Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8035,2,Mod(1,8035)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8035, 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("8035.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8035 = 5 \cdot 1607 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8035.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: | \(64.1597980241\) |
Analytic rank: | \(1\) |
Dimension: | \(140\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8035.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.36612 | −1.67310 | −0.836551 | − | 0.547889i | \(-0.815432\pi\) | ||||
−0.836551 | + | 0.547889i | \(0.815432\pi\) | |||||||
\(3\) | −3.07539 | −1.77558 | −0.887788 | − | 0.460252i | \(-0.847759\pi\) | ||||
−0.887788 | + | 0.460252i | \(0.847759\pi\) | |||||||
\(4\) | 3.59854 | 1.79927 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 7.27675 | 2.97072 | ||||||||
\(7\) | 3.28740 | 1.24252 | 0.621260 | − | 0.783604i | \(-0.286621\pi\) | ||||
0.621260 | + | 0.783604i | \(0.286621\pi\) | |||||||
\(8\) | −3.78235 | −1.33726 | ||||||||
\(9\) | 6.45802 | 2.15267 | ||||||||
\(10\) | 2.36612 | 0.748234 | ||||||||
\(11\) | −5.16172 | −1.55632 | −0.778159 | − | 0.628067i | \(-0.783846\pi\) | ||||
−0.778159 | + | 0.628067i | \(0.783846\pi\) | |||||||
\(12\) | −11.0669 | −3.19474 | ||||||||
\(13\) | −0.588339 | −0.163176 | −0.0815880 | − | 0.996666i | \(-0.525999\pi\) | ||||
−0.0815880 | + | 0.996666i | \(0.525999\pi\) | |||||||
\(14\) | −7.77839 | −2.07886 | ||||||||
\(15\) | 3.07539 | 0.794062 | ||||||||
\(16\) | 1.75242 | 0.438104 | ||||||||
\(17\) | −5.86859 | −1.42334 | −0.711671 | − | 0.702513i | \(-0.752061\pi\) | ||||
−0.711671 | + | 0.702513i | \(0.752061\pi\) | |||||||
\(18\) | −15.2805 | −3.60164 | ||||||||
\(19\) | −5.21720 | −1.19691 | −0.598454 | − | 0.801157i | \(-0.704218\pi\) | ||||
−0.598454 | + | 0.801157i | \(0.704218\pi\) | |||||||
\(20\) | −3.59854 | −0.804658 | ||||||||
\(21\) | −10.1100 | −2.20619 | ||||||||
\(22\) | 12.2133 | 2.60388 | ||||||||
\(23\) | −0.898889 | −0.187431 | −0.0937157 | − | 0.995599i | \(-0.529874\pi\) | ||||
−0.0937157 | + | 0.995599i | \(0.529874\pi\) | |||||||
\(24\) | 11.6322 | 2.37441 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.39208 | 0.273010 | ||||||||
\(27\) | −10.6348 | −2.04666 | ||||||||
\(28\) | 11.8298 | 2.23563 | ||||||||
\(29\) | −0.0172396 | −0.00320132 | −0.00160066 | − | 0.999999i | \(-0.500510\pi\) | ||||
−0.00160066 | + | 0.999999i | \(0.500510\pi\) | |||||||
\(30\) | −7.27675 | −1.32855 | ||||||||
\(31\) | 10.1623 | 1.82520 | 0.912600 | − | 0.408853i | \(-0.134071\pi\) | ||||
0.912600 | + | 0.408853i | \(0.134071\pi\) | |||||||
\(32\) | 3.41826 | 0.604268 | ||||||||
\(33\) | 15.8743 | 2.76336 | ||||||||
\(34\) | 13.8858 | 2.38140 | ||||||||
\(35\) | −3.28740 | −0.555672 | ||||||||
\(36\) | 23.2395 | 3.87324 | ||||||||
\(37\) | −0.677044 | −0.111305 | −0.0556527 | − | 0.998450i | \(-0.517724\pi\) | ||||
−0.0556527 | + | 0.998450i | \(0.517724\pi\) | |||||||
\(38\) | 12.3445 | 2.00255 | ||||||||
\(39\) | 1.80937 | 0.289731 | ||||||||
\(40\) | 3.78235 | 0.598042 | ||||||||
\(41\) | 5.24336 | 0.818875 | 0.409437 | − | 0.912338i | \(-0.365725\pi\) | ||||
0.409437 | + | 0.912338i | \(0.365725\pi\) | |||||||
\(42\) | 23.9216 | 3.69118 | ||||||||
\(43\) | 0.668571 | 0.101956 | 0.0509781 | − | 0.998700i | \(-0.483766\pi\) | ||||
0.0509781 | + | 0.998700i | \(0.483766\pi\) | |||||||
\(44\) | −18.5747 | −2.80024 | ||||||||
\(45\) | −6.45802 | −0.962705 | ||||||||
\(46\) | 2.12688 | 0.313592 | ||||||||
\(47\) | −10.7620 | −1.56980 | −0.784898 | − | 0.619625i | \(-0.787285\pi\) | ||||
−0.784898 | + | 0.619625i | \(0.787285\pi\) | |||||||
\(48\) | −5.38937 | −0.777888 | ||||||||
\(49\) | 3.80699 | 0.543856 | ||||||||
\(50\) | −2.36612 | −0.334620 | ||||||||
\(51\) | 18.0482 | 2.52725 | ||||||||
\(52\) | −2.11716 | −0.293598 | ||||||||
\(53\) | 2.11254 | 0.290179 | 0.145090 | − | 0.989419i | \(-0.453653\pi\) | ||||
0.145090 | + | 0.989419i | \(0.453653\pi\) | |||||||
\(54\) | 25.1632 | 3.42427 | ||||||||
\(55\) | 5.16172 | 0.696007 | ||||||||
\(56\) | −12.4341 | −1.66157 | ||||||||
\(57\) | 16.0449 | 2.12520 | ||||||||
\(58\) | 0.0407911 | 0.00535614 | ||||||||
\(59\) | 13.7279 | 1.78723 | 0.893613 | − | 0.448838i | \(-0.148162\pi\) | ||||
0.893613 | + | 0.448838i | \(0.148162\pi\) | |||||||
\(60\) | 11.0669 | 1.42873 | ||||||||
\(61\) | −2.99581 | −0.383574 | −0.191787 | − | 0.981437i | \(-0.561428\pi\) | ||||
−0.191787 | + | 0.981437i | \(0.561428\pi\) | |||||||
\(62\) | −24.0452 | −3.05375 | ||||||||
\(63\) | 21.2301 | 2.67474 | ||||||||
\(64\) | −11.5929 | −1.44911 | ||||||||
\(65\) | 0.588339 | 0.0729745 | ||||||||
\(66\) | −37.5606 | −4.62339 | ||||||||
\(67\) | −1.58919 | −0.194151 | −0.0970755 | − | 0.995277i | \(-0.530949\pi\) | ||||
−0.0970755 | + | 0.995277i | \(0.530949\pi\) | |||||||
\(68\) | −21.1183 | −2.56098 | ||||||||
\(69\) | 2.76443 | 0.332799 | ||||||||
\(70\) | 7.77839 | 0.929696 | ||||||||
\(71\) | 8.60165 | 1.02083 | 0.510414 | − | 0.859929i | \(-0.329492\pi\) | ||||
0.510414 | + | 0.859929i | \(0.329492\pi\) | |||||||
\(72\) | −24.4265 | −2.87869 | ||||||||
\(73\) | −6.33151 | −0.741047 | −0.370523 | − | 0.928823i | \(-0.620822\pi\) | ||||
−0.370523 | + | 0.928823i | \(0.620822\pi\) | |||||||
\(74\) | 1.60197 | 0.186225 | ||||||||
\(75\) | −3.07539 | −0.355115 | ||||||||
\(76\) | −18.7743 | −2.15356 | ||||||||
\(77\) | −16.9686 | −1.93376 | ||||||||
\(78\) | −4.28120 | −0.484750 | ||||||||
\(79\) | 8.41599 | 0.946873 | 0.473436 | − | 0.880828i | \(-0.343013\pi\) | ||||
0.473436 | + | 0.880828i | \(0.343013\pi\) | |||||||
\(80\) | −1.75242 | −0.195926 | ||||||||
\(81\) | 13.3320 | 1.48133 | ||||||||
\(82\) | −12.4064 | −1.37006 | ||||||||
\(83\) | −8.25560 | −0.906170 | −0.453085 | − | 0.891467i | \(-0.649677\pi\) | ||||
−0.453085 | + | 0.891467i | \(0.649677\pi\) | |||||||
\(84\) | −36.3814 | −3.96953 | ||||||||
\(85\) | 5.86859 | 0.636537 | ||||||||
\(86\) | −1.58192 | −0.170583 | ||||||||
\(87\) | 0.0530186 | 0.00568419 | ||||||||
\(88\) | 19.5234 | 2.08120 | ||||||||
\(89\) | −5.42031 | −0.574551 | −0.287276 | − | 0.957848i | \(-0.592750\pi\) | ||||
−0.287276 | + | 0.957848i | \(0.592750\pi\) | |||||||
\(90\) | 15.2805 | 1.61070 | ||||||||
\(91\) | −1.93411 | −0.202749 | ||||||||
\(92\) | −3.23469 | −0.337240 | ||||||||
\(93\) | −31.2530 | −3.24078 | ||||||||
\(94\) | 25.4642 | 2.62643 | ||||||||
\(95\) | 5.21720 | 0.535273 | ||||||||
\(96\) | −10.5125 | −1.07292 | ||||||||
\(97\) | 11.1628 | 1.13341 | 0.566703 | − | 0.823922i | \(-0.308219\pi\) | ||||
0.566703 | + | 0.823922i | \(0.308219\pi\) | |||||||
\(98\) | −9.00782 | −0.909927 | ||||||||
\(99\) | −33.3345 | −3.35025 | ||||||||
\(100\) | 3.59854 | 0.359854 | ||||||||
\(101\) | −2.23367 | −0.222258 | −0.111129 | − | 0.993806i | \(-0.535447\pi\) | ||||
−0.111129 | + | 0.993806i | \(0.535447\pi\) | |||||||
\(102\) | −42.7042 | −4.22835 | ||||||||
\(103\) | −9.11025 | −0.897659 | −0.448830 | − | 0.893617i | \(-0.648159\pi\) | ||||
−0.448830 | + | 0.893617i | \(0.648159\pi\) | |||||||
\(104\) | 2.22530 | 0.218209 | ||||||||
\(105\) | 10.1100 | 0.986638 | ||||||||
