3.27497 | −0.149016 | ||||||||
\(484\) | 144.756 | 6.57983 | ||||||||
\(485\) | 10.1614 | 0.461404 | ||||||||
\(486\) | 43.8816 | 1.99051 | ||||||||
\(487\) | −16.0977 | −0.729454 | −0.364727 | − | 0.931114i | \(-0.618838\pi\) | ||||
−0.364727 | + | 0.931114i | \(0.618838\pi\) | |||||||
\(488\) | 49.6937 | 2.24953 | ||||||||
\(489\) | 4.22560 | 0.191088 | ||||||||
\(490\) | −9.75100 | −0.440505 | ||||||||
\(491\) | 1.04602 | 0.0472063 | 0.0236031 | − | 0.999721i | \(-0.492486\pi\) | ||||
0.0236031 | + | 0.999721i | \(0.492486\pi\) | |||||||
\(492\) | −24.5011 | −1.10460 | ||||||||
\(493\) | 31.0363 | 1.39780 | ||||||||
\(494\) | 3.54836 | 0.159648 | ||||||||
\(495\) | 48.3802 | 2.17453 | ||||||||
\(496\) | −1.20747 | −0.0542172 | ||||||||
\(497\) | 13.6946 | 0.614288 | ||||||||
\(498\) | −2.87625 | −0.128888 | ||||||||
\(499\) | 18.8517 | 0.843919 | 0.421959 | − | 0.906615i | \(-0.361342\pi\) | ||||
0.421959 | + | 0.906615i | \(0.361342\pi\) | |||||||
\(500\) | 55.3861 | 2.47694 | ||||||||
\(501\) | −14.7135 | −0.657349 | ||||||||
\(502\) | −49.5114 | −2.20980 | ||||||||
\(503\) | −9.67865 | −0.431550 | −0.215775 | − | 0.976443i | \(-0.569228\pi\) | ||||
−0.215775 | + | 0.976443i | \(0.569228\pi\) | |||||||
\(504\) | 20.2130 | 0.900359 | ||||||||
\(505\) | 36.9050 | 1.64225 | ||||||||
\(506\) | 60.9568 | 2.70986 | ||||||||
\(507\) | 11.5104 | 0.511196 | ||||||||
\(508\) | −64.2862 | −2.85224 | ||||||||
\(509\) | 14.5048 | 0.642913 | 0.321457 | − | 0.946924i | \(-0.395828\pi\) | ||||
0.321457 | + | 0.946924i | \(0.395828\pi\) | |||||||
\(510\) | −36.3657 | −1.61030 | ||||||||
\(511\) | −13.2913 | −0.587974 | ||||||||
\(512\) | −27.8543 | −1.23100 | ||||||||
\(513\) | −13.9338 | −0.615192 | ||||||||
\(514\) | 5.03950 | 0.222283 | ||||||||
\(515\) | 22.5833 | 0.995139 | ||||||||
\(516\) | −54.2858 | −2.38980 | ||||||||
\(517\) | 38.8011 | 1.70647 | ||||||||
\(518\) | −12.2938 | −0.540157 | ||||||||
\(519\) | 0.134086 | 0.00588573 | ||||||||
\(520\) | −14.4526 | −0.633789 | ||||||||
\(521\) | −18.4533 | −0.808453 | −0.404226 | − | 0.914659i | \(-0.632459\pi\) | ||||
−0.404226 | + | 0.914659i | \(0.632459\pi\) | |||||||
\(522\) | −44.5753 | −1.95101 | ||||||||
\(523\) | 27.7331 | 1.21268 | 0.606342 | − | 0.795204i | \(-0.292636\pi\) | ||||
0.606342 | + | 0.795204i | \(0.292636\pi\) | |||||||
\(524\) | 56.6526 | 2.47488 | ||||||||
\(525\) | −7.06710 | −0.308434 | ||||||||
\(526\) | 41.8667 | 1.82548 | ||||||||
\(527\) | 0.350881 | 0.0152846 | ||||||||
\(528\) | 78.9585 | 3.43623 | ||||||||
\(529\) | −9.71815 | −0.422528 | ||||||||
\(530\) | 97.5328 | 4.23656 | ||||||||
\(531\) | −2.36672 | −0.102707 | ||||||||
\(532\) | −16.0989 | −0.697974 | ||||||||
\(533\) | 2.21048 | 0.0957466 | ||||||||
\(534\) | −34.2436 | −1.48186 | ||||||||
\(535\) | −49.8121 | −2.15357 | ||||||||
\(536\) | −3.95720 | −0.170925 | ||||||||
\(537\) | 7.38508 | 0.318690 | ||||||||
\(538\) | 50.1972 | 2.16416 | ||||||||
\(539\) | −6.15231 | −0.264999 | ||||||||
\(540\) | 90.2244 | 3.88264 | ||||||||
\(541\) | −22.1720 | −0.953249 | −0.476625 | − | 0.879107i | \(-0.658140\pi\) | ||||
−0.476625 | + | 0.879107i | \(0.658140\pi\) | |||||||
\(542\) | −5.42135 | −0.232867 | ||||||||
\(543\) | −19.1307 | −0.820979 | ||||||||
\(544\) | 84.6171 | 3.62793 | ||||||||
\(545\) | 31.0815 | 1.33138 | ||||||||
\(546\) | 1.06780 | 0.0456975 | ||||||||
\(547\) | 45.5619 | 1.94809 | 0.974043 | − | 0.226364i | \(-0.0726838\pi\) | ||||
0.974043 | + | 0.226364i | \(0.0726838\pi\) | |||||||
\(548\) | 26.3419 | 1.12527 | ||||||||