\(106\) | −4.99852 | −0.485499 | ||||||||
\(107\) | −13.6076 | −1.31549 | −0.657747 | − | 0.753239i | \(-0.728490\pi\) | ||||
−0.657747 | + | 0.753239i | \(0.728490\pi\) | |||||||
\(108\) | −38.2696 | −3.68250 | ||||||||
\(109\) | 11.1141 | 1.06454 | 0.532268 | − | 0.846576i | \(-0.321340\pi\) | ||||
0.532268 | + | 0.846576i | \(0.321340\pi\) | |||||||
\(110\) | −12.2133 | −1.16449 | ||||||||
\(111\) | 2.08217 | 0.197631 | ||||||||
\(112\) | 5.76090 | 0.544353 | ||||||||
\(113\) | −3.85274 | −0.362436 | −0.181218 | − | 0.983443i | \(-0.558004\pi\) | ||||
−0.181218 | + | 0.983443i | \(0.558004\pi\) | |||||||
\(114\) | −37.9643 | −3.55568 | ||||||||
\(115\) | 0.898889 | 0.0838218 | ||||||||
\(116\) | −0.0620376 | −0.00576004 | ||||||||
\(117\) | −3.79951 | −0.351264 | ||||||||
\(118\) | −32.4820 | −2.99021 | ||||||||
\(119\) | −19.2924 | −1.76853 | ||||||||
\(120\) | −11.6322 | −1.06187 | ||||||||
\(121\) | 15.6434 | 1.42213 | ||||||||
\(122\) | 7.08845 | 0.641758 | ||||||||
\(123\) | −16.1254 | −1.45397 | ||||||||
\(124\) | 36.5694 | 3.28403 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −50.2330 | −4.47511 | ||||||||
\(127\) | 5.74292 | 0.509602 | 0.254801 | − | 0.966994i | \(-0.417990\pi\) | ||||
0.254801 | + | 0.966994i | \(0.417990\pi\) | |||||||
\(128\) | 20.5936 | 1.82024 | ||||||||
\(129\) | −2.05612 | −0.181031 | ||||||||
\(130\) | −1.39208 | −0.122094 | ||||||||
\(131\) | 21.2655 | 1.85797 | 0.928986 | − | 0.370115i | \(-0.120682\pi\) | ||||
0.928986 | + | 0.370115i | \(0.120682\pi\) | |||||||
\(132\) | 57.1244 | 4.97204 | ||||||||
\(133\) | −17.1510 | −1.48718 | ||||||||
\(134\) | 3.76023 | 0.324834 | ||||||||
\(135\) | 10.6348 | 0.915294 | ||||||||
\(136\) | 22.1970 | 1.90338 | ||||||||
\(137\) | 1.45751 | 0.124524 | 0.0622618 | − | 0.998060i | \(-0.480169\pi\) | ||||
0.0622618 | + | 0.998060i | \(0.480169\pi\) | |||||||
\(138\) | −6.54099 | −0.556806 | ||||||||
\(139\) | 17.5384 | 1.48758 | 0.743792 | − | 0.668411i | \(-0.233025\pi\) | ||||
0.743792 | + | 0.668411i | \(0.233025\pi\) | |||||||
\(140\) | −11.8298 | −0.999804 | ||||||||
\(141\) | 33.0973 | 2.78729 | ||||||||
\(142\) | −20.3526 | −1.70795 | ||||||||
\(143\) | 3.03684 | 0.253954 | ||||||||
\(144\) | 11.3171 | 0.943096 | ||||||||
\(145\) | 0.0172396 | 0.00143167 | ||||||||
\(146\) | 14.9811 | 1.23985 | ||||||||
\(147\) | −11.7080 | −0.965659 | ||||||||
\(148\) | −2.43637 | −0.200268 | ||||||||
\(149\) | −14.1271 | −1.15733 | −0.578667 | − | 0.815564i | \(-0.696427\pi\) | ||||
−0.578667 | + | 0.815564i | \(0.696427\pi\) | |||||||
\(150\) | 7.27675 | 0.594144 | ||||||||
\(151\) | −0.306774 | −0.0249649 | −0.0124825 | − | 0.999922i | \(-0.503973\pi\) | ||||
−0.0124825 | + | 0.999922i | \(0.503973\pi\) | |||||||
\(152\) | 19.7333 | 1.60058 | ||||||||
\(153\) | −37.8994 | −3.06399 | ||||||||
\(154\) | 40.1499 | 3.23537 | ||||||||
\(155\) | −10.1623 | −0.816254 | ||||||||
\(156\) | 6.51110 | 0.521305 | ||||||||
\(157\) | 17.3500 | 1.38468 | 0.692341 | − | 0.721570i | \(-0.256579\pi\) | ||||
0.692341 | + | 0.721570i | \(0.256579\pi\) | |||||||
\(158\) | −19.9133 | −1.58421 | ||||||||
\(159\) | −6.49687 | −0.515235 | ||||||||
\(160\) | −3.41826 | −0.270237 | ||||||||
\(161\) | −2.95501 | −0.232887 | ||||||||
\(162\) | −31.5451 | −2.47842 | ||||||||
\(163\) | 2.35349 | 0.184339 | 0.0921696 | − | 0.995743i | \(-0.470620\pi\) | ||||
0.0921696 | + | 0.995743i | \(0.470620\pi\) | |||||||
\(164\) | 18.8684 | 1.47338 | ||||||||
\(165\) | −15.8743 | −1.23581 | ||||||||
\(166\) | 19.5338 | 1.51612 | ||||||||
\(167\) | 13.6983 | 1.06001 | 0.530005 | − | 0.847995i | \(-0.322190\pi\) | ||||
0.530005 | + | 0.847995i | \(0.322190\pi\) | |||||||
\(168\) | 38.2396 | 2.95025 | ||||||||
\(169\) | −12.6539 | −0.973374 | ||||||||
\(170\) | −13.8858 | −1.06499 | ||||||||
\(171\) | −33.6928 | −2.57655 | ||||||||
\(172\) | 2.40588 | 0.183447 | ||||||||
\(173\) | −4.21847 | −0.320724 | −0.160362 | − | 0.987058i | \(-0.551266\pi\) | ||||
−0.160362 | + | 0.987058i | \(0.551266\pi\) | |||||||
\(174\) | −0.125449 | −0.00951023 | ||||||||
\(175\) | 3.28740 | 0.248504 | ||||||||
\(176\) | −9.04549 | −0.681830 | ||||||||
\(177\) | −42.2188 | −3.17336 | ||||||||
\(178\) | 12.8251 | 0.961283 | ||||||||
\(179\) | −13.0669 | −0.976663 | −0.488332 | − | 0.872658i | \(-0.662394\pi\) | ||||
−0.488332 | + | 0.872658i | \(0.662394\pi\) | |||||||
\(180\) | −23.2395 | −1.73217 | ||||||||
\(181\) | 0.0904172 | 0.00672066 | 0.00336033 | − | 0.999994i | \(-0.498930\pi\) | ||||
0.00336033 | + | 0.999994i | \(0.498930\pi\) | |||||||
\(182\) | 4.57633 | 0.339220 | ||||||||
\(183\) | 9.21327 | 0.681065 | ||||||||
\(184\) | 3.39991 | 0.250645 | ||||||||
\(185\) | 0.677044 | 0.0497773 | ||||||||
\(186\) | 73.9484 | 5.42216 | ||||||||
\(187\) | 30.2920 | 2.21517 | ||||||||
\(188\) | −38.7274 | −2.82449 | ||||||||
\(189\) | −34.9607 | −2.54302 | ||||||||
\(190\) | −12.3445 | −0.895567 | ||||||||
\(191\) | 3.42710 | 0.247976 | 0.123988 | − | 0.992284i | \(-0.460432\pi\) | ||||
0.123988 | + | 0.992284i | \(0.460432\pi\) | |||||||
\(192\) | 35.6525 | 2.57300 | ||||||||
\(193\) | −8.29879 | −0.597360 | −0.298680 | − | 0.954353i | \(-0.596546\pi\) | ||||
−0.298680 | + | 0.954353i | \(0.596546\pi\) | |||||||
\(194\) | −26.4124 | −1.89630 | ||||||||
\(195\) | −1.80937 | −0.129572 | ||||||||
\(196\) | 13.6996 | 0.978545 | ||||||||
\(197\) | 11.1523 | 0.794568 | 0.397284 | − | 0.917696i | \(-0.369953\pi\) | ||||
0.397284 | + | 0.917696i | \(0.369953\pi\) | |||||||
\(198\) | 78.8736 | 5.60530 | ||||||||
\(199\) | 21.8295 | 1.54745 | 0.773727 | − | 0.633520i | \(-0.218390\pi\) | ||||
0.773727 | + | 0.633520i | \(0.218390\pi\) | |||||||
\(200\) | −3.78235 | −0.267452 | ||||||||
\(201\) | 4.88739 | 0.344730 | ||||||||
\(202\) | 5.28513 | 0.371860 | ||||||||
\(203\) | −0.0566736 | −0.00397771 | ||||||||
\(204\) | 64.9471 | 4.54721 | ||||||||
\(205\) | −5.24336 | −0.366212 | ||||||||
\(206\) | 21.5560 | 1.50188 | ||||||||
\(207\) | −5.80504 | −0.403478 | ||||||||
\(208\) | −1.03102 | −0.0714881 | ||||||||
\(209\) | 26.9297 | 1.86277 | ||||||||
\(210\) | −23.9216 | −1.65075 | ||||||||
\(211\) | −18.7450 | −1.29046 | −0.645230 | − | 0.763989i | \(-0.723238\pi\) | ||||
−0.645230 | + | 0.763989i | \(0.723238\pi\) | |||||||
\(212\) | 7.60205 | 0.522111 | ||||||||
\(213\) | −26.4534 | −1.81256 | ||||||||
\(214\) | 32.1972 | 2.20096 | ||||||||
\(215\) | −0.668571 | −0.0455962 | ||||||||
\(216\) | 40.2243 | 2.73692 | ||||||||
\(217\) | 33.4075 | 2.26785 | ||||||||
\(218\) | −26.2973 | −1.78108 | ||||||||
\(219\) | 19.4718 | 1.31579 | ||||||||
\(220\) | 18.5747 | 1.25230 | ||||||||
\(221\) | 3.45272 | 0.232255 | ||||||||
\(222\) | −4.92668 | −0.330657 | ||||||||
\(223\) | −10.4204 | −0.697803 | −0.348901 | − | 0.937159i | \(-0.613445\pi\) | ||||
−0.348901 | + | 0.937159i | \(0.613445\pi\) | |||||||
\(224\) | 11.2372 | 0.750815 | ||||||||
\(225\) | 6.45802 | 0.430535 | ||||||||
\(226\) | 9.11607 | 0.606392 | ||||||||
\(227\) | −6.01240 | −0.399057 | −0.199529 | − | 0.979892i | \(-0.563941\pi\) | ||||
−0.199529 | + | 0.979892i | \(0.563941\pi\) | |||||||
\(228\) | 57.7383 | 3.82381 | ||||||||
\(229\) | 17.5419 | 1.15920 | 0.579600 | − | 0.814901i | \(-0.303209\pi\) | ||||
0.579600 | + | 0.814901i | \(0.303209\pi\) | |||||||
\(230\) | −2.12688 | −0.140243 | ||||||||
\(231\) | 52.1852 | 3.43353 | ||||||||
\(232\) | 0.0652063 | 0.00428100 | ||||||||
\(233\) | −4.30961 | −0.282332 | −0.141166 | − | 0.989986i | \(-0.545085\pi\) | ||||
−0.141166 | + | 0.989986i | \(0.545085\pi\) | |||||||
\(234\) | 8.99010 | 0.587701 | ||||||||
\(235\) | 10.7620 | 0.702034 | ||||||||
\(236\) | 49.4006 | 3.21570 | ||||||||
\(237\) | −25.8824 | −1.68125 | ||||||||
\(238\) | 45.6482 | 2.95893 | ||||||||
\(239\) | 27.1554 | 1.75653 | 0.878267 | − | 0.478170i | \(-0.158700\pi\) | ||||
0.878267 | + | 0.478170i | \(0.158700\pi\) | |||||||
\(240\) | 5.38937 | 0.347882 | ||||||||
\(241\) | 27.9422 | 1.79992 | 0.899958 | − | 0.435976i | \(-0.143597\pi\) | ||||
0.899958 | + | 0.435976i | \(0.143597\pi\) | |||||||
\(242\) | −37.0142 | −2.37936 | ||||||||
\(243\) | −9.09671 | −0.583554 | ||||||||
\(244\) | −10.7805 | −0.690153 | ||||||||
\(245\) | −3.80699 | −0.243220 | ||||||||
\(246\) | 38.1546 | 2.43265 | ||||||||
\(247\) | 3.06948 | 0.195307 | ||||||||
\(248\) | −38.4373 | −2.44077 | ||||||||
\(249\) | 25.3892 | 1.60897 | ||||||||
\(250\) | 2.36612 | 0.149647 | ||||||||
\(251\) | −30.3794 | −1.91753 | −0.958766 | − | 0.284198i | \(-0.908273\pi\) | ||||
−0.958766 | + | 0.284198i | \(0.908273\pi\) | |||||||
\(252\) | 76.3974 | 4.81258 | ||||||||
\(253\) | 4.63982 | 0.291703 | ||||||||
\(254\) | −13.5885 | −0.852616 | ||||||||
\(255\) | −18.0482 | −1.13022 | ||||||||
\(256\) | −25.5413 | −1.59633 | ||||||||
\(257\) | 10.5086 | 0.655508 | 0.327754 | − | 0.944763i | \(-0.393708\pi\) | ||||
0.327754 | + | 0.944763i | \(0.393708\pi\) | |||||||
\(258\) | 4.86503 | 0.302883 | ||||||||
\(259\) | −2.22571 | −0.138299 | ||||||||
\(260\) | 2.11716 | 0.131301 | ||||||||
\(261\) | −0.111334 | −0.00689140 | ||||||||
\(262\) | −50.3167 | −3.10858 | ||||||||
\(263\) | 7.69863 | 0.474718 | 0.237359 | − | 0.971422i | \(-0.423718\pi\) | ||||
0.237359 | + | 0.971422i | \(0.423718\pi\) | |||||||
\(264\) | −60.0421 | −3.69534 | ||||||||
\(265\) | −2.11254 | −0.129772 | ||||||||
\(266\) | 40.5814 | 2.48821 | ||||||||
\(267\) | 16.6696 | 1.02016 | ||||||||
\(268\) | −5.71878 | −0.349330 | ||||||||
\(269\) | −10.1928 | −0.621465 | −0.310733 | − | 0.950497i | \(-0.600574\pi\) | ||||
−0.310733 | + | 0.950497i | \(0.600574\pi\) | |||||||
\(270\) | −25.1632 | −1.53138 | ||||||||
\(271\) | −28.1002 | −1.70696 | −0.853481 | − | 0.521123i | \(-0.825513\pi\) | ||||
−0.853481 | + | 0.521123i | \(0.825513\pi\) | |||||||
\(272\) | −10.2842 | −0.623572 | ||||||||
\(273\) | 5.94813 | 0.359997 | ||||||||
\(274\) | −3.44865 | −0.208341 | ||||||||
\(275\) | −5.16172 | −0.311264 | ||||||||
\(276\) | 9.94793 | 0.598795 | ||||||||
\(277\) | −12.8701 | −0.773291 | −0.386645 | − | 0.922229i | \(-0.626366\pi\) | ||||
−0.386645 | + | 0.922229i | \(0.626366\pi\) | |||||||
\(278\) | −41.4979 | −2.48888 | ||||||||
\(279\) | 65.6282 | 3.92906 | ||||||||
\(280\) | 12.4341 | 0.743079 | ||||||||
\(281\) | −14.6774 | −0.875578 | −0.437789 | − | 0.899078i | \(-0.644238\pi\) | ||||
−0.437789 | + | 0.899078i | \(0.644238\pi\) | |||||||
\(282\) | −78.3123 | −4.66343 | ||||||||
\(283\) | 17.7741 | 1.05656 | 0.528282 | − | 0.849069i | \(-0.322837\pi\) | ||||
0.528282 | + | 0.849069i | \(0.322837\pi\) | |||||||
\(284\) | 30.9534 | 1.83675 | ||||||||
\(285\) | −16.0449 | −0.950419 | ||||||||
\(286\) | −7.18555 | −0.424890 | ||||||||
\(287\) | 17.2370 | 1.01747 | ||||||||
\(288\) | 22.0752 | 1.30079 | ||||||||
\(289\) | 17.4403 | 1.02590 | ||||||||
\(290\) | −0.0407911 | −0.00239534 | ||||||||
\(291\) | −34.3298 | −2.01245 | ||||||||
\(292\) | −22.7842 | −1.33334 | ||||||||
\(293\) | −5.41529 | −0.316365 | −0.158182 | − | 0.987410i | \(-0.550563\pi\) | ||||
−0.158182 | + | 0.987410i | \(0.550563\pi\) | |||||||
\(294\) | 27.7025 | 1.61565 | ||||||||
\(295\) | −13.7279 | −0.799272 | ||||||||
\(296\) | 2.56081 | 0.148844 | ||||||||
\(297\) | 54.8937 | 3.18525 | ||||||||
\(298\) | 33.4264 | 1.93634 | ||||||||
\(299\) | 0.528852 | 0.0305843 | ||||||||
\(300\) | −11.0669 | −0.638949 | ||||||||
\(301\) | 2.19786 | 0.126683 | ||||||||
\(302\) | 0.725866 | 0.0417689 | ||||||||
\(303\) | 6.86939 | 0.394636 | ||||||||
\(304\) | −9.14271 | −0.524371 | ||||||||
\(305\) | 2.99581 | 0.171539 | ||||||||
\(306\) | 89.6748 | 5.12637 | ||||||||
\(307\) | −1.20893 | −0.0689976 | −0.0344988 | − | 0.999405i | \(-0.510983\pi\) | ||||
−0.0344988 | + | 0.999405i | \(0.510983\pi\) | |||||||
\(308\) | −61.0624 | −3.47935 | ||||||||
\(309\) | 28.0176 | 1.59386 | ||||||||
\(310\) | 24.0452 | 1.36568 | ||||||||
\(311\) | 12.5722 | 0.712903 | 0.356452 | − | 0.934314i | \(-0.383986\pi\) | ||||
0.356452 | + | 0.934314i | \(0.383986\pi\) | |||||||
\(312\) | −6.84367 | −0.387447 | ||||||||
\(313\) | 10.7037 | 0.605011 | 0.302506 | − | 0.953148i | \(-0.402177\pi\) | ||||
0.302506 | + | 0.953148i | \(0.402177\pi\) | |||||||
\(314\) | −41.0523 | −2.31672 | ||||||||
\(315\) | −21.2301 | −1.19618 | ||||||||
\(316\) | 30.2853 | 1.70368 | ||||||||
\(317\) | −23.0882 | −1.29676 | −0.648381 | − | 0.761316i | \(-0.724553\pi\) | ||||
−0.648381 | + | 0.761316i | \(0.724553\pi\) | |||||||
\(318\) | 15.3724 | 0.862041 | ||||||||
\(319\) | 0.0889863 | 0.00498227 | ||||||||
\(320\) | 11.5929 | 0.648060 | ||||||||
\(321\) | 41.8486 | 2.33576 | ||||||||
\(322\) | 6.99191 | 0.389644 | ||||||||
\(323\) | 30.6176 | 1.70361 | ||||||||
\(324\) | 47.9756 | 2.66531 | ||||||||
\(325\) | −0.588339 | −0.0326352 | ||||||||
\(326\) | −5.56864 | −0.308418 | ||||||||
\(327\) | −34.1801 | −1.89016 | ||||||||
\(328\) | −19.8322 | −1.09505 | ||||||||
\(329\) | −35.3789 | −1.95050 | ||||||||
\(330\) | 37.5606 | 2.06764 | ||||||||
\(331\) | −9.07569 | −0.498845 | −0.249423 | − | 0.968395i | \(-0.580241\pi\) | ||||
−0.249423 | + | 0.968395i | \(0.580241\pi\) | |||||||
\(332\) | −29.7081 | −1.63045 | ||||||||
\(333\) | −4.37236 | −0.239604 | ||||||||
\(334\) | −32.4120 | −1.77350 | ||||||||
\(335\) | 1.58919 | 0.0868270 | ||||||||
\(336\) | −17.7170 | −0.966541 | ||||||||
\(337\) | −1.84113 | −0.100293 | −0.0501464 | − | 0.998742i | \(-0.515969\pi\) | ||||
−0.0501464 | + | 0.998742i | \(0.515969\pi\) | |||||||
\(338\) | 29.9406 | 1.62855 | ||||||||
\(339\) | 11.8487 | 0.643532 | ||||||||
\(340\) | 21.1183 | 1.14530 | ||||||||
\(341\) | −52.4549 | −2.84059 | ||||||||
\(342\) | 79.7213 | 4.31083 | ||||||||
\(343\) | −10.4967 | −0.566768 | ||||||||
\(344\) | −2.52877 | −0.136342 | ||||||||
\(345\) | −2.76443 | −0.148832 | ||||||||
\(346\) | 9.98142 | 0.536605 | ||||||||
\(347\) | 27.8846 | 1.49692 | 0.748462 | − | 0.663177i | \(-0.230792\pi\) | ||||
0.748462 | + | 0.663177i | \(0.230792\pi\) | |||||||
\(348\) | 0.190790 | 0.0102274 | ||||||||
\(349\) | −34.1007 | −1.82537 | −0.912683 | − | 0.408668i | \(-0.865993\pi\) | ||||
−0.912683 | + | 0.408668i | \(0.865993\pi\) | |||||||
\(350\) | −7.77839 | −0.415773 | ||||||||
\(351\) | 6.25685 | 0.333966 | ||||||||
\(352\) | −17.6441 | −0.940434 | ||||||||
\(353\) | −10.0598 | −0.535431 | −0.267716 | − | 0.963498i | \(-0.586269\pi\) | ||||
−0.267716 | + | 0.963498i | \(0.586269\pi\) | |||||||
\(354\) | 99.8949 | 5.30935 | ||||||||