\(549\) | 11.8179 | 0.504375 | ||||||||
\(550\) | 131.540 | 5.60887 | ||||||||
\(551\) | 22.3317 | 0.951362 | ||||||||
\(552\) | 30.1928 | 1.28509 | ||||||||
\(553\) | 4.10176 | 0.174425 | ||||||||
\(554\) | −74.1527 | −3.15045 | ||||||||
\(555\) | −14.5748 | −0.618665 | ||||||||
\(556\) | −86.6701 | −3.67563 | ||||||||
\(557\) | −20.2511 | −0.858066 | −0.429033 | − | 0.903289i | \(-0.641146\pi\) | ||||
−0.429033 | + | 0.903289i | \(0.641146\pi\) | |||||||
\(558\) | −0.503947 | −0.0213338 | ||||||||
\(559\) | 4.89764 | 0.207148 | ||||||||
\(560\) | 51.2245 | 2.16463 | ||||||||
\(561\) | −22.9446 | −0.968723 | ||||||||
\(562\) | −59.1945 | −2.49697 | ||||||||
\(563\) | −3.17345 | −0.133745 | −0.0668724 | − | 0.997762i | \(-0.521302\pi\) | ||||
−0.0668724 | + | 0.997762i | \(0.521302\pi\) | |||||||
\(564\) | 30.5535 | 1.28654 | ||||||||
\(565\) | 43.6114 | 1.83474 | ||||||||
\(566\) | −42.3040 | −1.77817 | ||||||||
\(567\) | 2.38438 | 0.100135 | ||||||||
\(568\) | −126.254 | −5.29752 | ||||||||
\(569\) | −13.8716 | −0.581529 | −0.290764 | − | 0.956795i | \(-0.593910\pi\) | ||||
−0.290764 | + | 0.956795i | \(0.593910\pi\) | |||||||
\(570\) | −26.1664 | −1.09599 | ||||||||
\(571\) | −24.4837 | −1.02461 | −0.512305 | − | 0.858803i | \(-0.671208\pi\) | ||||
−0.512305 | + | 0.858803i | \(0.671208\pi\) | |||||||
\(572\) | −14.4968 | −0.606142 | ||||||||
\(573\) | −17.2932 | −0.722432 | ||||||||
\(574\) | −13.7494 | −0.573891 | ||||||||
\(575\) | 28.6611 | 1.19525 | ||||||||
\(576\) | −58.9046 | −2.45436 | ||||||||
\(577\) | −43.9290 | −1.82879 | −0.914393 | − | 0.404827i | \(-0.867332\pi\) | ||||
−0.914393 | + | 0.404827i | \(0.867332\pi\) | |||||||
\(578\) | −0.608630 | −0.0253157 | ||||||||
\(579\) | −1.53344 | −0.0637277 | ||||||||
\(580\) | −144.603 | −6.00430 | ||||||||
\(581\) | −1.17732 | −0.0488434 | ||||||||
\(582\) | 6.92135 | 0.286899 | ||||||||
\(583\) | 61.5375 | 2.54862 | ||||||||
\(584\) | 122.536 | 5.07058 | ||||||||
\(585\) | −3.43705 | −0.142104 | ||||||||
\(586\) | 55.3699 | 2.28731 | ||||||||
\(587\) | −15.8458 | −0.654027 | −0.327014 | − | 0.945020i | \(-0.606042\pi\) | ||||
−0.327014 | + | 0.945020i | \(0.606042\pi\) | |||||||
\(588\) | −4.84457 | −0.199787 | ||||||||
\(589\) | 0.252471 | 0.0104029 | ||||||||
\(590\) | −10.5260 | −0.433347 | ||||||||
\(591\) | 10.2418 | 0.421290 | ||||||||
\(592\) | 64.5823 | 2.65432 | ||||||||
\(593\) | 26.0204 | 1.06853 | 0.534264 | − | 0.845317i | \(-0.320589\pi\) | ||||
0.534264 | + | 0.845317i | \(0.320589\pi\) | |||||||
\(594\) | 78.0450 | 3.20223 | ||||||||
\(595\) | −14.8854 | −0.610241 | ||||||||
\(596\) | 87.7460 | 3.59422 | ||||||||
\(597\) | −16.5340 | −0.676691 | ||||||||
\(598\) | −4.33052 | −0.177088 | ||||||||
\(599\) | 16.7520 | 0.684466 | 0.342233 | − | 0.939615i | \(-0.388817\pi\) | ||||
0.342233 | + | 0.939615i | \(0.388817\pi\) | |||||||
\(600\) | 65.1535 | 2.65988 | ||||||||
\(601\) | −36.0258 | −1.46952 | −0.734762 | − | 0.678325i | \(-0.762706\pi\) | ||||
−0.734762 | + | 0.678325i | \(0.762706\pi\) | |||||||
\(602\) | −30.4639 | −1.24162 | ||||||||
\(603\) | −0.941082 | −0.0383238 | ||||||||
\(604\) | −67.3413 | −2.74008 | ||||||||
\(605\) | 96.3061 | 3.91540 | ||||||||
\(606\) | 25.1376 | 1.02114 | ||||||||
\(607\) | 30.4832 | 1.23728 | 0.618638 | − | 0.785676i | \(-0.287685\pi\) | ||||
0.618638 | + | 0.785676i | \(0.287685\pi\) | |||||||
\(608\) | 60.8849 | 2.46921 | ||||||||
\(609\) | 6.72020 | 0.272316 | ||||||||
\(610\) | 52.5598 | 2.12809 | ||||||||
\(611\) | −2.75653 | −0.111517 | ||||||||
\(612\) | 49.0544 | 1.98291 | ||||||||
\(613\) | −16.4618 | −0.664886 | −0.332443 | − | 0.943123i | \(-0.607873\pi\) | ||||
−0.332443 | + | 0.943123i | \(0.607873\pi\) | |||||||
\(614\) | −61.3334 | −2.47521 | ||||||||
\(615\) | −16.3006 | −0.657302 | ||||||||
\(616\) | 56.7198 | 2.28530 | ||||||||
\(617\) | −41.2887 | −1.66222 | −0.831110 | − | 0.556107i | \(-0.812294\pi\) | ||||
−0.831110 | + | 0.556107i | \(0.812294\pi\) | |||||||
\(618\) | 15.3824 | 0.618773 | ||||||||
\(619\) | −21.8387 | −0.877772 | −0.438886 | − | 0.898543i | \(-0.644627\pi\) | ||||
−0.438886 | + | 0.898543i | \(0.644627\pi\) | |||||||
\(620\) | −1.63481 | −0.0656555 | ||||||||
\(621\) | 17.0052 | 0.682395 | ||||||||
\(622\) | −32.5590 | −1.30550 | ||||||||
\(623\) | −14.0167 | −0.561568 | ||||||||
\(624\) | −5.60941 | −0.224556 | ||||||||
\(625\) | −2.47354 | −0.0989416 | ||||||||
\(626\) | −65.5274 | −2.61900 | ||||||||
\(627\) | −16.5095 | −0.659324 | ||||||||
\(628\) | 103.557 | 4.13237 | ||||||||
\(629\) | −18.7670 | −0.748291 | ||||||||
\(630\) | 21.3788 | 0.851753 | ||||||||
\(631\) | −8.38874 | −0.333951 | −0.166975 | − | 0.985961i | \(-0.553400\pi\) | ||||
−0.166975 | + | 0.985961i | \(0.553400\pi\) | |||||||
\(632\) | −37.8152 | −1.50421 | ||||||||
\(633\) | −5.27407 | −0.209626 | ||||||||
\(634\) | −18.6933 | −0.742405 | ||||||||
\(635\) | −42.7695 | −1.69725 | ||||||||
\(636\) | 48.4571 | 1.92145 | ||||||||
\(637\) | 0.437075 | 0.0173176 | ||||||||
\(638\) | −125.083 | −4.95207 | ||||||||
\(639\) | −30.0252 | −1.18778 | ||||||||
\(640\) | −115.720 | −4.57424 | ||||||||
\(641\) | 32.6795 | 1.29076 | 0.645382 | − | 0.763860i | \(-0.276698\pi\) | ||||
0.645382 | + | 0.763860i | \(0.276698\pi\) | |||||||
\(642\) | −33.9291 | −1.33908 | ||||||||
\(643\) | 14.7099 | 0.580100 | 0.290050 | − | 0.957012i | \(-0.406328\pi\) | ||||
0.290050 | + | 0.957012i | \(0.406328\pi\) | |||||||
\(644\) | 19.6475 | 0.774220 | ||||||||
\(645\) | −36.1162 | −1.42207 | ||||||||
\(646\) | −33.6928 | −1.32563 | ||||||||
\(647\) | 8.99013 | 0.353438 | 0.176719 | − | 0.984261i | \(-0.443452\pi\) | ||||
0.176719 | + | 0.984261i | \(0.443452\pi\) | |||||||
\(648\) | −21.9823 | −0.863545 | ||||||||
\(649\) | −6.64126 | −0.260692 | ||||||||
\(650\) | −9.34490 | −0.366537 | ||||||||
\(651\) | 0.0759753 | 0.00297771 | ||||||||
\(652\) | −25.3506 | −0.992807 | ||||||||
\(653\) | 14.7857 | 0.578610 | 0.289305 | − | 0.957237i | \(-0.406576\pi\) | ||||
0.289305 | + | 0.957237i | \(0.406576\pi\) | |||||||
\(654\) | 21.1709 | 0.827849 | ||||||||
\(655\) | 37.6909 | 1.47271 | ||||||||
\(656\) | 72.2294 | 2.82008 | ||||||||
\(657\) | 29.1409 | 1.13690 | ||||||||
\(658\) | 17.1459 | 0.668417 | ||||||||
\(659\) | 20.1464 | 0.784794 | 0.392397 | − | 0.919796i | \(-0.371646\pi\) | ||||
0.392397 | + | 0.919796i | \(0.371646\pi\) | |||||||
\(660\) | 106.903 | 4.16118 | ||||||||
\(661\) | 7.15641 | 0.278352 | 0.139176 | − | 0.990268i | \(-0.455555\pi\) | ||||
0.139176 | + | 0.990268i | \(0.455555\pi\) | |||||||
\(662\) | −82.0209 | −3.18783 | ||||||||
\(663\) | 1.63004 | 0.0633056 | ||||||||
\(664\) | 10.8540 | 0.421217 | ||||||||
\(665\) | −10.7105 | −0.415337 | ||||||||
\(666\) | 26.9538 | 1.04444 | ||||||||
\(667\) | −27.2542 | −1.05529 | ||||||||
\(668\) | 88.2704 | 3.41528 | ||||||||
\(669\) | 0.214656 | 0.00829907 | ||||||||
\(670\) | −4.18544 | −0.161698 | ||||||||
\(671\) | 33.1622 | 1.28021 | ||||||||
\(672\) | 18.3219 | 0.706782 | ||||||||
\(673\) | 5.64587 | 0.217632 | 0.108816 | − | 0.994062i | \(-0.465294\pi\) | ||||
0.108816 | + | 0.994062i | \(0.465294\pi\) | |||||||