\(355\) | −8.60165 | −0.456528 | ||||||||
\(356\) | −19.5052 | −1.03377 | ||||||||
\(357\) | 59.3316 | 3.14016 | ||||||||
\(358\) | 30.9178 | 1.63406 | ||||||||
\(359\) | −3.59741 | −0.189864 | −0.0949320 | − | 0.995484i | \(-0.530263\pi\) | ||||
−0.0949320 | + | 0.995484i | \(0.530263\pi\) | |||||||
\(360\) | 24.4265 | 1.28739 | ||||||||
\(361\) | 8.21918 | 0.432588 | ||||||||
\(362\) | −0.213938 | −0.0112443 | ||||||||
\(363\) | −48.1095 | −2.52510 | ||||||||
\(364\) | −6.95996 | −0.364801 | ||||||||
\(365\) | 6.33151 | 0.331406 | ||||||||
\(366\) | −21.7997 | −1.13949 | ||||||||
\(367\) | 6.66468 | 0.347893 | 0.173947 | − | 0.984755i | \(-0.444348\pi\) | ||||
0.173947 | + | 0.984755i | \(0.444348\pi\) | |||||||
\(368\) | −1.57523 | −0.0821145 | ||||||||
\(369\) | 33.8617 | 1.76277 | ||||||||
\(370\) | −1.60197 | −0.0832824 | ||||||||
\(371\) | 6.94475 | 0.360553 | ||||||||
\(372\) | −112.465 | −5.83105 | ||||||||
\(373\) | 5.81113 | 0.300889 | 0.150444 | − | 0.988618i | \(-0.451930\pi\) | ||||
0.150444 | + | 0.988618i | \(0.451930\pi\) | |||||||
\(374\) | −71.6747 | −3.70621 | ||||||||
\(375\) | 3.07539 | 0.158812 | ||||||||
\(376\) | 40.7055 | 2.09923 | ||||||||
\(377\) | 0.0101428 | 0.000522379 0 | ||||||||
\(378\) | 82.7213 | 4.25473 | ||||||||
\(379\) | −21.3947 | −1.09897 | −0.549487 | − | 0.835502i | \(-0.685177\pi\) | ||||
−0.549487 | + | 0.835502i | \(0.685177\pi\) | |||||||
\(380\) | 18.7743 | 0.963102 | ||||||||
\(381\) | −17.6617 | −0.904837 | ||||||||
\(382\) | −8.10893 | −0.414889 | ||||||||
\(383\) | 19.8857 | 1.01611 | 0.508055 | − | 0.861325i | \(-0.330365\pi\) | ||||
0.508055 | + | 0.861325i | \(0.330365\pi\) | |||||||
\(384\) | −63.3334 | −3.23197 | ||||||||
\(385\) | 16.9686 | 0.864802 | ||||||||
\(386\) | 19.6360 | 0.999445 | ||||||||
\(387\) | 4.31765 | 0.219478 | ||||||||
\(388\) | 40.1696 | 2.03930 | ||||||||
\(389\) | 10.3201 | 0.523251 | 0.261625 | − | 0.965169i | \(-0.415741\pi\) | ||||
0.261625 | + | 0.965169i | \(0.415741\pi\) | |||||||
\(390\) | 4.28120 | 0.216787 | ||||||||
\(391\) | 5.27521 | 0.266779 | ||||||||
\(392\) | −14.3994 | −0.727278 | ||||||||
\(393\) | −65.3996 | −3.29897 | ||||||||
\(394\) | −26.3877 | −1.32939 | ||||||||
\(395\) | −8.41599 | −0.423454 | ||||||||
\(396\) | −119.956 | −6.02800 | ||||||||
\(397\) | 0.116493 | 0.00584659 | 0.00292330 | − | 0.999996i | \(-0.499069\pi\) | ||||
0.00292330 | + | 0.999996i | \(0.499069\pi\) | |||||||
\(398\) | −51.6513 | −2.58905 | ||||||||
\(399\) | 52.7461 | 2.64061 | ||||||||
\(400\) | 1.75242 | 0.0876209 | ||||||||
\(401\) | −14.5740 | −0.727790 | −0.363895 | − | 0.931440i | \(-0.618553\pi\) | ||||
−0.363895 | + | 0.931440i | \(0.618553\pi\) | |||||||
\(402\) | −11.5642 | −0.576768 | ||||||||
\(403\) | −5.97887 | −0.297829 | ||||||||
\(404\) | −8.03794 | −0.399902 | ||||||||
\(405\) | −13.3320 | −0.662471 | ||||||||
\(406\) | 0.134097 | 0.00665511 | ||||||||
\(407\) | 3.49471 | 0.173227 | ||||||||
\(408\) | −68.2645 | −3.37960 | ||||||||
\(409\) | 12.0558 | 0.596121 | 0.298060 | − | 0.954547i | \(-0.403660\pi\) | ||||
0.298060 | + | 0.954547i | \(0.403660\pi\) | |||||||
\(410\) | 12.4064 | 0.612710 | ||||||||
\(411\) | −4.48241 | −0.221101 | ||||||||
\(412\) | −32.7836 | −1.61513 | ||||||||
\(413\) | 45.1292 | 2.22066 | ||||||||
\(414\) | 13.7355 | 0.675061 | ||||||||
\(415\) | 8.25560 | 0.405252 | ||||||||
\(416\) | −2.01109 | −0.0986020 | ||||||||
\(417\) | −53.9373 | −2.64132 | ||||||||
\(418\) | −63.7191 | −3.11660 | ||||||||
\(419\) | −16.6203 | −0.811957 | −0.405979 | − | 0.913883i | \(-0.633069\pi\) | ||||
−0.405979 | + | 0.913883i | \(0.633069\pi\) | |||||||
\(420\) | 36.3814 | 1.77523 | ||||||||
\(421\) | −7.30206 | −0.355881 | −0.177940 | − | 0.984041i | \(-0.556943\pi\) | ||||
−0.177940 | + | 0.984041i | \(0.556943\pi\) | |||||||
\(422\) | 44.3530 | 2.15907 | ||||||||
\(423\) | −69.5011 | −3.37926 | ||||||||
\(424\) | −7.99034 | −0.388045 | ||||||||
\(425\) | −5.86859 | −0.284668 | ||||||||
\(426\) | 62.5921 | 3.03260 | ||||||||
\(427\) | −9.84841 | −0.476598 | ||||||||
\(428\) | −48.9674 | −2.36693 | ||||||||
\(429\) | −9.33948 | −0.450914 | ||||||||
\(430\) | 1.58192 | 0.0762870 | ||||||||
\(431\) | 33.8206 | 1.62908 | 0.814541 | − | 0.580106i | \(-0.196989\pi\) | ||||
0.814541 | + | 0.580106i | \(0.196989\pi\) | |||||||
\(432\) | −18.6365 | −0.896651 | ||||||||
\(433\) | −1.81250 | −0.0871033 | −0.0435516 | − | 0.999051i | \(-0.513867\pi\) | ||||
−0.0435516 | + | 0.999051i | \(0.513867\pi\) | |||||||
\(434\) | −79.0462 | −3.79434 | ||||||||
\(435\) | −0.0530186 | −0.00254205 | ||||||||
\(436\) | 39.9945 | 1.91539 | ||||||||
\(437\) | 4.68968 | 0.224338 | ||||||||
\(438\) | −46.0728 | −2.20144 | ||||||||
\(439\) | −7.76897 | −0.370793 | −0.185396 | − | 0.982664i | \(-0.559357\pi\) | ||||
−0.185396 | + | 0.982664i | \(0.559357\pi\) | |||||||
\(440\) | −19.5234 | −0.930743 | ||||||||
\(441\) | 24.5856 | 1.17074 | ||||||||
\(442\) | −8.16956 | −0.388586 | ||||||||
\(443\) | −10.7822 | −0.512280 | −0.256140 | − | 0.966640i | \(-0.582451\pi\) | ||||
−0.256140 | + | 0.966640i | \(0.582451\pi\) | |||||||
\(444\) | 7.49279 | 0.355592 | ||||||||
\(445\) | 5.42031 | 0.256947 | ||||||||
\(446\) | 24.6560 | 1.16749 | ||||||||
\(447\) | 43.4462 | 2.05493 | ||||||||
\(448\) | −38.1103 | −1.80054 | ||||||||
\(449\) | 9.06052 | 0.427592 | 0.213796 | − | 0.976878i | \(-0.431417\pi\) | ||||
0.213796 | + | 0.976878i | \(0.431417\pi\) | |||||||
\(450\) | −15.2805 | −0.720328 | ||||||||
\(451\) | −27.0648 | −1.27443 | ||||||||
\(452\) | −13.8643 | −0.652120 | ||||||||
\(453\) | 0.943451 | 0.0443272 | ||||||||
\(454\) | 14.2261 | 0.667663 | ||||||||
\(455\) | 1.93411 | 0.0906723 | ||||||||
\(456\) | −60.6875 | −2.84195 | ||||||||
\(457\) | −21.8343 | −1.02136 | −0.510682 | − | 0.859770i | \(-0.670607\pi\) | ||||
−0.510682 | + | 0.859770i | \(0.670607\pi\) | |||||||
\(458\) | −41.5062 | −1.93946 | ||||||||
\(459\) | 62.4110 | 2.91310 | ||||||||
\(460\) | 3.23469 | 0.150818 | ||||||||
\(461\) | 10.0497 | 0.468062 | 0.234031 | − | 0.972229i | \(-0.424808\pi\) | ||||
0.234031 | + | 0.972229i | \(0.424808\pi\) | |||||||
\(462\) | −123.477 | −5.74465 | ||||||||
\(463\) | 33.3348 | 1.54920 | 0.774599 | − | 0.632452i | \(-0.217951\pi\) | ||||
0.774599 | + | 0.632452i | \(0.217951\pi\) | |||||||
\(464\) | −0.0302110 | −0.00140251 | ||||||||
\(465\) | 31.2530 | 1.44932 | ||||||||
\(466\) | 10.1971 | 0.472370 | ||||||||
\(467\) | 26.0048 | 1.20336 | 0.601678 | − | 0.798738i | \(-0.294499\pi\) | ||||
0.601678 | + | 0.798738i | \(0.294499\pi\) | |||||||
\(468\) | −13.6727 | −0.632020 | ||||||||
\(469\) | −5.22432 | −0.241236 | ||||||||
\(470\) | −25.4642 | −1.17457 | ||||||||
\(471\) | −53.3581 | −2.45861 | ||||||||
\(472\) | −51.9239 | −2.38999 | ||||||||
\(473\) | −3.45098 | −0.158676 | ||||||||
\(474\) | 61.2411 | 2.81289 | ||||||||
\(475\) | −5.21720 | −0.239382 | ||||||||
\(476\) | −69.4244 | −3.18206 | ||||||||
\(477\) | 13.6428 | 0.624661 | ||||||||
\(478\) | −64.2529 | −2.93886 | ||||||||
\(479\) | −5.92247 | −0.270604 | −0.135302 | − | 0.990804i | \(-0.543201\pi\) | ||||
−0.135302 | + | 0.990804i | \(0.543201\pi\) | |||||||
\(480\) | 10.5125 | 0.479827 | ||||||||
\(481\) | 0.398331 | 0.0181623 | ||||||||
\(482\) | −66.1147 | −3.01144 | ||||||||
\(483\) | 9.08780 | 0.413509 | ||||||||
\(484\) | 56.2934 | 2.55879 | ||||||||
\(485\) | −11.1628 | −0.506874 | ||||||||
\(486\) | 21.5239 | 0.976346 | ||||||||
\(487\) | 35.8580 | 1.62488 | 0.812442 | − | 0.583042i | \(-0.198138\pi\) | ||||
0.812442 | + | 0.583042i | \(0.198138\pi\) | |||||||
\(488\) | 11.3312 | 0.512938 | ||||||||
\(489\) | −7.23789 | −0.327309 | ||||||||
\(490\) | 9.00782 | 0.406932 | ||||||||
\(491\) | 21.2768 | 0.960208 | 0.480104 | − | 0.877211i | \(-0.340599\pi\) | ||||
0.480104 | + | 0.877211i | \(0.340599\pi\) | |||||||
\(492\) | −58.0278 | −2.61609 | ||||||||
\(493\) | 0.101172 | 0.00455657 | ||||||||
\(494\) | −7.26278 | −0.326768 | ||||||||
\(495\) | 33.3345 | 1.49828 | ||||||||
\(496\) | 17.8086 | 0.799628 | ||||||||
\(497\) | 28.2771 | 1.26840 | ||||||||
\(498\) | −60.0740 | −2.69198 | ||||||||
\(499\) | 36.6870 | 1.64233 | 0.821167 | − | 0.570688i | \(-0.193323\pi\) | ||||
0.821167 | + | 0.570688i | \(0.193323\pi\) | |||||||
\(500\) | −3.59854 | −0.160932 | ||||||||
\(501\) | −42.1277 | −1.88213 | ||||||||
\(502\) | 71.8814 | 3.20823 | ||||||||
\(503\) | −20.2739 | −0.903970 | −0.451985 | − | 0.892026i | \(-0.649284\pi\) | ||||
−0.451985 | + | 0.892026i | \(0.649284\pi\) | |||||||
\(504\) | −80.2996 | −3.57683 | ||||||||
\(505\) | 2.23367 | 0.0993968 | ||||||||
\(506\) | −10.9784 | −0.488049 | ||||||||
\(507\) | 38.9155 | 1.72830 | ||||||||
\(508\) | 20.6661 | 0.916911 | ||||||||
\(509\) | −1.62790 | −0.0721555 | −0.0360777 | − | 0.999349i | \(-0.511486\pi\) | ||||
−0.0360777 | + | 0.999349i | \(0.511486\pi\) | |||||||
\(510\) | 42.7042 | 1.89098 | ||||||||
\(511\) | −20.8142 | −0.920766 | ||||||||
\(512\) | 19.2467 | 0.850593 | ||||||||
\(513\) | 55.4837 | 2.44966 | ||||||||
\(514\) | −24.8646 | −1.09673 | ||||||||
\(515\) | 9.11025 | 0.401445 | ||||||||
\(516\) | −7.39902 | −0.325724 | ||||||||
\(517\) | 55.5504 | 2.44310 | ||||||||
\(518\) | 5.26631 | 0.231389 | ||||||||
\(519\) | 12.9734 | 0.569471 | ||||||||
\(520\) | −2.22530 | −0.0975860 | ||||||||
\(521\) | 18.9189 | 0.828852 | 0.414426 | − | 0.910083i | \(-0.363982\pi\) | ||||
0.414426 | + | 0.910083i | \(0.363982\pi\) | |||||||
\(522\) | 0.263430 | 0.0115300 | ||||||||
\(523\) | −5.81238 | −0.254157 | −0.127079 | − | 0.991893i | \(-0.540560\pi\) | ||||
−0.127079 | + | 0.991893i | \(0.540560\pi\) | |||||||
\(524\) | 76.5246 | 3.34299 | ||||||||
\(525\) | −10.1100 | −0.441238 | ||||||||
\(526\) | −18.2159 | −0.794251 | ||||||||
\(527\) | −59.6382 | −2.59788 | ||||||||
\(528\) | 27.8184 | 1.21064 | ||||||||
\(529\) | −22.1920 | −0.964869 | ||||||||
\(530\) | 4.99852 | 0.217122 | ||||||||
\(531\) | 88.6554 | 3.84731 | ||||||||
\(532\) | −61.7187 | −2.67584 | ||||||||
\(533\) | −3.08487 | −0.133621 | ||||||||
\(534\) | −39.4422 | −1.70683 | ||||||||
\(535\) | 13.6076 | 0.588307 | ||||||||
\(536\) | 6.01088 | 0.259631 | ||||||||
\(537\) | 40.1857 | 1.73414 | ||||||||
\(538\) | 24.1174 | 1.03977 | ||||||||
\(539\) | −19.6507 | −0.846413 | ||||||||
\(540\) | 38.2696 | 1.64686 | ||||||||
\(541\) | 9.28912 | 0.399370 | 0.199685 | − | 0.979860i | \(-0.436008\pi\) | ||||
0.199685 | + | 0.979860i | \(0.436008\pi\) | |||||||
\(542\) | 66.4884 | 2.85592 | ||||||||
\(543\) | −0.278068 | −0.0119330 | ||||||||
\(544\) | −20.0603 | −0.860080 | ||||||||
\(545\) | −11.1141 | −0.476075 | ||||||||
\(546\) | −14.0740 | −0.602312 | ||||||||
\(547\) | 16.3683 | 0.699858 | 0.349929 | − | 0.936776i | \(-0.386206\pi\) | ||||
0.349929 | + | 0.936776i | \(0.386206\pi\) | |||||||
\(548\) | 5.24491 | 0.224052 | ||||||||
\(549\) | −19.3470 | −0.825709 | ||||||||
\(550\) | 12.2133 | 0.520776 | ||||||||
\(551\) | 0.0899427 | 0.00383169 | ||||||||
\(552\) | −10.4560 | −0.445039 | ||||||||
\(553\) | 27.6667 | 1.17651 | ||||||||
\(554\) | 30.4523 | 1.29379 | ||||||||
\(555\) | −2.08217 | −0.0883833 | ||||||||
\(556\) | 63.1125 | 2.67657 | ||||||||
\(557\) | −8.66389 | −0.367101 | −0.183550 | − | 0.983010i | \(-0.558759\pi\) | ||||
−0.183550 | + | 0.983010i | \(0.558759\pi\) | |||||||
\(558\) | −155.285 | −6.57372 | ||||||||
\(559\) | −0.393347 | −0.0166368 | ||||||||
\(560\) | −5.76090 | −0.243442 | ||||||||
\(561\) | −93.1598 | −3.93321 | ||||||||
\(562\) | 34.7285 | 1.46493 | ||||||||
\(563\) | 44.9070 | 1.89260 | 0.946302 | − | 0.323283i | \(-0.104787\pi\) | ||||
0.946302 | + | 0.323283i | \(0.104787\pi\) | |||||||
\(564\) | 119.102 | 5.01510 | ||||||||
\(565\) | 3.85274 | 0.162086 | ||||||||
\(566\) | −42.0558 | −1.76774 | ||||||||
\(567\) | 43.8275 | 1.84058 | ||||||||
\(568\) | −32.5344 | −1.36511 | ||||||||
\(569\) | 26.8612 | 1.12608 | 0.563040 | − | 0.826430i | \(-0.309632\pi\) | ||||
0.563040 | + | 0.826430i | \(0.309632\pi\) | |||||||
\(570\) | 37.9643 | 1.59015 | ||||||||
\(571\) | 10.9228 | 0.457104 | 0.228552 | − | 0.973532i | \(-0.426601\pi\) | ||||
0.228552 | + | 0.973532i | \(0.426601\pi\) | |||||||
\(572\) | 10.9282 | 0.456931 | ||||||||
\(573\) | −10.5397 | −0.440300 | ||||||||
\(574\) | −40.7849 | −1.70233 | ||||||||
\(575\) | −0.898889 | −0.0374863 | ||||||||
\(576\) | −74.8669 | −3.11945 | ||||||||
\(577\) | 8.39183 | 0.349356 | 0.174678 | − | 0.984626i | \(-0.444112\pi\) | ||||
0.174678 | + | 0.984626i | \(0.444112\pi\) | |||||||
\(578\) | −41.2659 | −1.71644 | ||||||||
\(579\) | 25.5220 | 1.06066 | ||||||||
\(580\) | 0.0620376 | 0.00257597 | ||||||||
\(581\) | −27.1395 | −1.12593 | ||||||||
\(582\) | 81.2286 | 3.36703 | ||||||||
\(583\) | −10.9043 | −0.451611 | ||||||||
\(584\) | 23.9480 | 0.990973 | ||||||||
\(585\) | 3.79951 | 0.157090 | ||||||||
\(586\) | 12.8133 | 0.529311 | ||||||||
\(587\) | −5.46457 | −0.225547 | −0.112773 | − | 0.993621i | \(-0.535973\pi\) | ||||
−0.112773 | + | 0.993621i | \(0.535973\pi\) | |||||||
\(588\) | −42.1317 | −1.73748 | ||||||||
\(589\) | −53.0187 | −2.18460 | ||||||||
\(590\) | 32.4820 | 1.33726 | ||||||||
\(591\) | −34.2976 | −1.41082 | ||||||||
\(592\) | −1.18646 | −0.0487633 | ||||||||
\(593\) | 6.14451 | 0.252325 | 0.126162 | − | 0.992010i | \(-0.459734\pi\) | ||||
0.126162 | + | 0.992010i | \(0.459734\pi\) | |||||||
\(594\) | −129.885 | −5.32926 | ||||||||
\(595\) | 19.2924 | 0.790911 | ||||||||
\(596\) | −50.8368 | −2.08236 | ||||||||
\(597\) | −67.1342 | −2.74762 | ||||||||
\(598\) | −1.25133 | −0.0511706 | ||||||||
\(599\) | −10.3899 | −0.424521 | −0.212261 | − | 0.977213i | \(-0.568083\pi\) | ||||
−0.212261 | + | 0.977213i | \(0.568083\pi\) | |||||||
\(600\) | 11.6322 | 0.474882 | ||||||||
\(601\) | −29.1871 | −1.19057 | −0.595284 | − | 0.803516i | \(-0.702960\pi\) | ||||
−0.595284 | + | 0.803516i | \(0.702960\pi\) | |||||||
\(602\) | −5.20041 | −0.211953 | ||||||||
\(603\) | −10.2630 | −0.417944 | ||||||||
\(604\) | −1.10394 | −0.0449187 | ||||||||
\(605\) | −15.6434 | −0.635994 | ||||||||
\(606\) | −16.2538 | −0.660267 | ||||||||
\(607\) | 36.0792 | 1.46441 | 0.732204 | − | 0.681085i | \(-0.238492\pi\) | ||||
0.732204 | + | 0.681085i | \(0.238492\pi\) | |||||||
\(608\) | −17.8337 | −0.723253 | ||||||||
\(609\) | 0.174293 | 0.00706272 | ||||||||
\(610\) | −7.08845 | −0.287003 | ||||||||
\(611\) | 6.33169 | 0.256153 | ||||||||