\(674\) | 85.3974 | 3.28939 | ||||||||
\(675\) | 36.6958 | 1.41242 | ||||||||
\(676\) | −69.0545 | −2.65594 | ||||||||
\(677\) | −35.2244 | −1.35378 | −0.676892 | − | 0.736083i | \(-0.736673\pi\) | ||||
−0.676892 | + | 0.736083i | \(0.736673\pi\) | |||||||
\(678\) | 29.7056 | 1.14084 | ||||||||
\(679\) | 2.83308 | 0.108724 | ||||||||
\(680\) | 137.232 | 5.26261 | ||||||||
\(681\) | 20.9635 | 0.803323 | ||||||||
\(682\) | −1.41412 | −0.0541496 | ||||||||
\(683\) | −14.2553 | −0.545463 | −0.272732 | − | 0.962090i | \(-0.587927\pi\) | ||||
−0.272732 | + | 0.962090i | \(0.587927\pi\) | |||||||
\(684\) | 35.2964 | 1.34959 | ||||||||
\(685\) | 17.5252 | 0.669604 | ||||||||
\(686\) | −2.71866 | −0.103799 | ||||||||
\(687\) | 20.3705 | 0.777182 | ||||||||
\(688\) | 160.035 | 6.10126 | ||||||||
\(689\) | −4.37178 | −0.166551 | ||||||||
\(690\) | 31.9342 | 1.21571 | ||||||||
\(691\) | 2.85379 | 0.108563 | 0.0542817 | − | 0.998526i | \(-0.482713\pi\) | ||||
0.0542817 | + | 0.998526i | \(0.482713\pi\) | |||||||
\(692\) | −0.804422 | −0.0305795 | ||||||||
\(693\) | 13.4888 | 0.512397 | ||||||||
\(694\) | 1.16856 | 0.0443580 | ||||||||
\(695\) | −57.6615 | −2.18722 | ||||||||
\(696\) | −61.9552 | −2.34841 | ||||||||
\(697\) | −20.9892 | −0.795023 | ||||||||
\(698\) | −64.5621 | −2.44371 | ||||||||
\(699\) | 10.5462 | 0.398894 | ||||||||
\(700\) | 42.3976 | 1.60248 | ||||||||
\(701\) | −4.62937 | −0.174849 | −0.0874245 | − | 0.996171i | \(-0.527864\pi\) | ||||
−0.0874245 | + | 0.996171i | \(0.527864\pi\) | |||||||
\(702\) | −5.54451 | −0.209264 | ||||||||
\(703\) | −13.5035 | −0.509295 | ||||||||
\(704\) | −165.292 | −6.22969 | ||||||||
\(705\) | 20.3272 | 0.765567 | ||||||||
\(706\) | 4.98918 | 0.187770 | ||||||||
\(707\) | 10.2894 | 0.386974 | ||||||||
\(708\) | −5.22959 | −0.196540 | ||||||||
\(709\) | −12.1823 | −0.457515 | −0.228758 | − | 0.973483i | \(-0.573466\pi\) | ||||
−0.228758 | + | 0.973483i | \(0.573466\pi\) | |||||||
\(710\) | −133.536 | −5.01153 | ||||||||
\(711\) | −8.99301 | −0.337264 | ||||||||
\(712\) | 129.224 | 4.84287 | ||||||||
\(713\) | −0.308123 | −0.0115393 | ||||||||
\(714\) | −10.1391 | −0.379445 | ||||||||
\(715\) | −9.64470 | −0.360691 | ||||||||
\(716\) | −44.3053 | −1.65577 | ||||||||
\(717\) | −22.8554 | −0.853550 | ||||||||
\(718\) | −45.5004 | −1.69806 | ||||||||
\(719\) | −17.4261 | −0.649882 | −0.324941 | − | 0.945734i | \(-0.605344\pi\) | ||||
−0.324941 | + | 0.945734i | \(0.605344\pi\) | |||||||
\(720\) | −112.308 | −4.18549 | ||||||||
\(721\) | 6.29641 | 0.234491 | ||||||||
\(722\) | 27.4114 | 1.02015 | ||||||||
\(723\) | 4.32802 | 0.160961 | ||||||||
\(724\) | 114.771 | 4.26543 | ||||||||
\(725\) | −58.8123 | −2.18423 | ||||||||
\(726\) | 65.5982 | 2.43458 | ||||||||
\(727\) | −0.430594 | −0.0159698 | −0.00798492 | − | 0.999968i | \(-0.502542\pi\) | ||||
−0.00798492 | + | 0.999968i | \(0.502542\pi\) | |||||||
\(728\) | −4.02951 | −0.149344 | ||||||||
\(729\) | 7.35143 | 0.272275 | ||||||||
\(730\) | 129.604 | 4.79685 | ||||||||
\(731\) | −46.5046 | −1.72003 | ||||||||
\(732\) | 26.1132 | 0.965173 | ||||||||
\(733\) | −15.5938 | −0.575969 | −0.287984 | − | 0.957635i | \(-0.592985\pi\) | ||||
−0.287984 | + | 0.957635i | \(0.592985\pi\) | |||||||
\(734\) | −85.1630 | −3.14342 | ||||||||
\(735\) | −3.22309 | −0.118885 | ||||||||
\(736\) | −74.3057 | −2.73894 | ||||||||
\(737\) | −2.64077 | −0.0972740 | ||||||||
\(738\) | 30.1453 | 1.10967 | ||||||||
\(739\) | −22.4872 | −0.827206 | −0.413603 | − | 0.910457i | \(-0.635730\pi\) | ||||
−0.413603 | + | 0.910457i | \(0.635730\pi\) | |||||||
\(740\) | 87.4384 | 3.21430 | ||||||||
\(741\) | 1.17287 | 0.0430866 | ||||||||
\(742\) | 27.1930 | 0.998285 | ||||||||
\(743\) | −31.3730 | −1.15096 | −0.575481 | − | 0.817815i | \(-0.695185\pi\) | ||||
−0.575481 | + | 0.817815i | \(0.695185\pi\) | |||||||
\(744\) | −0.700436 | −0.0256792 | ||||||||
\(745\) | 58.3773 | 2.13878 | ||||||||
\(746\) | 13.9647 | 0.511284 | ||||||||
\(747\) | 2.58124 | 0.0944427 | ||||||||
\(748\) | 137.652 | 5.03304 | ||||||||
\(749\) | −13.8880 | −0.507458 | ||||||||
\(750\) | 25.0990 | 0.916484 | ||||||||
\(751\) | 47.3544 | 1.72799 | 0.863993 | − | 0.503505i | \(-0.167956\pi\) | ||||
0.863993 | + | 0.503505i | \(0.167956\pi\) | |||||||
\(752\) | −90.0719 | −3.28458 | ||||||||
\(753\) | −16.3655 | −0.596391 | ||||||||
\(754\) | 8.88618 | 0.323616 | ||||||||
\(755\) | −44.8020 | −1.63051 | ||||||||
\(756\) | 25.1553 | 0.914890 | ||||||||
\(757\) | 32.1157 | 1.16726 | 0.583632 | − | 0.812018i | \(-0.301631\pi\) | ||||
0.583632 | + | 0.812018i | \(0.301631\pi\) | |||||||
\(758\) | 5.74107 | 0.208525 | ||||||||
\(759\) | 20.1486 | 0.731348 | ||||||||
\(760\) | 98.7433 | 3.58179 | ||||||||
\(761\) | 41.6987 | 1.51158 | 0.755788 | − | 0.654816i | \(-0.227254\pi\) | ||||
0.755788 | + | 0.654816i | \(0.227254\pi\) | |||||||
\(762\) | −29.1321 | −1.05535 | ||||||||
\(763\) | 8.66578 | 0.313722 | ||||||||
\(764\) | 103.747 | 3.75343 | ||||||||
\(765\) | 32.6358 | 1.17995 | ||||||||
\(766\) | −53.0186 | −1.91564 | ||||||||
\(767\) | 0.471812 | 0.0170361 | ||||||||
\(768\) | −30.5358 | −1.10186 | ||||||||
\(769\) | 32.8642 | 1.18511 | 0.592556 | − | 0.805529i | \(-0.298119\pi\) | ||||
0.592556 | + | 0.805529i | \(0.298119\pi\) | |||||||
\(770\) | 59.9912 | 2.16193 | ||||||||
\(771\) | 1.66575 | 0.0599906 | ||||||||
\(772\) | 9.19958 | 0.331100 | ||||||||
\(773\) | −22.3320 | −0.803227 | −0.401613 | − | 0.915809i | \(-0.631550\pi\) | ||||
−0.401613 | + | 0.915809i | \(0.631550\pi\) | |||||||
\(774\) | 66.7913 | 2.40077 | ||||||||
\(775\) | −0.664904 | −0.0238840 | ||||||||
\(776\) | −26.1189 | −0.937613 | ||||||||
\(777\) | −4.06357 | −0.145780 | ||||||||
\(778\) | 37.3570 | 1.33931 | ||||||||
\(779\) | −15.1025 | −0.541102 | ||||||||
\(780\) | −7.59462 | −0.271931 | ||||||||
\(781\) | −84.2536 | −3.01483 | ||||||||
\(782\) | 41.1196 | 1.47044 | ||||||||
\(783\) | −34.8945 | −1.24703 | ||||||||
\(784\) | 14.2818 | 0.510065 | ||||||||
\(785\) | 68.8962 | 2.45901 | ||||||||
\(786\) | 25.6729 | 0.915721 | ||||||||
\(787\) | −21.2017 | −0.755758 | −0.377879 | − | 0.925855i | \(-0.623346\pi\) | ||||
−0.377879 | + | 0.925855i | \(0.623346\pi\) | |||||||
\(788\) | −61.4435 | −2.18883 | ||||||||
\(789\) | 13.8386 | 0.492667 | ||||||||
\(790\) | −39.9962 | −1.42300 | ||||||||
\(791\) | 12.1592 | 0.432332 | ||||||||
\(792\) | −124.357 | −4.41882 | ||||||||
\(793\) | −2.35592 | −0.0836613 | ||||||||
\(794\) | −83.2809 | −2.95553 | ||||||||
\(795\) | 32.2384 | 1.14338 | ||||||||
\(796\) | 99.1923 | 3.51578 | ||||||||
\(797\) | 35.2053 | 1.24704 | 0.623518 | − | 0.781809i | \(-0.285703\pi\) | ||||
0.623518 | + | 0.781809i | \(0.285703\pi\) | |||||||
\(798\) | −7.29540 | −0.258255 | ||||||||
\(799\) | 26.1741 | 0.925972 | ||||||||
\(800\) | −160.345 | −5.66907 | ||||||||
\(801\) | 30.7313 | 1.08584 | ||||||||
\(802\) | −25.4859 | −0.899937 | ||||||||
\(803\) | 81.7724 | 2.88568 | ||||||||
\(804\) | −2.07945 | −0.0733364 | ||||||||
\(805\) | 13.0714 | 0.460708 | ||||||||
\(806\) | 0.100463 | 0.00353865 | ||||||||
\(807\) | 16.5921 | 0.584071 | ||||||||
\(808\) | −94.8609 | −3.33720 | ||||||||