\(612\) | −136.383 | −5.51294 | ||||||||
\(613\) | −26.4548 | −1.06850 | −0.534250 | − | 0.845327i | \(-0.679406\pi\) | ||||
−0.534250 | + | 0.845327i | \(0.679406\pi\) | |||||||
\(614\) | 2.86049 | 0.115440 | ||||||||
\(615\) | 16.1254 | 0.650237 | ||||||||
\(616\) | 64.1813 | 2.58594 | ||||||||
\(617\) | −28.9200 | −1.16427 | −0.582137 | − | 0.813091i | \(-0.697783\pi\) | ||||
−0.582137 | + | 0.813091i | \(0.697783\pi\) | |||||||
\(618\) | −66.2930 | −2.66670 | ||||||||
\(619\) | 43.9134 | 1.76503 | 0.882514 | − | 0.470286i | \(-0.155849\pi\) | ||||
0.882514 | + | 0.470286i | \(0.155849\pi\) | |||||||
\(620\) | −36.5694 | −1.46866 | ||||||||
\(621\) | 9.55947 | 0.383608 | ||||||||
\(622\) | −29.7473 | −1.19276 | ||||||||
\(623\) | −17.8187 | −0.713892 | ||||||||
\(624\) | 3.17077 | 0.126933 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −25.3264 | −1.01225 | ||||||||
\(627\) | −82.8195 | −3.30749 | ||||||||
\(628\) | 62.4348 | 2.49142 | ||||||||
\(629\) | 3.97329 | 0.158425 | ||||||||
\(630\) | 50.2330 | 2.00133 | ||||||||
\(631\) | −9.39118 | −0.373857 | −0.186928 | − | 0.982374i | \(-0.559853\pi\) | ||||
−0.186928 | + | 0.982374i | \(0.559853\pi\) | |||||||
\(632\) | −31.8322 | −1.26622 | ||||||||
\(633\) | 57.6482 | 2.29131 | ||||||||
\(634\) | 54.6295 | 2.16961 | ||||||||
\(635\) | −5.74292 | −0.227901 | ||||||||
\(636\) | −23.3793 | −0.927048 | ||||||||
\(637\) | −2.23980 | −0.0887442 | ||||||||
\(638\) | −0.210553 | −0.00833585 | ||||||||
\(639\) | 55.5496 | 2.19751 | ||||||||
\(640\) | −20.5936 | −0.814034 | ||||||||
\(641\) | 17.8921 | 0.706695 | 0.353348 | − | 0.935492i | \(-0.385043\pi\) | ||||
0.353348 | + | 0.935492i | \(0.385043\pi\) | |||||||
\(642\) | −99.0190 | −3.90797 | ||||||||
\(643\) | −4.94125 | −0.194864 | −0.0974320 | − | 0.995242i | \(-0.531063\pi\) | ||||
−0.0974320 | + | 0.995242i | \(0.531063\pi\) | |||||||
\(644\) | −10.6337 | −0.419027 | ||||||||
\(645\) | 2.05612 | 0.0809595 | ||||||||
\(646\) | −72.4450 | −2.85031 | ||||||||
\(647\) | −29.0644 | −1.14264 | −0.571320 | − | 0.820727i | \(-0.693568\pi\) | ||||
−0.571320 | + | 0.820727i | \(0.693568\pi\) | |||||||
\(648\) | −50.4261 | −1.98092 | ||||||||
\(649\) | −70.8599 | −2.78149 | ||||||||
\(650\) | 1.39208 | 0.0546020 | ||||||||
\(651\) | −102.741 | −4.02674 | ||||||||
\(652\) | 8.46912 | 0.331676 | ||||||||
\(653\) | 4.18506 | 0.163774 | 0.0818870 | − | 0.996642i | \(-0.473905\pi\) | ||||
0.0818870 | + | 0.996642i | \(0.473905\pi\) | |||||||
\(654\) | 80.8744 | 3.16244 | ||||||||
\(655\) | −21.2655 | −0.830910 | ||||||||
\(656\) | 9.18855 | 0.358753 | ||||||||
\(657\) | −40.8890 | −1.59523 | ||||||||
\(658\) | 83.7109 | 3.26339 | ||||||||
\(659\) | −7.20160 | −0.280535 | −0.140267 | − | 0.990114i | \(-0.544796\pi\) | ||||
−0.140267 | + | 0.990114i | \(0.544796\pi\) | |||||||
\(660\) | −57.1244 | −2.22356 | ||||||||
\(661\) | −1.65025 | −0.0641873 | −0.0320937 | − | 0.999485i | \(-0.510217\pi\) | ||||
−0.0320937 | + | 0.999485i | \(0.510217\pi\) | |||||||
\(662\) | 21.4742 | 0.834619 | ||||||||
\(663\) | −10.6185 | −0.412387 | ||||||||
\(664\) | 31.2256 | 1.21179 | ||||||||
\(665\) | 17.1510 | 0.665088 | ||||||||
\(666\) | 10.3456 | 0.400882 | ||||||||
\(667\) | 0.0154965 | 0.000600028 0 | ||||||||
\(668\) | 49.2940 | 1.90724 | ||||||||
\(669\) | 32.0468 | 1.23900 | ||||||||
\(670\) | −3.76023 | −0.145270 | ||||||||
\(671\) | 15.4635 | 0.596963 | ||||||||
\(672\) | −34.5587 | −1.33313 | ||||||||
\(673\) | 9.04261 | 0.348567 | 0.174284 | − | 0.984696i | \(-0.444239\pi\) | ||||
0.174284 | + | 0.984696i | \(0.444239\pi\) | |||||||
\(674\) | 4.35634 | 0.167800 | ||||||||
\(675\) | −10.6348 | −0.409332 | ||||||||
\(676\) | −45.5354 | −1.75136 | ||||||||
\(677\) | 23.9548 | 0.920657 | 0.460328 | − | 0.887749i | \(-0.347732\pi\) | ||||
0.460328 | + | 0.887749i | \(0.347732\pi\) | |||||||
\(678\) | −28.0355 | −1.07670 | ||||||||
\(679\) | 36.6964 | 1.40828 | ||||||||
\(680\) | −22.1970 | −0.851217 | ||||||||
\(681\) | 18.4905 | 0.708557 | ||||||||
\(682\) | 124.115 | 4.75260 | ||||||||
\(683\) | 16.0727 | 0.615005 | 0.307503 | − | 0.951547i | \(-0.400507\pi\) | ||||
0.307503 | + | 0.951547i | \(0.400507\pi\) | |||||||
\(684\) | −121.245 | −4.63591 | ||||||||
\(685\) | −1.45751 | −0.0556886 | ||||||||
\(686\) | 24.8365 | 0.948260 | ||||||||
\(687\) | −53.9481 | −2.05825 | ||||||||
\(688\) | 1.17162 | 0.0446674 | ||||||||
\(689\) | −1.24289 | −0.0473502 | ||||||||
\(690\) | 6.54099 | 0.249011 | ||||||||
\(691\) | −28.0749 | −1.06802 | −0.534009 | − | 0.845479i | \(-0.679315\pi\) | ||||
−0.534009 | + | 0.845479i | \(0.679315\pi\) | |||||||
\(692\) | −15.1803 | −0.577070 | ||||||||
\(693\) | −109.584 | −4.16275 | ||||||||
\(694\) | −65.9785 | −2.50451 | ||||||||
\(695\) | −17.5384 | −0.665268 | ||||||||
\(696\) | −0.200535 | −0.00760125 | ||||||||
\(697\) | −30.7711 | −1.16554 | ||||||||
\(698\) | 80.6864 | 3.05402 | ||||||||
\(699\) | 13.2537 | 0.501302 | ||||||||
\(700\) | 11.8298 | 0.447126 | ||||||||
\(701\) | −1.44616 | −0.0546208 | −0.0273104 | − | 0.999627i | \(-0.508694\pi\) | ||||
−0.0273104 | + | 0.999627i | \(0.508694\pi\) | |||||||
\(702\) | −14.8045 | −0.558759 | ||||||||
\(703\) | 3.53227 | 0.133222 | ||||||||
\(704\) | 59.8391 | 2.25527 | ||||||||
\(705\) | −33.0973 | −1.24652 | ||||||||
\(706\) | 23.8028 | 0.895831 | ||||||||
\(707\) | −7.34295 | −0.276160 | ||||||||
\(708\) | −151.926 | −5.70973 | ||||||||
\(709\) | −17.8710 | −0.671161 | −0.335580 | − | 0.942012i | \(-0.608932\pi\) | ||||
−0.335580 | + | 0.942012i | \(0.608932\pi\) | |||||||
\(710\) | 20.3526 | 0.763818 | ||||||||
\(711\) | 54.3506 | 2.03831 | ||||||||
\(712\) | 20.5015 | 0.768325 | ||||||||
\(713\) | −9.13477 | −0.342100 | ||||||||
\(714\) | −140.386 | −5.25381 | ||||||||
\(715\) | −3.03684 | −0.113572 | ||||||||
\(716\) | −47.0216 | −1.75728 | ||||||||
\(717\) | −83.5133 | −3.11886 | ||||||||
\(718\) | 8.51191 | 0.317662 | ||||||||
\(719\) | 52.4303 | 1.95532 | 0.977660 | − | 0.210193i | \(-0.0674091\pi\) | ||||
0.977660 | + | 0.210193i | \(0.0674091\pi\) | |||||||
\(720\) | −11.3171 | −0.421765 | ||||||||
\(721\) | −29.9490 | −1.11536 | ||||||||
\(722\) | −19.4476 | −0.723765 | ||||||||
\(723\) | −85.9332 | −3.19589 | ||||||||
\(724\) | 0.325370 | 0.0120923 | ||||||||
\(725\) | −0.0172396 | −0.000640264 0 | ||||||||
\(726\) | 113.833 | 4.22474 | ||||||||
\(727\) | 26.8833 | 0.997046 | 0.498523 | − | 0.866876i | \(-0.333876\pi\) | ||||
0.498523 | + | 0.866876i | \(0.333876\pi\) | |||||||
\(728\) | 7.31546 | 0.271129 | ||||||||
\(729\) | −12.0200 | −0.445184 | ||||||||
\(730\) | −14.9811 | −0.554476 | ||||||||
\(731\) | −3.92357 | −0.145118 | ||||||||
\(732\) | 33.1543 | 1.22542 | ||||||||
\(733\) | −11.1616 | −0.412265 | −0.206132 | − | 0.978524i | \(-0.566088\pi\) | ||||
−0.206132 | + | 0.978524i | \(0.566088\pi\) | |||||||
\(734\) | −15.7695 | −0.582061 | ||||||||
\(735\) | 11.7080 | 0.431856 | ||||||||
\(736\) | −3.07263 | −0.113259 | ||||||||
\(737\) | 8.20298 | 0.302161 | ||||||||
\(738\) | −80.1210 | −2.94929 | ||||||||
\(739\) | 12.7281 | 0.468212 | 0.234106 | − | 0.972211i | \(-0.424784\pi\) | ||||
0.234106 | + | 0.972211i | \(0.424784\pi\) | |||||||