\(809\) | 6.41510 | 0.225543 | 0.112771 | − | 0.993621i | \(-0.464027\pi\) | ||||
0.112771 | + | 0.993621i | \(0.464027\pi\) | |||||||
\(810\) | −23.2501 | −0.816926 | ||||||||
\(811\) | 12.0851 | 0.424366 | 0.212183 | − | 0.977230i | \(-0.431943\pi\) | ||||
0.212183 | + | 0.977230i | \(0.431943\pi\) | |||||||
\(812\) | −40.3164 | −1.41483 | ||||||||
\(813\) | −1.79197 | −0.0628471 | ||||||||
\(814\) | 75.6351 | 2.65101 | ||||||||
\(815\) | −16.8657 | −0.590780 | ||||||||
\(816\) | 53.2631 | 1.86458 | ||||||||
\(817\) | −33.4617 | −1.17068 | ||||||||
\(818\) | −44.3708 | −1.55139 | ||||||||
\(819\) | −0.958277 | −0.0334849 | ||||||||
\(820\) | 97.7918 | 3.41504 | ||||||||
\(821\) | −7.47828 | −0.260994 | −0.130497 | − | 0.991449i | \(-0.541657\pi\) | ||||
−0.130497 | + | 0.991449i | \(0.541657\pi\) | |||||||
\(822\) | 11.9372 | 0.416356 | ||||||||
\(823\) | 46.6206 | 1.62509 | 0.812547 | − | 0.582896i | \(-0.198080\pi\) | ||||
0.812547 | + | 0.582896i | \(0.198080\pi\) | |||||||
\(824\) | −58.0482 | −2.02221 | ||||||||
\(825\) | 43.4790 | 1.51375 | ||||||||
\(826\) | −2.93472 | −0.102112 | ||||||||
\(827\) | −19.7120 | −0.685454 | −0.342727 | − | 0.939435i | \(-0.611351\pi\) | ||||
−0.342727 | + | 0.939435i | \(0.611351\pi\) | |||||||
\(828\) | −43.0767 | −1.49702 | ||||||||
\(829\) | 10.1066 | 0.351017 | 0.175508 | − | 0.984478i | \(-0.443843\pi\) | ||||
0.175508 | + | 0.984478i | \(0.443843\pi\) | |||||||
\(830\) | 11.4800 | 0.398477 | ||||||||
\(831\) | −24.5104 | −0.850255 | ||||||||
\(832\) | 11.7428 | 0.407108 | ||||||||
\(833\) | −4.15017 | −0.143795 | ||||||||
\(834\) | −39.2757 | −1.36001 | ||||||||
\(835\) | 58.7261 | 2.03230 | ||||||||
\(836\) | 99.0452 | 3.42555 | ||||||||
\(837\) | −0.394500 | −0.0136359 | ||||||||
\(838\) | −48.7416 | −1.68375 | ||||||||
\(839\) | 7.33493 | 0.253230 | 0.126615 | − | 0.991952i | \(-0.459589\pi\) | ||||
0.126615 | + | 0.991952i | \(0.459589\pi\) | |||||||
\(840\) | 29.7145 | 1.02525 | ||||||||
\(841\) | 26.9254 | 0.928460 | ||||||||
\(842\) | 24.6838 | 0.850659 | ||||||||
\(843\) | −19.5661 | −0.673892 | ||||||||
\(844\) | 31.6407 | 1.08912 | ||||||||
\(845\) | −45.9418 | −1.58045 | ||||||||
\(846\) | −37.5920 | −1.29244 | ||||||||
\(847\) | 26.8509 | 0.922609 | ||||||||
\(848\) | −142.852 | −4.90554 | ||||||||
\(849\) | −13.9831 | −0.479900 | ||||||||
\(850\) | 88.7328 | 3.04351 | ||||||||
\(851\) | 16.4801 | 0.564930 | ||||||||
\(852\) | −66.3446 | −2.27293 | ||||||||
\(853\) | −27.7324 | −0.949539 | −0.474770 | − | 0.880110i | \(-0.657469\pi\) | ||||
−0.474770 | + | 0.880110i | \(0.657469\pi\) | |||||||
\(854\) | 14.6541 | 0.501454 | ||||||||
\(855\) | 23.4826 | 0.803088 | ||||||||
\(856\) | 128.037 | 4.37623 | ||||||||
\(857\) | −49.5757 | −1.69347 | −0.846737 | − | 0.532012i | \(-0.821436\pi\) | ||||
−0.846737 | + | 0.532012i | \(0.821436\pi\) | |||||||
\(858\) | −6.56942 | −0.224276 | ||||||||
\(859\) | 5.67823 | 0.193739 | 0.0968694 | − | 0.995297i | \(-0.469117\pi\) | ||||
0.0968694 | + | 0.995297i | \(0.469117\pi\) | |||||||
\(860\) | 216.672 | 7.38845 | ||||||||
\(861\) | −4.54473 | −0.154884 | ||||||||
\(862\) | −72.6217 | −2.47351 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | −95.1360 | −3.23659 | ||||||||
\(865\) | −0.535181 | −0.0181967 | ||||||||
\(866\) | 70.0044 | 2.37885 | ||||||||
\(867\) | −0.201176 | −0.00683230 | ||||||||
\(868\) | −0.455798 | −0.0154708 | ||||||||
\(869\) | −25.2353 | −0.856049 | ||||||||
\(870\) | −65.5286 | −2.22163 | ||||||||
\(871\) | 0.187607 | 0.00635681 | ||||||||
\(872\) | −79.8921 | −2.70549 | ||||||||
\(873\) | −6.21146 | −0.210226 | ||||||||
\(874\) | 29.5870 | 1.00080 | ||||||||
\(875\) | 10.2736 | 0.347312 | ||||||||
\(876\) | 64.3908 | 2.17556 | ||||||||
\(877\) | −47.0585 | −1.58905 | −0.794527 | − | 0.607229i | \(-0.792281\pi\) | ||||
−0.794527 | + | 0.607229i | \(0.792281\pi\) | |||||||
\(878\) | −49.0310 | −1.65472 | ||||||||
\(879\) | 18.3019 | 0.617308 | ||||||||
\(880\) | −315.149 | −10.6237 | ||||||||
\(881\) | 39.7337 | 1.33866 | 0.669331 | − | 0.742964i | \(-0.266581\pi\) | ||||
0.669331 | + | 0.742964i | \(0.266581\pi\) | |||||||
\(882\) | 5.96060 | 0.200704 | ||||||||
\(883\) | −2.08887 | −0.0702961 | −0.0351481 | − | 0.999382i | \(-0.511190\pi\) | ||||
−0.0351481 | + | 0.999382i | \(0.511190\pi\) | |||||||
\(884\) | −9.77911 | −0.328907 | ||||||||
\(885\) | −3.47924 | −0.116953 | ||||||||
\(886\) | −92.3082 | −3.10116 | ||||||||
\(887\) | −25.1053 | −0.842955 | −0.421477 | − | 0.906839i | \(-0.638488\pi\) | ||||
−0.421477 | + | 0.906839i | \(0.638488\pi\) | |||||||
\(888\) | 37.4631 | 1.25718 | ||||||||
\(889\) | −11.9245 | −0.399934 | ||||||||
\(890\) | 136.677 | 4.58142 | ||||||||
\(891\) | −14.6695 | −0.491446 | ||||||||
\(892\) | −1.28778 | −0.0431182 | ||||||||
\(893\) | 18.8332 | 0.630228 | ||||||||
\(894\) | 39.7632 | 1.32988 | ||||||||
\(895\) | −29.4762 | −0.985282 | ||||||||
\(896\) | −32.2637 | −1.07786 | ||||||||
\(897\) | −1.43141 | −0.0477933 | ||||||||
\(898\) | −97.6445 | −3.25844 | ||||||||
\(899\) | 0.632265 | 0.0210872 | ||||||||
\(900\) | −92.9559 | −3.09853 | ||||||||
\(901\) | 41.5114 | 1.38294 | ||||||||
\(902\) | 84.5909 | 2.81657 | ||||||||
\(903\) | −10.0695 | −0.335092 | ||||||||
\(904\) | −112.099 | −3.72836 | ||||||||
\(905\) | 76.3569 | 2.53819 | ||||||||
\(906\) | −30.5166 | −1.01385 | ||||||||
\(907\) | 3.58011 | 0.118876 | 0.0594378 | − | 0.998232i | \(-0.481069\pi\) | ||||
0.0594378 | + | 0.998232i | \(0.481069\pi\) | |||||||
\(908\) | −125.766 | −4.17370 | ||||||||
\(909\) | −22.5593 | −0.748246 | ||||||||
\(910\) | −4.26192 | −0.141281 | ||||||||
\(911\) | −36.1281 | −1.19698 | −0.598489 | − | 0.801131i | \(-0.704232\pi\) | ||||
−0.598489 | + | 0.801131i | \(0.704232\pi\) | |||||||
\(912\) | 38.3246 | 1.26906 | ||||||||
\(913\) | 7.24322 | 0.239716 | ||||||||
\(914\) | −42.8588 | −1.41764 | ||||||||
\(915\) | 17.3731 | 0.574336 | ||||||||
\(916\) | −122.208 | −4.03788 | ||||||||
\(917\) | 10.5085 | 0.347022 | ||||||||
\(918\) | 52.6468 | 1.73760 | ||||||||
\(919\) | 33.8793 | 1.11757 | 0.558787 | − | 0.829311i | \(-0.311267\pi\) | ||||
0.558787 | + | 0.829311i | \(0.311267\pi\) | |||||||
\(920\) | −120.509 | −3.97307 | ||||||||
\(921\) | −20.2731 | −0.668021 | ||||||||
\(922\) | 3.02859 | 0.0997414 | ||||||||
\(923\) | 5.98558 | 0.197018 | ||||||||
\(924\) | 29.8053 | 0.980523 | ||||||||
\(925\) | 35.5627 | 1.16929 | ||||||||
\(926\) | 26.3284 | 0.865205 | ||||||||
\(927\) | −13.8047 | −0.453407 | ||||||||
\(928\) | 152.474 | 5.00522 | ||||||||
\(929\) | 35.1702 | 1.15390 | 0.576949 | − | 0.816780i | \(-0.304243\pi\) | ||||
0.576949 | + | 0.816780i | \(0.304243\pi\) | |||||||
\(930\) | −0.740835 | −0.0242929 | ||||||||
\(931\) | −2.98619 | −0.0978684 | ||||||||
\(932\) | −63.2699 | −2.07247 | ||||||||
\(933\) | −10.7620 | −0.352333 | ||||||||
\(934\) | 44.1017 | 1.44305 | ||||||||
\(935\) | 91.5794 | 2.99497 | ||||||||
\(936\) | 8.83461 | 0.288768 | ||||||||
\(937\) | 7.59282 | 0.248047 | 0.124023 | − | 0.992279i | \(-0.460420\pi\) | ||||
0.124023 | + | 0.992279i | \(0.460420\pi\) | |||||||