\(740\) | 2.43637 | 0.0895628 | ||||||||
\(741\) | −9.43986 | −0.346782 | ||||||||
\(742\) | −16.4321 | −0.603243 | ||||||||
\(743\) | −48.6917 | −1.78633 | −0.893163 | − | 0.449732i | \(-0.851519\pi\) | ||||
−0.893163 | + | 0.449732i | \(0.851519\pi\) | |||||||
\(744\) | 118.210 | 4.33377 | ||||||||
\(745\) | 14.1271 | 0.517575 | ||||||||
\(746\) | −13.7499 | −0.503418 | ||||||||
\(747\) | −53.3149 | −1.95069 | ||||||||
\(748\) | 109.007 | 3.98569 | ||||||||
\(749\) | −44.7335 | −1.63453 | ||||||||
\(750\) | −7.27675 | −0.265709 | ||||||||
\(751\) | −54.4956 | −1.98857 | −0.994287 | − | 0.106744i | \(-0.965957\pi\) | ||||
−0.994287 | + | 0.106744i | \(0.965957\pi\) | |||||||
\(752\) | −18.8595 | −0.687734 | ||||||||
\(753\) | 93.4285 | 3.40472 | ||||||||
\(754\) | −0.0239990 | −0.000873993 0 | ||||||||
\(755\) | 0.306774 | 0.0111647 | ||||||||
\(756\) | −125.808 | −4.57558 | ||||||||
\(757\) | −22.6406 | −0.822888 | −0.411444 | − | 0.911435i | \(-0.634975\pi\) | ||||
−0.411444 | + | 0.911435i | \(0.634975\pi\) | |||||||
\(758\) | 50.6226 | 1.83870 | ||||||||
\(759\) | −14.2692 | −0.517941 | ||||||||
\(760\) | −19.7333 | −0.715801 | ||||||||
\(761\) | 45.4808 | 1.64868 | 0.824339 | − | 0.566097i | \(-0.191547\pi\) | ||||
0.824339 | + | 0.566097i | \(0.191547\pi\) | |||||||
\(762\) | 41.7898 | 1.51388 | ||||||||
\(763\) | 36.5364 | 1.32271 | ||||||||
\(764\) | 12.3325 | 0.446176 | ||||||||
\(765\) | 37.8994 | 1.37026 | ||||||||
\(766\) | −47.0519 | −1.70005 | ||||||||
\(767\) | −8.07669 | −0.291632 | ||||||||
\(768\) | 78.5495 | 2.83441 | ||||||||
\(769\) | −29.6728 | −1.07003 | −0.535013 | − | 0.844844i | \(-0.679693\pi\) | ||||
−0.535013 | + | 0.844844i | \(0.679693\pi\) | |||||||
\(770\) | −40.1499 | −1.44690 | ||||||||
\(771\) | −32.3180 | −1.16391 | ||||||||
\(772\) | −29.8636 | −1.07481 | ||||||||
\(773\) | 5.69643 | 0.204886 | 0.102443 | − | 0.994739i | \(-0.467334\pi\) | ||||
0.102443 | + | 0.994739i | \(0.467334\pi\) | |||||||
\(774\) | −10.2161 | −0.367210 | ||||||||
\(775\) | 10.1623 | 0.365040 | ||||||||
\(776\) | −42.2214 | −1.51566 | ||||||||
\(777\) | 6.84494 | 0.245561 | ||||||||
\(778\) | −24.4187 | −0.875452 | ||||||||
\(779\) | −27.3556 | −0.980117 | ||||||||
\(780\) | −6.51110 | −0.233135 | ||||||||
\(781\) | −44.3993 | −1.58873 | ||||||||
\(782\) | −12.4818 | −0.446348 | ||||||||
\(783\) | 0.183339 | 0.00655202 | ||||||||
\(784\) | 6.67144 | 0.238266 | ||||||||
\(785\) | −17.3500 | −0.619249 | ||||||||
\(786\) | 154.743 | 5.51952 | ||||||||
\(787\) | 13.5510 | 0.483042 | 0.241521 | − | 0.970396i | \(-0.422354\pi\) | ||||
0.241521 | + | 0.970396i | \(0.422354\pi\) | |||||||
\(788\) | 40.1320 | 1.42964 | ||||||||
\(789\) | −23.6763 | −0.842898 | ||||||||
\(790\) | 19.9133 | 0.708482 | ||||||||
\(791\) | −12.6655 | −0.450334 | ||||||||
\(792\) | 126.083 | 4.48015 | ||||||||
\(793\) | 1.76255 | 0.0625900 | ||||||||
\(794\) | −0.275636 | −0.00978195 | ||||||||
\(795\) | 6.49687 | 0.230420 | ||||||||
\(796\) | 78.5544 | 2.78429 | ||||||||
\(797\) | −1.90869 | −0.0676094 | −0.0338047 | − | 0.999428i | \(-0.510762\pi\) | ||||
−0.0338047 | + | 0.999428i | \(0.510762\pi\) | |||||||
\(798\) | −124.804 | −4.41800 | ||||||||
\(799\) | 63.1576 | 2.23436 | ||||||||
\(800\) | 3.41826 | 0.120854 | ||||||||
\(801\) | −35.0045 | −1.23682 | ||||||||
\(802\) | 34.4838 | 1.21767 | ||||||||
\(803\) | 32.6815 | 1.15330 | ||||||||
\(804\) | 17.5875 | 0.620263 | ||||||||
\(805\) | 2.95501 | 0.104150 | ||||||||
\(806\) | 14.1467 | 0.498298 | ||||||||
\(807\) | 31.3468 | 1.10346 | ||||||||
\(808\) | 8.44850 | 0.297217 | ||||||||
\(809\) | 44.7879 | 1.57466 | 0.787330 | − | 0.616532i | \(-0.211463\pi\) | ||||
0.787330 | + | 0.616532i | \(0.211463\pi\) | |||||||
\(810\) | 31.5451 | 1.10838 | ||||||||
\(811\) | −9.37215 | −0.329101 | −0.164550 | − | 0.986369i | \(-0.552617\pi\) | ||||
−0.164550 | + | 0.986369i | \(0.552617\pi\) | |||||||
\(812\) | −0.203942 | −0.00715697 | ||||||||
\(813\) | 86.4189 | 3.03084 | ||||||||
\(814\) | −8.26892 | −0.289826 | ||||||||
\(815\) | −2.35349 | −0.0824390 | ||||||||
\(816\) | 31.6280 | 1.10720 | ||||||||
\(817\) | −3.48807 | −0.122032 | ||||||||
\(818\) | −28.5255 | −0.997371 | ||||||||
\(819\) | −12.4905 | −0.436453 | ||||||||
\(820\) | −18.8684 | −0.658914 | ||||||||
\(821\) | −27.2939 | −0.952565 | −0.476283 | − | 0.879292i | \(-0.658016\pi\) | ||||
−0.476283 | + | 0.879292i | \(0.658016\pi\) | |||||||
\(822\) | 10.6059 | 0.369925 | ||||||||
\(823\) | −8.22499 | −0.286705 | −0.143353 | − | 0.989672i | \(-0.545788\pi\) | ||||
−0.143353 | + | 0.989672i | \(0.545788\pi\) | |||||||
\(824\) | 34.4581 | 1.20041 | ||||||||
\(825\) | 15.8743 | 0.552673 | ||||||||
\(826\) | −106.781 | −3.71540 | ||||||||
\(827\) | −41.2479 | −1.43433 | −0.717165 | − | 0.696904i | \(-0.754560\pi\) | ||||
−0.717165 | + | 0.696904i | \(0.754560\pi\) | |||||||
\(828\) | −20.8897 | −0.725967 | ||||||||
\(829\) | −5.81355 | −0.201913 | −0.100956 | − | 0.994891i | \(-0.532190\pi\) | ||||
−0.100956 | + | 0.994891i | \(0.532190\pi\) | |||||||
\(830\) | −19.5338 | −0.678027 | ||||||||
\(831\) | 39.5806 | 1.37304 | ||||||||
\(832\) | 6.82053 | 0.236459 | ||||||||
\(833\) | −22.3417 | −0.774093 | ||||||||
\(834\) | 127.622 | 4.41920 | ||||||||
\(835\) | −13.6983 | −0.474051 | ||||||||
\(836\) | 96.9078 | 3.35163 | ||||||||
\(837\) | −108.073 | −3.73556 | ||||||||
\(838\) | 39.3258 | 1.35849 | ||||||||
\(839\) | −29.2434 | −1.00959 | −0.504797 | − | 0.863238i | \(-0.668433\pi\) | ||||
−0.504797 | + | 0.863238i | \(0.668433\pi\) | |||||||
\(840\) | −38.2396 | −1.31939 | ||||||||
\(841\) | −28.9997 | −0.999990 | ||||||||
\(842\) | 17.2776 | 0.595425 | ||||||||
\(843\) | 45.1386 | 1.55466 | ||||||||
\(844\) | −67.4547 | −2.32189 | ||||||||
\(845\) | 12.6539 | 0.435306 | ||||||||
\(846\) | 164.448 | 5.65384 | ||||||||
\(847\) | 51.4261 | 1.76702 | ||||||||
\(848\) | 3.70204 | 0.127129 | ||||||||
\(849\) | −54.6624 | −1.87601 | ||||||||
\(850\) | 13.8858 | 0.476279 | ||||||||
\(851\) | 0.608587 | 0.0208621 | ||||||||
\(852\) | −95.1937 | −3.26128 | ||||||||
\(853\) | −36.5160 | −1.25028 | −0.625142 | − | 0.780511i | \(-0.714959\pi\) | ||||
−0.625142 | + | 0.780511i | \(0.714959\pi\) | |||||||
\(854\) | 23.3026 | 0.797397 | ||||||||
\(855\) | 33.6928 | 1.15227 | ||||||||
\(856\) | 51.4686 | 1.75916 | ||||||||
\(857\) | −31.8144 | −1.08676 | −0.543380 | − | 0.839487i | \(-0.682856\pi\) | ||||
−0.543380 | + | 0.839487i | \(0.682856\pi\) | |||||||
\(858\) | 22.0984 | 0.754426 | ||||||||
\(859\) | −36.2894 | −1.23818 | −0.619089 | − | 0.785321i | \(-0.712498\pi\) | ||||
−0.619089 | + | 0.785321i | \(0.712498\pi\) | |||||||
\(860\) | −2.40588 | −0.0820398 | ||||||||
\(861\) | −53.0105 | −1.80659 | ||||||||
\(862\) | −80.0238 | −2.72562 | ||||||||
\(863\) | −41.4523 | −1.41105 | −0.705526 | − | 0.708684i | \(-0.749289\pi\) | ||||
−0.705526 | + | 0.708684i | \(0.749289\pi\) | |||||||
\(864\) | −36.3523 | −1.23673 | ||||||||
\(865\) | 4.21847 | 0.143432 | ||||||||
\(866\) | 4.28860 | 0.145733 | ||||||||
\(867\) | −53.6357 | −1.82156 | ||||||||
\(868\) | 120.218 | 4.08047 | ||||||||
\(869\) | −43.4410 | −1.47364 | ||||||||
\(870\) | 0.125449 | 0.00425311 | ||||||||