\(938\) | −1.16694 | −0.0381018 | ||||||||
\(939\) | −21.6594 | −0.706827 | ||||||||
\(940\) | −121.949 | −3.97754 | ||||||||
\(941\) | −38.4311 | −1.25282 | −0.626408 | − | 0.779495i | \(-0.715476\pi\) | ||||
−0.626408 | + | 0.779495i | \(0.715476\pi\) | |||||||
\(942\) | 46.9281 | 1.52900 | ||||||||
\(943\) | 18.4315 | 0.600211 | ||||||||
\(944\) | 15.4169 | 0.501776 | ||||||||
\(945\) | 16.7358 | 0.544415 | ||||||||
\(946\) | 187.423 | 6.09366 | ||||||||
\(947\) | −23.8402 | −0.774703 | −0.387351 | − | 0.921932i | \(-0.626610\pi\) | ||||
−0.387351 | + | 0.921932i | \(0.626610\pi\) | |||||||
\(948\) | −19.8713 | −0.645389 | ||||||||
\(949\) | −5.80931 | −0.188578 | ||||||||
\(950\) | 63.8463 | 2.07145 | ||||||||
\(951\) | −6.17886 | −0.200363 | ||||||||
\(952\) | 38.2615 | 1.24006 | ||||||||
\(953\) | −19.7189 | −0.638758 | −0.319379 | − | 0.947627i | \(-0.603474\pi\) | ||||
−0.319379 | + | 0.947627i | \(0.603474\pi\) | |||||||
\(954\) | −59.6199 | −1.93027 | ||||||||
\(955\) | 69.0225 | 2.23352 | ||||||||
\(956\) | 137.116 | 4.43466 | ||||||||
\(957\) | −41.3447 | −1.33649 | ||||||||
\(958\) | −66.3373 | −2.14326 | ||||||||
\(959\) | 4.88617 | 0.157783 | ||||||||
\(960\) | −86.5937 | −2.79480 | ||||||||
\(961\) | −30.9929 | −0.999769 | ||||||||
\(962\) | −5.37330 | −0.173242 | ||||||||
\(963\) | 30.4492 | 0.981211 | ||||||||
\(964\) | −25.9650 | −0.836278 | ||||||||
\(965\) | 6.12047 | 0.197025 | ||||||||
\(966\) | 8.90352 | 0.286466 | ||||||||
\(967\) | 35.2356 | 1.13310 | 0.566550 | − | 0.824027i | \(-0.308278\pi\) | ||||
0.566550 | + | 0.824027i | \(0.308278\pi\) | |||||||
\(968\) | −247.546 | −7.95642 | ||||||||
\(969\) | −11.1368 | −0.357765 | ||||||||
\(970\) | −27.6253 | −0.886996 | ||||||||
\(971\) | 2.30692 | 0.0740326 | 0.0370163 | − | 0.999315i | \(-0.488215\pi\) | ||||
0.0370163 | + | 0.999315i | \(0.488215\pi\) | |||||||
\(972\) | −87.0173 | −2.79108 | ||||||||
\(973\) | −16.0765 | −0.515389 | ||||||||
\(974\) | 43.7640 | 1.40229 | ||||||||
\(975\) | −3.08886 | −0.0989226 | ||||||||
\(976\) | −76.9819 | −2.46413 | ||||||||
\(977\) | 29.8815 | 0.955995 | 0.477997 | − | 0.878361i | \(-0.341363\pi\) | ||||
0.477997 | + | 0.878361i | \(0.341363\pi\) | |||||||
\(978\) | −11.4880 | −0.367344 | ||||||||
\(979\) | 86.2353 | 2.75609 | ||||||||
\(980\) | 19.3362 | 0.617674 | ||||||||
\(981\) | −18.9995 | −0.606608 | ||||||||
\(982\) | −2.84377 | −0.0907485 | ||||||||
\(983\) | −49.1865 | −1.56881 | −0.784403 | − | 0.620252i | \(-0.787030\pi\) | ||||
−0.784403 | + | 0.620252i | \(0.787030\pi\) | |||||||
\(984\) | 41.8990 | 1.33569 | ||||||||
\(985\) | −40.8782 | −1.30249 | ||||||||
\(986\) | −84.3771 | −2.68711 | ||||||||
\(987\) | 5.66740 | 0.180395 | ||||||||
\(988\) | −7.03641 | −0.223858 | ||||||||
\(989\) | 40.8376 | 1.29856 | ||||||||
\(990\) | −131.529 | −4.18027 | ||||||||
\(991\) | −27.9441 | −0.887675 | −0.443837 | − | 0.896107i | \(-0.646383\pi\) | ||||
−0.443837 | + | 0.896107i | \(0.646383\pi\) | |||||||
\(992\) | 1.72380 | 0.0547308 | ||||||||
\(993\) | −27.1111 | −0.860345 | ||||||||
\(994\) | −37.2310 | −1.18090 | ||||||||
\(995\) | 65.9925 | 2.09210 | ||||||||
\(996\) | 5.70360 | 0.180725 | ||||||||
\(997\) | 58.9359 | 1.86652 | 0.933259 | − | 0.359205i | \(-0.116952\pi\) | ||||
0.933259 | + | 0.359205i | \(0.116952\pi\) | |||||||
\(998\) | −51.2514 | −1.62233 | ||||||||
\(999\) | 21.1000 | 0.667574 |
(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 | 6041.2.a.f.1.5 | ✓ | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.f.1.5 | ✓ | 132 | 1.1 | even | 1 | trivial |