\(871\) | 0.934985 | 0.0316808 | ||||||||
\(872\) | −42.0373 | −1.42356 | ||||||||
\(873\) | 72.0893 | 2.43985 | ||||||||
\(874\) | −11.0964 | −0.375340 | ||||||||
\(875\) | −3.28740 | −0.111134 | ||||||||
\(876\) | 70.0703 | 2.36745 | ||||||||
\(877\) | 36.7965 | 1.24253 | 0.621265 | − | 0.783600i | \(-0.286619\pi\) | ||||
0.621265 | + | 0.783600i | \(0.286619\pi\) | |||||||
\(878\) | 18.3823 | 0.620374 | ||||||||
\(879\) | 16.6541 | 0.561730 | ||||||||
\(880\) | 9.04549 | 0.304924 | ||||||||
\(881\) | 42.3021 | 1.42520 | 0.712598 | − | 0.701573i | \(-0.247519\pi\) | ||||
0.712598 | + | 0.701573i | \(0.247519\pi\) | |||||||
\(882\) | −58.1727 | −1.95878 | ||||||||
\(883\) | 14.8430 | 0.499507 | 0.249754 | − | 0.968309i | \(-0.419650\pi\) | ||||
0.249754 | + | 0.968309i | \(0.419650\pi\) | |||||||
\(884\) | 12.4248 | 0.417890 | ||||||||
\(885\) | 42.2188 | 1.41917 | ||||||||
\(886\) | 25.5121 | 0.857096 | ||||||||
\(887\) | 36.1070 | 1.21235 | 0.606177 | − | 0.795330i | \(-0.292702\pi\) | ||||
0.606177 | + | 0.795330i | \(0.292702\pi\) | |||||||
\(888\) | −7.87550 | −0.264285 | ||||||||
\(889\) | 18.8793 | 0.633190 | ||||||||
\(890\) | −12.8251 | −0.429899 | ||||||||
\(891\) | −68.8159 | −2.30542 | ||||||||
\(892\) | −37.4983 | −1.25554 | ||||||||
\(893\) | 56.1474 | 1.87890 | ||||||||
\(894\) | −102.799 | −3.43812 | ||||||||
\(895\) | 13.0669 | 0.436777 | ||||||||
\(896\) | 67.6994 | 2.26168 | ||||||||
\(897\) | −1.62642 | −0.0543047 | ||||||||
\(898\) | −21.4383 | −0.715406 | ||||||||
\(899\) | −0.175194 | −0.00584305 | ||||||||
\(900\) | 23.2395 | 0.774648 | ||||||||
\(901\) | −12.3976 | −0.413024 | ||||||||
\(902\) | 64.0386 | 2.13225 | ||||||||
\(903\) | −6.75928 | −0.224935 | ||||||||
\(904\) | 14.5724 | 0.484671 | ||||||||
\(905\) | −0.0904172 | −0.00300557 | ||||||||
\(906\) | −2.23232 | −0.0741639 | ||||||||
\(907\) | −25.5209 | −0.847409 | −0.423704 | − | 0.905800i | \(-0.639270\pi\) | ||||
−0.423704 | + | 0.905800i | \(0.639270\pi\) | |||||||
\(908\) | −21.6359 | −0.718012 | ||||||||
\(909\) | −14.4251 | −0.478449 | ||||||||
\(910\) | −4.57633 | −0.151704 | ||||||||
\(911\) | −26.3449 | −0.872846 | −0.436423 | − | 0.899742i | \(-0.643755\pi\) | ||||
−0.436423 | + | 0.899742i | \(0.643755\pi\) | |||||||
\(912\) | 28.1174 | 0.931060 | ||||||||
\(913\) | 42.6131 | 1.41029 | ||||||||
\(914\) | 51.6626 | 1.70885 | ||||||||
\(915\) | −9.21327 | −0.304581 | ||||||||
\(916\) | 63.1251 | 2.08571 | ||||||||
\(917\) | 69.9081 | 2.30857 | ||||||||
\(918\) | −147.672 | −4.87391 | ||||||||
\(919\) | −38.8064 | −1.28011 | −0.640053 | − | 0.768331i | \(-0.721087\pi\) | ||||
−0.640053 | + | 0.768331i | \(0.721087\pi\) | |||||||
\(920\) | −3.39991 | −0.112092 | ||||||||
\(921\) | 3.71795 | 0.122510 | ||||||||
\(922\) | −23.7789 | −0.783115 | ||||||||
\(923\) | −5.06069 | −0.166575 | ||||||||
\(924\) | 187.791 | 6.17786 | ||||||||
\(925\) | −0.677044 | −0.0222611 | ||||||||
\(926\) | −78.8742 | −2.59197 | ||||||||
\(927\) | −58.8342 | −1.93237 | ||||||||
\(928\) | −0.0589295 | −0.00193446 | ||||||||
\(929\) | 9.65784 | 0.316864 | 0.158432 | − | 0.987370i | \(-0.449356\pi\) | ||||
0.158432 | + | 0.987370i | \(0.449356\pi\) | |||||||
\(930\) | −73.9484 | −2.42486 | ||||||||
\(931\) | −19.8618 | −0.650946 | ||||||||
\(932\) | −15.5083 | −0.507991 | ||||||||
\(933\) | −38.6644 | −1.26581 | ||||||||
\(934\) | −61.5305 | −2.01334 | ||||||||
\(935\) | −30.2920 | −0.990655 | ||||||||
\(936\) | 14.3710 | 0.469732 | ||||||||
\(937\) | −53.1044 | −1.73484 | −0.867422 | − | 0.497572i | \(-0.834225\pi\) | ||||
−0.867422 | + | 0.497572i | \(0.834225\pi\) | |||||||
\(938\) | 12.3614 | 0.403613 | ||||||||
\(939\) | −32.9182 | −1.07424 | ||||||||
\(940\) | 38.7274 | 1.26315 | ||||||||
\(941\) | −50.8426 | −1.65742 | −0.828710 | − | 0.559678i | \(-0.810925\pi\) | ||||
−0.828710 | + | 0.559678i | \(0.810925\pi\) | |||||||
\(942\) | 126.252 | 4.11351 | ||||||||
\(943\) | −4.71320 | −0.153483 | ||||||||
\(944\) | 24.0571 | 0.782992 | ||||||||
\(945\) | 34.9607 | 1.13727 | ||||||||
\(946\) | 8.16544 | 0.265481 | ||||||||
\(947\) | 7.21175 | 0.234350 | 0.117175 | − | 0.993111i | \(-0.462616\pi\) | ||||
0.117175 | + | 0.993111i | \(0.462616\pi\) | |||||||
\(948\) | −93.1390 | −3.02501 | ||||||||
\(949\) | 3.72507 | 0.120921 | ||||||||
\(950\) | 12.3445 | 0.400510 | ||||||||
\(951\) | 71.0051 | 2.30250 | ||||||||
\(952\) | 72.9705 | 2.36499 | ||||||||
\(953\) | −43.7221 | −1.41630 | −0.708149 | − | 0.706063i | \(-0.750469\pi\) | ||||
−0.708149 | + | 0.706063i | \(0.750469\pi\) | |||||||
\(954\) | −32.2805 | −1.04512 | ||||||||
\(955\) | −3.42710 | −0.110898 | ||||||||
\(956\) | 97.7197 | 3.16048 | ||||||||
\(957\) | −0.273667 | −0.00884641 | ||||||||
\(958\) | 14.0133 | 0.452749 | ||||||||
\(959\) | 4.79142 | 0.154723 | ||||||||
\(960\) | −35.6525 | −1.15068 | ||||||||
\(961\) | 72.2720 | 2.33136 | ||||||||
\(962\) | −0.942501 | −0.0303875 | ||||||||
\(963\) | −87.8780 | −2.83183 | ||||||||
\(964\) | 100.551 | 3.23854 | ||||||||
\(965\) | 8.29879 | 0.267148 | ||||||||
\(966\) | −21.5029 | −0.691843 | ||||||||
\(967\) | −6.07106 | −0.195232 | −0.0976160 | − | 0.995224i | \(-0.531122\pi\) | ||||
−0.0976160 | + | 0.995224i | \(0.531122\pi\) | |||||||
\(968\) | −59.1687 | −1.90176 | ||||||||
\(969\) | −94.1610 | −3.02489 | ||||||||
\(970\) | 26.4124 | 0.848053 | ||||||||
\(971\) | −22.4637 | −0.720895 | −0.360447 | − | 0.932780i | \(-0.617376\pi\) | ||||
−0.360447 | + | 0.932780i | \(0.617376\pi\) | |||||||
\(972\) | −32.7349 | −1.04997 | ||||||||
\(973\) | 57.6556 | 1.84835 | ||||||||
\(974\) | −84.8446 | −2.71860 | ||||||||
\(975\) | 1.80937 | 0.0579463 | ||||||||
\(976\) | −5.24990 | −0.168045 | ||||||||
\(977\) | 27.8058 | 0.889585 | 0.444793 | − | 0.895634i | \(-0.353277\pi\) | ||||
0.444793 | + | 0.895634i | \(0.353277\pi\) | |||||||
\(978\) | 17.1257 | 0.547621 | ||||||||
\(979\) | 27.9781 | 0.894185 | ||||||||
\(980\) | −13.6996 | −0.437618 | ||||||||
\(981\) | 71.7749 | 2.29160 | ||||||||
\(982\) | −50.3435 | −1.60653 | ||||||||
\(983\) | 18.1185 | 0.577891 | 0.288945 | − | 0.957346i | \(-0.406695\pi\) | ||||
0.288945 | + | 0.957346i | \(0.406695\pi\) | |||||||
\(984\) | 60.9917 | 1.94434 | ||||||||
\(985\) | −11.1523 | −0.355342 | ||||||||
\(986\) | −0.239386 | −0.00762361 | ||||||||
\(987\) | 108.804 | 3.46327 | ||||||||
\(988\) | 11.0457 | 0.351409 | ||||||||
\(989\) | −0.600971 | −0.0191098 | ||||||||
\(990\) | −78.8736 | −2.50677 | ||||||||
\(991\) | 54.8813 | 1.74336 | 0.871681 | − | 0.490073i | \(-0.163030\pi\) | ||||
0.871681 | + | 0.490073i | \(0.163030\pi\) | |||||||
\(992\) | 34.7373 | 1.10291 | ||||||||
\(993\) | 27.9113 | 0.885738 | ||||||||
\(994\) | −66.9070 | −2.12216 | ||||||||
\(995\) | −21.8295 | −0.692042 | ||||||||
\(996\) | 91.3641 | 2.89498 | ||||||||
\(997\) | −56.0612 | −1.77548 | −0.887738 | − | 0.460350i | \(-0.847724\pi\) | ||||
−0.887738 | + | 0.460350i | \(0.847724\pi\) | |||||||
\(998\) | −86.8059 | −2.74779 | ||||||||
\(999\) | 7.20020 | 0.227804 |
(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 | 8035.2.a.d.1.19 | ✓ | 140 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8035.2.a.d.1.19 | ✓ | 140 | 1.1 | even | 1 | trivial |